From Mission Analysis to Systems Engineering of the OUFTI-Next Nanosatellite

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Master thesis : From mission analysis to systems engineering of the OUFTI-Next nanosatellite

Auteur : Dandumont, Colin Promoteur(s) : Kerschen, Gaetan Faculté : Faculté des Sciences appliquées Diplôme : Master en ingénieur civil en aérospatiale, à finalité spécialisée en "aerospace engineering" Année académique : 2017-2018 URI/URL : http://hdl.handle.net/2268.2/4538

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ATFE0005-1

From mission analysis to systems engineering of the OUFTI-Next nanosatellite

Author Dandumont Colin (20112143)

Academic Advisor Prof. Kerschen Gaëtan

Graduation Studies conducted for obtaining the Master’s degree in Aerospace Engineering by Colin Dandumont

Academic year 2017-2018 Abstract

OUFTI-Next is the new CubeSat project of the University of Liège. This mission was imagined after the success of OUFTI-1. The goal of this nanosatellite is to detect hydric stress of agricultural fields around the world. It is equipped with a Mid-Wavelength InfraRed (MWIR) detector. It will be a world premiere with such a small satellite (3U or 30 cm × 10 cm × 10 cm). From the data, the temperature of the crop will be extracted and the irrigation status assessed. This satellite is a technology demonstrator for an ambitious project. The final goal is indeed to create a smart irrigation program with a daily revisit over a location. It will provide tools for farmers to improve the irrigation, increase the yield of their fields and spare less drinkable water. With only one satellite, it is unfortunately impossible. OUFTI-Next’s mission is no less important because it will demonstrate that the integration of a MWIR detector is feasible. This master thesis is the continuity of a feasibility study done last year (2016-2017). From the requirements, primordial aspects of the satellite are developed. Orbits, communication, power budget, attitude strategy, ... are typical topics introduced in this work. It offers an overview of the satellite and a link between different subjects addressed in other master theses (the detector’s cooling system, the optical design and the thermal aspect). At the end, some configurations, thought as simple as possible, are introduced and discussed. All subsystems are reviewed with the will to find an optimal configuration. Of course, concessions are done and assumptions made. At this stage of the development, it is natural that some information is missing.

i Acknowledgements

First of all, I would like to thank Xavier Werner. His advice and answers really helped me during all this project. He was always present and guided my work in the right direction. I also wish to thank my promoter Gaëtan Kerschen as well as Prof. Serge Habraken and Jerôme Loicq for their encouragement and advice during the diﬀerent meetings. Without them, working on this fabulous academic project would never have been possible. I sincerely thank them. I discovered many aspects of CubeSats and learn a lot about them. Other students of this project, Anna, Lidiia, Anthony, Donatien, Pierre and Victor are also warmly thanked. It is a great team project. OUFTI-Next can only exist because we have all worked in order to provide the best of ourselves. We can only hope to see in a few years the launch of this small satellite. For helping me to realize this work, I’m thankful to SpaceBel and specially Joachim Gémis. He helped me to apprehend VTS, a wonderful visualization tool developed in collaboration with CNES. It allowed me to discover all their software. Although I have never met in person my interlocutors at CNES, without them, this work would probably not have been possible. They always answered in short delays to my questions and in detail. Finally, thanks to Elise, Alex, Juan and Thibault. They endured me during all lunchtimes and never complained to hear me speak constantly about this nanosatellite.

ii Contents

Abstract i

Acknowledgements ii

Acronyms v

Introduction 1

1 Mission 3 1.1 Objectives ...... 3 1.1.1 Water stress ...... 3 1.1.2 Thermal infrared ...... 4 1.1.3 Region of interest ...... 6 1.2 Global mission requirements ...... 9 1.3 Demonstrator requirements ...... 9

2 Nominal scenarios 11 2.1 Orbits ...... 11 2.1.1 Crossing times ...... 12 2.1.2 Recurrence with no tilting ...... 20 2.1.3 Recurrence with tilting ...... 23 2.1.4 Orbit perturbations ...... 28 2.1.5 Eclipse duration ...... 31 2.1.6 Lifetime ...... 32 2.1.7 Conclusion ...... 35 2.2 Communication strategy ...... 36 2.2.1 Frequency bands and data rate ...... 36 2.2.2 Data budget ...... 37 2.3 Acquisition strategy ...... 40 2.3.1 Acquisition possibilities ...... 40 2.3.2 MWIR detector ...... 42 2.3.3 Visible detector ...... 43 2.4 Attitude strategy ...... 43 2.4.1 Global Navigation Satellite System (GNSS) ...... 43 2.4.2 Accuracy ...... 44 2.5 Power consumption ...... 45 2.5.1 Full illumination ...... 46

iii Contents

2.5.2 Eclipses ...... 48 2.5.3 Mean consumption ...... 49

3 Cubesat conﬁgurations comparison 51 3.1 Payload ...... 53 3.2 Platform ...... 56 3.2.1 ADCS ...... 56 3.2.2 COM ...... 60 3.2.3 OBC ...... 64 3.2.4 PWR ...... 64 3.2.5 STR ...... 65 3.3 Power budget ...... 66 3.3.1 Power generation ...... 66 3.3.2 Power margin ...... 70 3.3.3 Battery capacity ...... 72 3.4 Thermal budget ...... 74 3.4.1 Full passive solution ...... 75 3.4.2 Mixed solution ...... 77 3.4.3 Full active solution ...... 77 3.5 Mass budget ...... 78 3.6 6U structure ...... 80

4 Optimal conﬁguration & scenario 82 4.1 Conﬁguration ...... 82 4.1.1 Payload orientation ...... 82 4.1.2 Power & cooling system ...... 82 4.1.3 Radiator & cooling system ...... 83 4.1.4 Conclusion ...... 83 4.2 Scenario ...... 84 4.2.1 Orbit & acquisition ...... 84 4.2.2 Communication ...... 85

Conclusion 86

A Software 88 A.1 Celestlab ...... 88 A.2 IDM-CIC ...... 88 A.3 Ixion ...... 88 A.4 Simu-CIC ...... 89 A.5 STELA ...... 89 A.6 VTS ...... 89

B Orbit 90

C Power Budget 93

Bibliography 96

CONTENTS iv Acronyms

ADCS Attitude Determination and Control System.

AOCS Attitude and Orbit Control System.

BCN Beacon.

BOL Beginning Of Life.

CMOS Complementary Metal Oxide Semiconductor.

CNES Centre National d’Etudes Spatiales.

COM Communication.

COP Coeﬃcient Of Performance.

COTS Commercial Oﬀ-The-Shelf.

DOD Depth Of Discharge.

ECEF Earth-Centered, Earth-Fixed.

EFL Eﬀective Focal Length.

EPS Electrical Power System.

ESA European Space Agency.

FAO Food and Agriculture Organization of the United Nations.

FOV Field Of View.

GEO Geostationary Earth Orbit.

GLONASS Globalnaya Navigatsionnaya Sputnikovaya Sistema (Global Navigation Satel- lite System).

GNSS Global Navigation Satellite System.

GPS Global Positioning System.

v Acronyms

GSD Ground Sampling Distance.

GTO Geostationary Transfert Orbit. iFOV Instantaneous Field Of View.

ISIS Innovative Solutions In Space.

ISS International Space Station.

JAXA Japan Aerospace Exploration Agency.

JEMRMS Japanese Experiment Module Remote Manipulator System.

LAT Local Apparent Solar Time.

LEO Low Earth Orbit.

LMT Local Mean Time.

LWIR Long-WaveLength InfraRed.

MWIR Mid-Wavelength InfraRed.

NAVSTAR GPS NAVigation System with Time and Ranging Global Positioning Sys- tem.

NRCSD NanoRacks CubeSat Deployer.

OBC On-Board Computer.

OUFTI-1 Orbital Utility For Telecommunication Innovation.

OUFTI-Next Orbital Utility For Thermal Imaging Next.

PCB Printed Circuit Board.

RAAN Right Ascension of the Ascending Node.

S/C Spacecraft.

SNR Signal to Noise Ratio.

SRP Solar Radiation Pressure.

SSO Sun-Synchronous Orbit.

STELA Semi-analytic Tool for End of Life Analysis.

TDI Time Delay Integration.

Acronyms vi Acronyms

UAV Unmanned Aerial Vehicle.

VIS Visible.

VTS Visualisation Tool for Space data.

Acronyms vii Introduction

OUFTI-Next is the new CubeSat project of the University of Liège and the Liège Space Center. It will be the third nanosatellite of this academic institution. OUFTI-1 was a 1U CubeSat (10 cm × 10 cm × 10 cm) and was launched in 2016 as part of the ESA’s Fly Your Satellite! (FYS) program. It was dedicated to telecommunication and the use of the D-star communication protocol. Unfortunately, the contact with the satellite was lost 12 days after the launch. OUFTI-2 is its little brother and will be launched in the near future. The payload is again the D-star module since it was not possible to test it on OUFTI-1. Two other scientific payloads are also present. The first one is related to radiation shielding and the second one to attitude control measurement. For the third satellite, the goal is totally different. OUFTI-Next stands for Orbital Utility For Thermal Imaging Next. It will be a remote sensing CubeSat. A thermal infrared detector is the main payload. The objective is to image agricultural fields and measure hydric stress. Targets are irrigated fields. Their yield is 3.5 times greater than non- irrigated fields (rainwater). Unfortunately, the mean efficiency is only 40% and irrigation represents 70% of fresh water consumed in the world. There is therefore a real need of a reliable measurement system and a control of irrigation. This will avoid enormous waste of freshwater. This infrared detector will especially detect poorly irrigated areas. The final goal is to create a smart irrigation method based on data acquired by the satellite.

To effectively create this ambitious project, several satellites are needed. The situation on the ground can indeed evolve quickly and so a small revisit time is needed. Earth coverage is also important and it will be discussed in the first chapter of the thesis. Irrigated zones are situated in all latitudes (Australia, Brazil, China, Europe, India, the USA, etc.). A constellation of satellites prevails for the final project to obtain a global coverage.

OUFTI-Next is a demonstrator. The detector needs to be tested on orbit since it is developed for Earth applications, mainly in the military ﬁeld. The mission objective is to demonstrate the reliability of the measurement and the capability to obtain data with an exploitable spatial precision.

The development of this project started last year (2017) with two feasibility studies in the framework of master theses: one about the satellite and the other one about the infrared detector. They prove that this mission is viable and can be completed. Compared to OUFTI-Next, the satellite grew up and is intended to be a 3U (30 cm × 10 cm × 10 cm). This year, six master theses are related to the project: three about the optical design [1][2][3], one about the thermal analysis [4], one about the cooling system of the infrared detector [5] and the present one. This master thesis proposes a global view of the satellite and its technical challenges.

1 Introduction

From the mission analysis some requirements for the demonstrator will be derived. It is the first chapter. The second one is dedicated to nominal scenarios. Orbits, communication, acquisition strategy and other typical parameters of a satellite are discussed there. No assumption on the configuration, except that it is a CubeSat, is made. The third one is about the subsystems and configurations available to fulfill the scenarios derived previously. The last chapter is a conclusion that connect the configuration and the requirements. Its goal is to give a working model with the least possible assumptions. It is also there to highlight the elements that need a more in-depth approach in the future phases of the project. Fig.0.0.1 summarize the way of this thesis is articulated.

OUFTI-NEXT CONCLUSION MISSION

Chapter 1 Chapter 4

Chapter 4 DEMONSTRATOR CONFIGURATION REQUIREMENTS DISCUSSION

Chapter 2 Chapter 3

NOMINAL SCENARIOS

Fig. 0.0.1: Organizational plan of the master thesis.

2 1| Mission

In this chapter, the mission and the requirements of the demonstrator are analyzed. Some interesting information about irrigation is ﬁrst presented. After that, some technical characteristics of the thermal infrared are given. Even if it is not the main purpose of this master thesis, the global mission is introduced. To end this chapter, the demonstrator requirements are discussed.

1.1 Objectives

As stated in the introduction, the OUFTI-Next mission has the will to detect hydric/water stress and image irrigated agricultural ﬁelds. The ﬁrst question that comes to mind is: What is exactly hydric stress?

1.1.1 Water stress The hydric stress, water stress or also osmotic stress, arises when the water demand from the plant exceeds the available amount during a certain growth period.[6] Several factors can create this state. The main one is simply a drought but it can also be a salinity increase or a cold. In the case of a drought, the water content of the plant will decrease by osmotic eﬀect. For the salinity or the cold, it is related to the soil water potential.[7] One possible reaction of the plant is the water avoidance stress. Plants naturally evaporate water, it is called the evapotranspiration. A means to keep a high water potential is to close its stomata. These are small pores located on leaves and used for gas exchange. They are involved in the photosynthesis and the respiration. If the plant is in water avoidance stress, it productivity decreases.[8] The leaves temperature rises up since there is no more transpiration. It can be up to several degrees higher than the air temperature (4-8 ◦C). For instance, 1°C increase in average temperature can decrease the rice yields up to 9%.[9]

The thermal emission is maximum near midday.[10] There is an emission window starting at 12:00 with a peak at 14:00. It follows the sun angle in the sky with a shift due to thermal inertia. It is the called the diurnal cycle. Fig.1.1.1 represents this eﬀect on a ﬁeld in India.

The evapotranspiration is one of the best-known applications of thermal infrared and it explains why OUFTI-Next will be equipped with a detector in such wavelengths. In the visible domain, hydric stress can be detected (browned and curled leaves) but it’s usually

3 1.1. Objectives too late to save the plant. In infrared, it is more preventative and water stress can be detected very early.

Fig. 1.1.1: "Diurnal temperature data recorded in Fatehpur. Rajasthan, India, (latitude 27° 37’ N) in June 1989, Each measurement is the mean value from three thermocouples placed at either 5 cm depth of soil (N); 0.5 cm depth of soil (•); or 150 cm above the soil surface ()".[11]

1.1.2 Thermal infrared The full infrared spectrum comes from 700 nm to 1 mm. It is subdivided in many bands, each with a particular scientiﬁc interest. The thermal infrared band is between 3 to 15 µm. This band is decomposed into two reduced band, the Mid-Wavelength InfraRed (MWIR) one (3 to 5 µm) and the Long-WaveLength InfraRed (LWIR) one (8 to 14 µm). Theses bands do not cover the whole thermal infrared spectrum since the atmosphere is not transparent in speciﬁc wavelengths. As shown in Fig. 1.1.2, between 5 to 8 µm, it is impossible to acquire data.

In these bands, the temperature can be derived from the thermal emission, especially if the surface material is known.

OUFTI-Next will used a MWIR detector. Compared to LWIR, this band oﬀers many advantages. Even if it has no interest in our application, MWIR signal can be used to image at night. Diﬀraction is also less present and the detector is less disturbed by its own radiation. It is a major advantage. To acquire data, the detector needs indeed to be cool down to avoid this problematic. At ambient temperature (25 ◦C), the detector is blinded by its own thermal emission. So, if these radiations are less important, the ∆T is smaller. This reduces the constraints on the cooling system. A whole discussion about it is available in Chapt. 2.

CHAPTER 1. MISSION 4 1.1. Objectives

Fig. 1.1.2: Transmittance of the atmosphere. The MWIR band is between 3 to 8 µm. Due to absorbing molecules (H2O), it is reduced to 3 to 5 µm. From [12].

With the miniaturization of cryocooler technology, the MWIR is accessible for such a small satellite. During years, it was only used in big satellites for military applications. Wavelengths between 3 to 5 µm are mainly used for heat-seeking system embedded in missiles.[12] OUFTI-Next will probably use one these MWIR detectors. They are however not yet well spread in agricultural application and irrigation. For instance, Cornerstone mapping, a US company, proposes an irrigation management with an airplane but they don’t use a MWIR detector. They prefer a LWIR one. According to us, performance is degraded but it is cheaper and easier to use.[13] Fig. 1.1.3 represents typical airborne thermal imaging of circular irrigated ﬁelds from this company. They can detect such details as clogged nozzles (light blue line).

Fig. 1.1.3: Airborne thermal imaging used to detect irrigation problem. Light blue rings indicate clogged nozzles. Temperature in °F (80°F = 26 ◦C and 100°F = 38 ◦C). Spatial resolution of 6 ft (1.8 m). From [14].

Of course, with a CubeSat, this spatial precision can not be obtained but this is not the goal. The main advantage of the satellite is its regularity and the no maintenance costs. Once in orbit, it acquires data until the end of the mission. It requires little infrastructure except a ground station. The constraints are really diﬀerent from those of an airplane. The swath, so the size of one image, is also very wide with a satellite (more than 35 km × 30 km).

CHAPTER 1. MISSION 5 1.1. Objectives

OUFTI-Next can therefore cover large areas in a few overﬂights. The ideal scenarios would be a correlation between the two methods since they are complementary. The MWIR detector can potentially be integrated on an UAV since volume and mass constraints are quite identical.

A listing of small satellites using MWIR detector was done last year in [15]. CubeSats are not common due to the complexity of the cooling system. However, let’s mention that the 6U CubeSat Arkyd-6 from Planetary Resources was successfully launched on January 12, 2018. Fig 1.1.4 shows a MWIR image of a refinery in Algeria. A visible camera is also included and allows to easily locate the target and compare it in different wavelengths. It also has a better media impact than a MWIR image, often more difficult to analyze. This is the reason why a visible detector is also envisaged in OUFTI-Next.

(a) Visible spectrum (b) MWIR spectrum

Fig. 1.1.4: Planetary Resources Arkyd-6 orbital MWIR image of a reﬁnery in Algeria. Qualitative scale (hot = white and black = cold). From [16].

If the main mission is the monitoring of agricultural fields, thermal infrared can be used in other domains. The principal one is the forest fire detection. Plume can also be detected from space. Another application is the vegetation discriminated since their emissivity response spectrum is different. It leads to a more military domain, the camouflage detection. This can be differentiated from vegetation in the thermal infrared.[17] Of course, temperature for all kinds of targets can be analyzed, from ocean to factories to quantify thermal insulation.

1.1.3 Region of interest The Food and Agriculture Organization of the United Nations (FAO) lists all irrigated areas over the world since 1961 and provides free data about them. Many statistical information can be derived. One can for instance see in Fig. 1.1.5 that the total area equipped for irrigation doubled in 40 years. From 2010 to 2015, the growth was 7.3%. It completely legitimates the mission. The potential growth is huge since irrigated area represents only 6.8% of the total agriculture areas. Let’s just mention that it does not mean that all these lands are used. Some of them may be fallow. Moreover, only artiﬁcial irrigation is considered like water sprinkler or ﬂood irrigation.[18]

CHAPTER 1. MISSION 6 1.1. Objectives

105 3.5

2.5

1.5

0.5

Total area equipped for irrigation (x 1000 ha) 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Fig. 1.1.5: Total area equipped for irrigation from 1961 to 2015. Units are 1000 ha. From FAO and processed in Matlab.[18].

Now, it is interesting to know where these areas are, especially in latitude. For the year 2015, the last one available, Fig. 1.1.6 represents the percentage of irrigated land in speciﬁc regions. These regions are visible in a world map in Fig. 1.1.7. The ﬁve most irrigated countries are China (21.5%), India (21.1%), the USA (8.0%), Pakistan (6.1%) and Iran (2.9%). High irrigated countries are below 60°N and are all located in the North hemisphere.

1% 5% 8% 9%

Africa Northern America South America Asia Europe Oceania

73%

Fig. 1.1.6: Percentage of the total area equipped for irrigation in the world. Year: 2015. From FAO and processed in Matlab.[18].

CHAPTER 1. MISSION 7

1.1. Objectives

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Fig. 1.1.7: Global map of irrigation areas. Year 2013. From the FAO.[18]

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CHAPTER 1. MISSION 8 1.2. Global mission requirements

1.2 Global mission requirements

The ultimate goal of the OUFTI-Next project is to oﬀer a temporal resolution as small as possible like 1 day. If it is possible to do a daily revisit with one satellite, a constellation is needed to have a global coverage of the Earth. Last year, it was computed that a constellation of only 8 satellites at 800 km in two diﬀerent SSO is required.[15] Unfortunately, the hour of passage, as it will be discussed, is a new requirement. Regarding the spatial resolution, it must be below 50 m with the ambition to have 25 m.

These temporal and spatial resolutions would be an innovation. Satellites would be able to provide to farmers reliable measurements with a good precision. It would not be possible to detect speciﬁc problems like a clogged nozzle on the irrigation system but it would give a more general information over large areas. An entire region can be easily monitored. Irrigation can also be intermittent and the satellites could be used to create a fully autonomous irrigation method based on the collected data.

1.3 Demonstrator requirements

To prepare this audacious program, a demonstrator needs to be built. To integrate the MWIR detector, a 3U CubeSat was selected. The main goal of this small satellite is to show that taking MWIR pictures from space with a good temperature precision and good spatial resolution is feasible.

The MWIR detector is therefore the main payload as well as its cooling system. These detectors are very sensitive to noise and they must be cool down to very low temperature, 90 K or 150 K depending on the technology. A panchromatic (RGB) VIS detector is also envisaged. It would oﬀer, as already mentioned, a good way to locate the target but also an eﬀective communication tool. Its integration should not, however, become a constraint.

The main constraint of a CubeSat is really its size. The optical design needs to be compact. This impacts unfortunately the spatial resolution. To obtain exploitable data, the maximum bound is 100 m. The goal is to tend to a GSD of 50 m.

The thermal precision is directly related to the Signal to Noise Ratio (SNR) of the detector and so its temperature. 1-2 K is a possible value (cf.[19]) and is aimed. A temperature range from 0 to 60 ◦C is suﬃcient for the application.

With only one satellite, it is impossible to offer a daily coverage of the Earth. At most daily recurrence over a specific place can be achieved. For the demonstrator, there is no requirement on this parameter. No specific target is either considered. The temporal resolution and the scientific feedback, for instance the development of a smart irrigation process, are secondary requirements and can not over-constrain the design (orbit, optic, etc.). If a recurrent orbit of less than 10 days is accessible, tests will be conducted in the direction of this smart irrigation method.

As explained in Sect. 1.1.1, the best moment to acquire data is between 12:00 and 14:00. The orbit is constrained by this requirement. Since the Earth is around 72% water

CHAPTER 1. MISSION 9 1.3. Demonstrator requirements covered, it leads to some discussion about acquisition possibilities over several days in Sect. 2.1.

The lifetime can also be a requirement. If OUFTI-Next is launched from the ISS, it can be very short, like less than 2 months. It will be discussed in Chapt. 2. As a demonstrator, the satellite does not need to stay in orbit during years but a minimum lifetime of 3 months seems reasonable. Below, it will be too dangerous since it is strongly dependent on space weather.

All the requirements for OUFTI-Next are summarized in Tab. 1.3.1.

Requirements Structure 3U CubeSat MWIR detector + cooling system Payload VIS detector if possible Thermal precision 1-2 ◦C Thermal range 0 to 60 ◦C Spatial resolution < 100 m (GSD) Temporal resolution One image a day - No speciﬁc target Hour of passage From 12:00 to 14:00 Lifetime > 3 months

Table 1.3.1: Requirements of the demonstrator OUFTI-Next.

CHAPTER 1. MISSION 10 2| Nominal scenarios

This chapter is dedicated to nominal scenarios for the mission without any assumption on the CubeSat conﬁguration. From the demonstrator requirements described in Sect. 1.3, many important characteristics for the mission, as the orbit or the communication strategy, will be reviewed. In each section, the goal is to meet the requirements with the simplest solution. This chapter leads the way to Chapt. 3 where satellite conﬁgurations will be discussed in detail based on results obtained here.

2.1 Orbits

The orbit is the key parameter for a satellite. Almost all subsystems and budgets depend directly on its characteristics. Power or thermal budgets are for instance sensitive to the duration of the eclipse. The resolution on the ground, the GSD, depends directly on the altitude of the satellite. The orbit also determines acquisition strategy through the crossing time and the recurrence over a place. These two important concepts will be discussed in detail in this section.

With a classical satellite, the orbit is chosen in consultation with a rocket launch company, for instance Arianespace. For CubeSats, it does not happen the same way. It exists some intermediates, like Innovative Solutions In Space (ISIS) via its ISILaunch Services, which offer piggyback launch opportunities. CubeSats are therefore considered as secondary payloads and the orbit is constrained by the main payload. Twenty-six opportunities launches are available with ISIS until Q2 2020 and nineteen aims a Sun- Synchronous Orbit (SSO) with an altitude between 450 and 800 km. Only one SSO is at 800 km, the majority is below 600 km.[20] A second solution is to be deployed from the International Space Station (ISS) at 400-415 km with an inclination of 51.6° by the NanoRacks CubeSat Deployer (NRCSD) or the JEMRMS of JAXA.[21] The American company also offers a deployment from the cargo Cygnus (Orbital ATK), just above the ISS after departs from the station, at 500 km. According to Nanoracks, it adds approximately two years of lifetime compared to its ISS NRCSD deployment program.[22] One last solution, which is emerging more and more, is small launchers dedicated to nanosatellites and CubeSats. For instance, Rocket Lab via its Electron rocket will provide frequent opportunities in the coming months. The nominal orbit, for the rideshare service, is a SSO at 500 km with a payload of 150 kg. It also exists dedicated launch with specific orbit but it is more intended to small satellites (100 kg).[23]

11 2.1. Orbits

As shown, finding a deployment possibility for a CubeSat is not a major problem. Of course, it will depend on the available budget and services provided. The price for a launch as piggyback or with a specific launcher is different. The size of the CubeSat (1U/2U/3U) also plays an important role. For indication only, a 1U CubeSat deployment from the ISS begins at US$85,000 and from the Electron rocket at US$80,000. For a 3U CubeSat, the intended size for OUFTI-Next, it is US$240,000 with the same rocket.[21][23]

Regarding the fact that it is an Earth observation mission, two types of orbits are discussed in the rest of this section, the ISS one and a SSO one. The hour of passage, an important requirement (cf. Sect. 1.3), will be discussed for both orbits. After that, the recurrence scheme over a place without tilting the satellite, so by always pointing nadir, will also be determined. The tilt of the S/C is then introduced. Once all these parameters are known, perturbations of the diﬀerent orbits, as the drift in local time or maintenance of a recurrent orbit, will be assessed. The eclipse of typical orbits are then discussed. It is an important parameter for the power budget. At the end, the lifetime of orbits will be determined.

2.1.1 Crossing times For the application, as described in Sect. 1.3, it is important be over an area of interest between 12:00 and 14:00 in solar time. It is also known as the Local Mean Time (LMT). This is the local time on the ground tracks. This value is based on the mean motion of the sun. One can also deﬁne the Local Apparent Solar Time (LAT) but this value depends of the date. The diﬀerence, ET = LMT − LAT , known as the equation of time, is represented in Fig. 2.1.1. The maximum deviation is around -14 min in February and 16 min in November.[24]

Equation of time 15 min between 1950 and 2050 max between 1950 and 2050 10 2000

−5

−10

Mean local time minus true (mn) −15

−20 JFMAMJJASOND

Fig. 2.1.1: Equation of time. Diﬀerence between the Local Mean Time (LMT) and the Local Apparent Solar Time (LAT). Made with Celestlab, from CNES.

CHAPTER 2. NOMINAL SCENARIOS 12 2.1. Orbits

It is therefore needed to know the LMT on the ground tracks. SimuCIC, the orbital propagator from CNES, computes the true satellite time (LAT) at each time step. Since the interval 12:00 - 14:00 is empirical and the diﬀerence between both is maximum 16 min, the distinction is not be done in the following and the LMT is used. For indication, this time depends on the longitude on Earth as λ UT1 = LMT − (2.1.1) 15 where UT1 is the universal time expressed in hours and λ the longitude expressed in degrees (convention -W/+E). The factor 15 depends on the units (360°/24 h = 15 ° h−1). For example, one of the potential regions of interest is the Tadla Region in Morocco (λ = −6°). The window in LMT becomes 12:24 and 14:24 UTC.1

In the case of a Sun-Synchronous Orbit (SSO), the LMT crossing time at a given latitude is constant. In other words, the LMT crossing time at a given meridian depends only on the latitude.[25] As a reminder, this type of orbit has its "orbital plane which makes a constant angle α with the radial of the sun. The orbital plane rotates in inertial space with the angular velocity of the Earth in its orbit around the Sun, which is 360° per 365.26 days, or 0.9856° per day. With the orbital plane precessing eastward at this rate the ascending node will lie at a fixed local time."[26] It is shown in Fig. 2.1.2. This effect is due to the Earth oblateness (J2 effect) which creates a nodal regression. For a SSO, the semi-major axis a and the inclination i are directly related.

Fig. 2.1.2: Sun-Synchronous Orbit (SSO) explanation. From [26].

For a non-SSO, the LMT changes at every passage for a given latitude and longitude. In this case, the cycle CS, which is the cycle with respect to the sun, can be introduced. It gives the needed time to cross the same point with the same LMT. It is typically 60 days for a LEO satellite. One can also see this parameter as the number of days to wait to increase or decrease by 24 h the crossing time.

1Leap seconds are not considered and UTC time is used instead of UT1.

CHAPTER 2. NOMINAL SCENARIOS 13 2.1. Orbits

The cycle, if we consider a circular orbit for the Earth around the Sun, is given with approximate numerical values by 365.25 CS = − (2.1.2) 10.11(R/a)7/2 cos i + 1 and is only function of the semi-major axis a (km) and the inclination i (deg). In the case of a SSO, CS is equal to inﬁnity. It means that the crossing time of the satellite at the crossing node is constant as explained before.[25]

ISS orbit The International Space Station is not on a Sun-Synchronous Orbit. The orbit is inclined by 51° whereas SSO are closer to 98°. The LMT varies therefore with time. The cycle, according to Eq. 2.1.2 and with an altitude of 400 km, is equal to 365.25 365.25 CS = − = − = −59.46 d. (2.1.3) 10.11(R/a)7/2 cos i + 1 10.11(6378/(6778)7/2 cos 51 + 1

Fig. 2.1.3 shows the LMT at the equator for a period of 3 months (from October 26, 2017 to January 26, 2018). The cycle of ≈ 59 days is visible.

Fig. 2.1.3: Local Mean Time (LMT) at the ascending node (equator) for the International Space Station (ISS) from October 26, 2017 to January 26, 2018. Made with Ixion.

CHAPTER 2. NOMINAL SCENARIOS 14 2.1. Orbits

If OUFTI-Next is deployed from the ISS, it is impossible to have a smart irrigation strategy due to this varying LMT. The recurrence over the place is also a problem and will be discussed in detail. As introduced in the requirements, it is interesting to know where the satellite will be between 12:00 and 14:00 LMT. With its inclination of 51°, almost all the South hemisphere is seen from the ISS orbit (not the Antarctic). For the North hemisphere, the maximum latitude is closed to 51°N and so Russia, Canada or Scandinavian countries can not be imaged. Countries with large irrigated areas as like China, India, Iran, are visible. However, during one orbit, only a small portion of the ground tracks is between 12:00 and 14:00 LMT and it is mostly over oceans since Earth is 72% water covered. Fig. 2.1.4 shows the ground tracks of the ISS orbit during one day. Highlighted zones are between the required hours of passage.

Day 13 90 Sea 60 Land Coast 30

-30 Latitude [deg]

-60

-90 -180 -120 -60 0 60 120 180 Longitude [deg] Fig. 2.1.4: Ground tracks of the ISS for an arbitrary day. Highlighted zones are between 12:00 and 14:00 LMT.

From the data of Simu-CIC, it is possible to determine the percentage of sea, land and coast seen by the satellite. So, during one cycle of 59 days, the percentage of overflown land is 23% (Fig. 2.1.5) but this is not uniform as shown in Fig. 2.1.6 for only 31 days2. It depends of course of initial parameters (epoch, argument of perigee ω, RAAN Ω and true anomaly ν) but since it is a cycle, it is constant if no orbital perturbations are considered. It does not mean that each day an area of interest is seen but it shows that taking one image a day is feasible. Let’s mention that during about 3-4 days in South hemisphere, the only land overflown is the south of Argentina and Chile (Tierra del Fuego). This stagnation over few degrees of latitude also happens in North hemisphere during the cycle but it less problematic since it is over Europe, U.S.A. and Asia. This phenomenon is shown in Fig. 2.1.7. The ISS orbit fulfills the requirements even if the revisit time, as it will be discussed, is long. One picture a day can be achieved but it will depend of areas of interest and of course on the data strategy (Sect. 2.2).

2It was reduced for the sake of clarity. The number of days is not a limiting factor in the code.

CHAPTER 2. NOMINAL SCENARIOS 15 2.1. Orbits

Between Day 1-59 9%

23%

68%

Sea Land Coast

Fig. 2.1.5: Percentage of sea (blue), land (green) and coast (red) overﬂown by OUFTI-Next on the ISS orbit during 1 cycle (60 days). Epoch: January 1, 2019. Data obtained with Simu-CIC from CNES and processed in Matlab.

Between Day 1-30 100 Sea Land 80 Coast

40 Percentage %

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Day number Fig. 2.1.6: Percentage of sea (blue), land (green) and coast (red) overﬂown by day by OUFTI-Next on the ISS orbit for a duration of 31 days. Epoch: January 1, 2019. Data obtained with Simu-CIC from CNES and processed in Matlab.

CHAPTER 2. NOMINAL SCENARIOS 16 2.1. Orbits

Between Day 1-3 Between Day 1-3 100 90 Sea Sea Land 60 Land 80 Coast Coast

30 60 0 40 Latitude [deg]

Percentage % -30

20 -60

0 -90 1 2 3 -180 -120 -60 0 60 120 180 Day number Longitude [deg] (a) Percentage over 4 days (b) Ground tracks where highlighted zones are between 12:00 and 14:00 LMT

Fig. 2.1.7: Stagnation over the South hemisphere (Argentina and Chile) during 4 days for the ISS orbit. Epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

Sun-Synchronous Orbit

For a SSO, we often refer to the local time at the ascending node, τAN, or at the descending node, τDN (τAN = 12 + τDN mod 24). τ expresses the fact that the time is given in LMT. As stated above, the LMT crossing time at a given latitude is constant for this particular orbit. Therefore, a relation between the geodetic latitude (ψ) and the crossing time at the equator is needed. It is directly related to the inclination i such that

1 tan ψ ! ∆τ = arcsin , (2.1.4) 15 tan i or ψ = arctan (tan i sin 15∆τ) . (2.1.5)

The function ψ (∆t) can be seen in Fig. 2.1.8 for a SSO with τAN = 00 : 00 and so τDN = 12 : 00. A change of the crossing time at the equator only induces a lateral shift of the curve.

The τAN depends on the targets. If both hemisphere are on an equal footing, τAN needs to be equal to 13:00. ∆τ = ± 1:00 is available and the orbit is bounded by ψ = ± 62° according to Eq. 2.1.5 at 600 km (i = 97.98°). This is a very wide band in latitude. This orbit can be seen in Fig. 2.1.9. The fact is that many remote sensing satellites, especially for Earth resources, are either on a SSO with τAN = 22 : 30 (τDN = 10 : 30) or τAN = 13 : 30 to avoid specular reﬂection (sun glint).[25][15] With some acquisitions around 12:00 LMT, the detector will not avoid theses sun glints. Since the mission is dedicated to irrigation, water is present, especially in ﬂood irrigation (rice), and it can become a problem.

CHAPTER 2. NOMINAL SCENARIOS 17 2.1. Orbits

Fig. 2.1.8: ψ (∆t), the relation between the geodetic latitude (ψ) and the LMT time diﬀerence for a Sun-Synchronous satellite with τAN = 00 : 00. From [25].

The first orbit, τDN = 10 : 30, is named "morning crossing" because it passes over the North hemisphere during the morning and the second one is called "afternoon crossing" for a similar reason. These orbits are popular and so, it offers more launch opportunities. In the case of OUFTI-Next, both orbits are possible. For τAN = 22 : 30, only regions between 70°N - 80°N are in the range of 12:00 - 14:00 LMT. If τAN = 10 : 30 is considered, it is between 70°S - 80°S. This is over poles for both orbits. These areas are clearly not cultivated. If τAN = 13 : 30 is chosen, a ∆τ = 1:30 is available for the North hemisphere (time is decreasing when ascending) and only a ∆τ = 0:30 in the South hemisphere. Imaging areas are bounded by 43°S and 70°N as shown in Fig. 2.1.10. Figures for τAN = 22 : 30 and τAN = 10 : 30 are available in Appendix B. Since OUFTI-Next, as a CubeSat, will not be on maintained Sun-Synchronous Orbit (no propulsion). It is therefore interesting to look at the drift in local crossing time. It is assessed in Sect. 2.1.4. To close this discussion about the crossing time, let’s just talk about the relation between the Right Ascension of the Ascending Node (RAAN), Ω, and this LMT. It has a interested since the first one is often used to describe orbits. It is given by m Ω = α + (τAN − 12) (2.1.6) m where α is the right ascension of the mean Sun (deg) at the time of the ascending node crossing. It can be decomposed as m a α = α + EqT (2.1.7) a with α being the right ascension of the apparent Sun and EqT the equation of time, the one described in the beginning of this section. Ω is therefore dependent of the launch date and can not be determined without it. Celestlab, from CNES, offers a function to compute it directly from the date and the LMT at the ascending node.

CHAPTER 2. NOMINAL SCENARIOS 18 2.1. Orbits

Between Day 1-5 90 Sea Land Between Day 1-5 60 80 Coast Sea Land 30 Coast 60 0

Latitude [deg] -30 Percentage % 20 -60

-90 0 1 2 3 4 5 -180 -120 -60 0 60 120 180 Day number Longitude [deg] (a) Percentage over 6 days (b) Ground tracks where highlighted zones are between 12:00 and 14:00 LMT

Fig. 2.1.9: SSO (600 km) with τAN = 13 : 00. Epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

Between Day 1-5 90 Sea Land Between Day 1-5 60 70 Coast Sea 60 Land 30 Coast 50 0 40

30 Latitude [deg] -30

Percentage % 20 -60 10 -90 0 1 2 3 4 5 -180 -120 -60 0 60 120 180 Day number Longitude [deg] (a) Percentage over 6 days (b) Ground tracks where highlighted zones are between 12:00 and 14:00 LMT

Fig. 2.1.10: SSO (600 km) with τAN = 13 : 30. Epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

CHAPTER 2. NOMINAL SCENARIOS 19 2.1. Orbits

2.1.2 Recurrence with no tilting In this subsection, the recurrence over a place is discussed. The satellite will always pointing Nadir and so the recurrence is deﬁned for a vertical crossing or, at least for a visibility in the FOV. It is easy to understand that a tilt of the satellite, perpendicular to its movement, will increase the recurrence over a place. This situation is introduced in the next subsection since some important concepts needs to be explained before.

If a recurrence of 10 days is available over a target, for instance Morocco, some tests can be conducted on a smart irrigation method. However, this is an important constraint for the orbit.

Let’s introduce CT which is the cycle of recurrence with respect to the Earth. It is not necessarily an integer. CT0 detonates the whole number. It has to be noted that the recurrence does not inﬂuence directly the crossing time. CS, which is cycle w.r.t. Sun, can remain constant while CT can take any value. A relation exists however between CT , CT0 and CS,

CT0 CT = . (2.1.8) 1 − 1/CS

For a SSO, CS is infinite and CT = CT0 . "For a recurrent satellite, if it is a Sun- Synchronous, its ground track always returns to the same point at the same time."[27] Recurrence is often presented with recurrence triple, three values that define unequivo- cally the recurrence pattern. Some parameters need first to be defined before introducing these three values.

The length L is the time interval between two crossings at the same ascending node λ0,

L = CT DM = NT0 Td (2.1.9) where DM is a mean day (DM = 86400 s), NT0 the number of round trips and Td the nodal period or draconitic period (period between two passages at ascending node). Since the ground track is recurrent, the orbital plane makes a whole number of round trips, k0, during this time and so ˙ ˙ L(ΩT − Ω) = 2πk0 (2.1.10) −1 with Ω˙ T the angular speed of the Earth (Ω˙ T = 360.985 559 ° d ) and Ω˙ the angular speed of the longitude Ω of the ascending node (m s−1). The daily recurrence frequency is given by

nd ν κ = = 1−P (2.1.11) Ω˙ T − Ω˙ 1 + 0 Nyr where nd is the mean motion when the ascending node is taken as origin, ν the daily orbital frequency (dimensionless), P the nodal precession in round trips per year (dimensionless) 0 and Nyr the number of days in tropical year. κ "allows to compare the Earth’s rotation, the satellite motion, and its nodal precession via the angular speeds." For a SSO, P = 1 and so κ = ν.[27] If we come back to Eq. 2.1.9,

DM CT DM = NT , (2.1.12) 0 ν

CHAPTER 2. NOMINAL SCENARIOS 20 2.1. Orbits and so, for a cycle relative to the Earth,

NT0 CT = . (2.1.13) ν From Eqs. 2.1.11 and 2.1.9,

nd NT Td = 2πk0 (2.1.14) 0 κ and since Td = 2π/nd, NT κ = 0 . (2.1.15) k0 For a recurrent orbit, κ, the daily recurrence frequency, is a rational number. The whole number k0 can denoted by CT0 and

NT0 CT = (2.1.16) 0 κ or NT κ = 0 . (2.1.17) CT0 As any rational number can be rewritten as the summation of an integer number and a fractional part,

DT0 κ = ν0 + (2.1.18) CT0 where ν0 is the whole number closest to κ and DT0 is the unique integer such DT0 =

NT0 − ν0CT0 . [ν0,DT0 ,CT0 ] deﬁne the recurrence triple of the satellite. This recurrence can be deﬁned by these three values or the pair of whole numbers NT0 and CT0 .[27]

ISS orbit It is only possible to give the recurrence triple of the International Space Station for a period of time. It will indeed vary since the daily recurrence frequency (Eq. 2.1.11) depends on the daily orbital frequency ν and the nodal precession P . They are both function of the semi-major a and the inclination i. a constantly varies with time due to the large atmospheric drag at this altitude. According to Ixion, recurrence triple for ISS is [15, +35, 117] in February 2018. It means that the station will pass over the same place after 117 days. It shows that it is impossible to compare data. The revisit time is too high. The irrigation state can change drastically in almost 4 months.

It must be kept in mind that the FOV is only of 5°. With a larger one, or a tilt of the satellite, the same target can be seen more often from the ISS orbit.

CHAPTER 2. NOMINAL SCENARIOS 21 2.1. Orbits

Sun-Synchronous Orbit Exact calculation can be made for a recurrent Sun-Synchronous satellite. The daily orbital frequency ν is equal to the daily recurrence frequency κ. Moreover, it only depends on the semi-major axis since i and a are related. Eq. 2.1.18 can therefore be rewritten as

DT0 ν = ν0 + (2.1.19) CT0 and the satellite ground track repeats every CT0 days, after NT0 = νCT0 revolutions.[27]

The recurrence triple can be visualized in Fig. 2.1.11 with a recurrence diagram from an altitude between 500 and 800 km. Each point represents a recurrent orbit with a certain number of planet revolutions (CT0 ). Four orbits with an exact recurrence of 10 days exist. Of course the number increases if the constraint of the recurrence is relaxed.

Sun−synchronous repeat orbits (Ecc = 0)

4 Number of planet revolutions (Q)

0 6 900 6 9507 000 7 0507 100 7 150 Semi major axis [km]

Fig. 2.1.11: Recurrence diagram for a Sun-Synchronous Orbit (SSO). Each point represents a recurrent orbit with Q (≡ CT0 ) planet revolutions at a speciﬁc altitude. Made with Celeslab.

The satellite creates a grid on the surface of the Earth. Since it is recurrent, the grid interval can be computed directly from the recurrence triple. Two intervals are often used. The ﬁrst one, δR, is the interval between ascending nodes for two consecutive revolutions. It is equal to the standard equatorial shift. The second one, δD, is the interval between ascending nodes for 2 consecutive days. To compute them, the grid interval, δ, is used. It is given by 2π δ = . (2.1.20) NT0 and so, δR = CT0 δ and δD = DT0 δ.[27] To clarify everything, Fig. 2.1.12 summarizes these three δ parameters.

CHAPTER 2. NOMINAL SCENARIOS 22 2.1. Orbits

Fig. 2.1.12: Recurrence grid. "(a) Two consecutive ground tracks from day 0 determine the base interval ∆λE, denoted here by δR. These ground tracks are plotted in bold type. (b) One ground track of day 1 passes through the base interval. (c) The ground tracks for the following days 2, 3,..., D pass through the base interval. (d) All ground tracks up to day CT0 − 1 deﬁne the grid interval."[27]

Characteristics (triple recurrence, inclination, semi-major axis, shift of longitude at equator) for the 43 orbits with at least 10 days of recurrence are available in Appendix B. Celestlab was used to compute them. From the recurrence triple, the draconitic period is determined (Td = 1440CT0 /NT0 ). A ﬁrst estimation of a can be computed with the classical period formula, same as i since they are SSO. By taken into account the secular variations (only mean drifts), recursive formulas are used to achieve a more precise value for i and a.

2.1.3 Recurrence with tilting In this subsection, a tilt of the satellite, perpendicular to the motion, is envisaged. With a Nadir pointing, the revisit time (duration between two revisits) is simply equal to the repeat cycle if the satellite is precisely over the area of interest. If it is allowed to tilt, this value will of course decrease. It depends on δ, the grid interval. If δ is high, the tilt can be too important to acquire data from the adjacent cross track. For a smaller δ, it may be envisaged to even look from the second or third adjacent orbit. The situation is shown in Fig. 2.1.13. One may pay attention to the created pixel distortion. It leads to a change of Ground Sampling Distance.

ISS orbit For the ISS, since it is not a recurrent orbit, the discussion over δ is not needed and it is easier to artiﬁcially increase the FOV.

CHAPTER 2. NOMINAL SCENARIOS 23 2.1. Orbits

Fig. 2.1.13: Tilt of the satellite by a angle α to decrease the revisit time. From [28].

The Tadla Region in Morocco is selected as a target (32°N, 6°W). With propagation of 31 days from January 1, 2018, this region is not visible from the ISS orbit if a FOV of 5° is considered. If the satellite is tilted up to 20°, or the half-swath angle artiﬁcially increase to 22.5°, Ixion gives 10 occurrences during the month. This result can be seen in Fig. 2.1.14. The problem is that the crossing time, as explained earlier, varies with time and there is no pass between the window selected (12:00 to 14:00 LMT). Even with a tilt angle, the recurrence of the ISS orbit is too high and tests about smart irrigation can not be conducted with this orbit.

Sun-Synchronous Orbit In the case of a SSO, if it is recurrent, δ is the main parameter. It is an angle and from geometrical consideration, the distance l between two ground tracks can be deduced,

l = RE sin δ (2.1.21) with RE the Earth radius (6378 km). For a typical value δ = 3°, l = 333 km. It is used to compute αj, the tilt angle from the jth adjacent orbit.

CHAPTER 2. NOMINAL SCENARIOS 24 2.1. Orbits both side with an ° -axis the day of the month. Made with Ixion. y . for the satellite, it is equivalent to a tilt of 20 ° -axis represents the Local Mean Time and x . The ° Fig. 2.1.14: Occurrence of a satellite over theeﬀective Tadla FOV region of in 5 Morocco for the International Space Station orbit with a propagation of 31 days from January 1, 2018. The Field Of View is set to 45

CHAPTER 2. NOMINAL SCENARIOS 25 2.1. Orbits

It is given by 0 ! RE sin jδ sin i αj = arctan (2.1.22) h + RE (1 − cos jδ) where h is the altitude of the satellite (km) and i0 the apparent inclination (deg). The latter is the angle between the equator and the ground track (Fig. 2.1.15). It is computed by sin i tan i0 = . (2.1.23) cos i − 1/ν

Values of α1, the tilt angle from the ﬁrst adjacent orbit, are also available in Appendix B. It is between 16.77° and 67.37°. These tilts angles will introduce a pixel deformation along and perpendicular to the tilt direction. For a SSO at 600 km, Fig. 2.1.16 represents this pixel deformation. An angle of 25° is feasible but it will induce an enlargement factor non-negligible. If a GSD of 50 m is achieved, it will become 62.5 m along tilt direction and 55 m perpendicular to the direction. This is a comprise between the quality of the acquisition and the revisit time. Since α is large, a tilt from the second adjacent orbit is not considered. It will be close to 40°, which is too high regarding the pixel deformations.

Fig. 2.1.15: Apparent inclination i0 and distance l between two adjacent ground tracks. From [28].

Now that the required tilt angle is known, the revisit time needs to be computed. The satellite does not pass necessarily, as explained before, at an angle/distance δ at the equator after one revolution. It takes a few days. As stated in [28], the triple recurrence deﬁnes Eq. 2.1.19 where DT0 and CT0 are co-prime integers (gcd(DT0 ,CT0 ) = 1). According to the Bezout’s theorem and since this equation is Diophantine, there are integers S and m such that

DT0 S + CT0 m = 1. (2.1.24) S represents the number of days (integer) until the ground track of the satellite is oﬀset by an angle/distance δ from the initial track. It can be −δ (westward pass) or δ (eastward pass) since it is a cycle and Eq. 2.1.24 become

DT0 S + CT0 m = ±1. (2.1.25)

Two values of S can be computed, Smin and Smax (Smax = CT0 − Smin). These values are also available in Tab B.0.1 in Appendix B for all recurrent orbits considered.

CHAPTER 2. NOMINAL SCENARIOS 26 2.1. Orbits

Enlargment factor (Altitude=600km) 2

1.9 along tilt dir. 1.8 perp. to tilt dir.

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1 0510 15 20 25 30 35 40 Tilt angle to vertical (deg)

Fig. 2.1.16: Deformation of a conic sensor. The tilt angle is the angle between the vertical and the cone axis. The 2 curves represent the semi major axis and semi minor axis of the intersection of the cone with the horizontal plane at altitude 0. Valid for small cone opening angles. Satellite at 600 km. Made with Celestlab.

To summarize and clarify all the concept introduced here, an orbit can be looked more in detail. At 655 km (cf. Fig. 2.1.11), a Sun-Synchronous Orbit is available (i = 98.01° and triple recurrence is [14, 7, 10]). For this orbit, δ = 2.45° in longitude or l ≈ 272 km. It means that the angle α needed to point the adjacent ground track is 22°. It will introduce an enlargement factor of 1.09 perpendicular to the tilt direction and 1.2 along the direction of propagation (Fig. 2.1.16). This is the maximum value possible. If the target is not perfectly on a ground track, it will lay whatever happens between two adjacent tracks. A tilt angle will be required at each passage but it will be in ]0, α[. Values computed here are at the equator but the tracks can be assumed parallel until high latitude. The latitude of the target is not taken into account. For the revisit time, Fig. 2.1.17 gives the recurrence pattern. It can be seen that after 7 days, the satellite passes at the position 1 (= 1 × δ) and since the orbit is recurrent

(CT0 = 10), it passes after 3 days at −1 × δ (position 9). Eq. 2.1.25 gives Smin = 3 and

Smax = 7, which are the values observed graphically. During one cycle of CT0 days, if the tilt of the satellite is allowed, three acquisitions can be done: 1 the ﬁrst day, 1 after 3 days, and 1 after 7 days. The 10th day, a second cycle begins.

To conclude this discussion, one may note that it exists 1 orbit with 1 day of cycle with an altitude of 561 km. With a tilt, up to CT0 = 3, it is possible to have a daily pass over a target.

CHAPTER 2. NOMINAL SCENARIOS 27 2.1. Orbits

N,P,Q = (14,7,10)

Positions of ground tracks 2

0 12 3 4 5 6 7 8 9 10 Number of planet revolutions

Fig. 2.1.17: Recurrence pattern of a Sun-Synchronous Orbit (SSO) with the recurrence triple [14, 7, 10]. The position of ground tracks is the same as δ (position 1 = 1 × δ). Characteristics of this orbit are available in Tab B.0.1 in Appendix B. Made with Celestlab, from CNES.

2.1.4 Orbit perturbations OUFTI-Next will not have a maintained orbit. No propulsion is considered, even if it exists for speciﬁc CubeSats. Gravitational perturbations (Sun, Moon) or non-gravitational eﬀects (remaining atmosphere) will cause variations of orbital parameters. In the case of a SSO, the satellite will drift and the local crossing time will change. If a recurrence is considered, it will be lost.

In this subsection, the goal is to determine these variations and quantify them. One may keep in mind that OUFTI-Next is a demonstrator and the constraints are of course less restrictive. Only SSO orbits are considered. On the ISS orbit, the local crossing time is already time dependent and an extra drift does not change the conclusion. Furthermore, there is no interest to talk about a change of recurrence for this orbit.

Drift in local crossing time According to [25], the drift in local crossing time is due to variations in inclination. In theory, di/dt = 0 but due to perturbations, i varies on the order of hundredths of a degree per year. This variation directly impacts the local crossing time. The drift, in local time at the ascending node, is given by

dτAN 1 = Ω˙ H (2.1.26) dt K

CHAPTER 2. NOMINAL SCENARIOS 28 2.1. Orbits

where Ω˙ H = Ω˙ (a, i) − Ω˙ S = 0 for a perfectly maintained Sun-Synchronous Orbit and K is a constant depending on the units (already used in Eq. 2.1.1 and equals to 15 ° h−1). Ω˙ (a, i), the variation of the right ascension of the S/C and Ω˙ S, the variation of the right ascension of the Sun, are deﬁned as

a −7/2 Ω(˙ a, i) = −K0 cos i (2.1.27) R and a −7/2 Ω˙ S = −K0 cos iHS (2.1.28) R 3 q µ −6 −1 with K0 a constant equals to 2 J2 R3 = 2.2012788 × 10 rad s and iHS the inclination of the SSO without perturbations.3

To evaluate this drift, variations of i and a need to be computed. For this, a SSO is chosen. For consistency, it is the same orbit as the one used to summarize the recurrence pattern. Its orbital characteristics are listed in Tab. 2.1.1. For the propagation, STELA is used with the NRLMSIS 00 model for the atmospheric drag, mean solar activity and a random tumbling of the S/C4. A standard coeﬃcient of 2.2 is used for the drag.[15] All these parameters will be discussed more in detail in Sect. 2.1.6 about the lifetime of the orbit.

Date a [km] h [km] i [deg] e [-] Ω [deg] ω [deg] M [deg] 2019-01-01 00:00:00 7033.4 655 98.01 0 124.71 0 0

Table 2.1.1: Keplerian parameters of a Sun-Synchronous Orbit (SSO) with triple recurrence equals to [14, 7, 10]

From the propagation, Ω˙ H can be computed and so τAN according to Eq. 2.1.26 with a time step of 1 day. Results are shown in Fig. 2.1.18 for 5 years of propagation. τAN(t) is a quadratic function (parabola) of time. Theses calculations are specific for this orbit. It is therefore important to have an overview of the situation. This drift depends directly on a, which is the main difference between orbits since the inclination is closed to 97°-98° for all SSO. Two extreme recurrent orbits are considered: one at 530 km and one at 786 km (respectively [15, 1, 10] and [14, 3, 10]). Tab. 2.1.2 resumes results for different duration (1 month, 6 months, 1 year, 2 years, etc.). During 1 year, the drift is very low and the mission can be fulfilled. After 1 year, the drift increases more and more. Beyond τAN = 14:00, so between 3 and 4 years, the South hemisphere can be no more acquired. Indeed, the LMT decreases when ascending. For the first orbit (530 km), the S/C reenters the atmosphere during the second year. It explains the lack of data.

3These expressions are simplified in [25] but it is based on an assumption on the variation of the semi-major axis and inclination that is not verified in the case of OUFTI-Next. 4The cross configuration, which will be discussed in chapter 3, is used for the area. It is the worst configuration for the drag since it has the largest area exposed to the remaining atmosphere.

CHAPTER 2. NOMINAL SCENARIOS 29 2.1. Orbits

1 month 6 months 1 year 2 years 3 years 4 years 5 years a [km] h [km] ∆τ τAN ∆τ τAN ∆τ τAN ∆τ τAN ∆τ τAN ∆τ τAN ∆τ τAN 6908.4 530 00:00 13:30 00:00 13:30 00:02 13:32 / / / / / / / / 7033.4 655 00:00 13:30 00:00 13:30 00:03 13:33 00:10 13:40 00:20 13:50 00:45 14:15 01:12 14:42 7164.3 786 00:00 13:30 00:00 13:30 00:03 13:33 00:11 13:41 00:20 13:50 00:43 14:13 01:08 14:38

Table 2.1.2: Drift in local crossing time for three SSO (triple recurrence: [15, 1, 10], [14, 7, 10], [14, 3, 10]). Keplerian parameters obtained with STELA from CNES with NRLMSIS 00 model for the atmospheric drag, mean solar activity, a random tumbling of the S/C and a CD = 2.2.

98.2 14:45 98.18

14:30 98.16

98.14

14:15 98.12

98.1 14:00 98.08

98.06 13:45 98.04

98.02 13:30 98 0 1 2 3 4 5 Year (from 2019-01-01 00:00:00)

Fig. 2.1.18: Drift in local crossing time for a SSO with triple recurrence equals to [14, 7, 10]. Keplerian parameters obtained with STELA from CNES with NRLMSIS 00 model for the atmospheric drag, mean solar activity, a random tumbling of the S/C and a CD = 2.2.

Shift of the ground track Due to atmospheric drag and solar radiation pressure, the S/C looses altitude. The daily shift, ∆lD, is directly related to this variation of a according to ∆a 1 ∆lD = −3πRE 1 − (2.1.29) a CS where CS is equal to infinity for a SSO as described earlier.[27] The daily shift can be computed for the three orbits already considered. Since ∆a < 0, ∆lD > 0 and so it is a westward shift. Fig. 2.1.19 represents this shift for 5 years. It is not negligible for the first orbit at 530 km since atmospheric drag is still important at this altitude. For the two other orbits, the shift during the first year is limited. Tab. 2.1.3 shows the value for specific duration. One important information is that a Nadir pointing will not be possible if the exact same place needs to be imaged. After 6 months, for the second orbit, the most promising, the shift is closed to the swath of the detector (≈ 57 km).

CHAPTER 2. NOMINAL SCENARIOS 30 2.1. Orbits

To conclude, since all ground tracks will shift, the recurrence is not really lost when a shift of 150-200 km arises. The distance l between adjacent ground track is on the same order (272 km for the orbit at 655 km).

3500 SSO 530 km 3000 SSO 655 km SSO 786 km 2500

2000

1500

1000

500

0 0 1 2 3 4 5 Year (from 2019-01-01 00:00:00) Fig. 2.1.19: Shift of the ground track for three SSO (triple recurrence: [15, 1, 10], [14, 7, 10], [14, 3, 10]). Keplerian parameters obtained with STELA from CNES with NRLMSIS 00 model for the atmospheric drag, mean solar activity, a random tumbling of the S/C and a CD = 2.2.

1 month 6 month 1 year 2 years 3 years 4 years 5 years a [km] h [km] ∆l [km] ∆l [km] ∆l [km] ∆l [km] ∆l [km] ∆l [km] ∆l [km] 6908.4 530 33.86 245.78 678.50 / / / / 7033.4 655 5.98 37.96 78.43 167.83 236.84 394.22 542.46 7164.3 786 1.27 8.11 16.25 32.90 44.55 67.51 85.61

Table 2.1.3: Shift of the ground track for three recurrent SSO (triple recurrence: [15, 1, 10], [14, 7, 10], [14, 3, 10]). Keplerian parameters obtained with STELA from CNES with NRLMSIS 00 model for the atmospheric drag, mean solar activity, a random tumbling of the S/C and CD = 2.2.

2.1.5 Eclipse duration OUFTI-Next will undergo solar eclipse. It is a critical parameter since during eclipses, no power is produced. It also aﬀects the thermal equilibrium of the structure as the temperature of the S/C will decrease. Knowing the duration of theses eclipses is therefore important.

This duration (∆te) depends directly on β, the angle between the orbital plane and the solar direction. For a SSO, β is directly related to H0, the local crossing time in degrees.

CHAPTER 2. NOMINAL SCENARIOS 31 2.1. Orbits

H0 = 15(τ0 − 12) where τ0 is the initial LMT at the ascending node (τAN(t0) = τ0). This angle, for a SSO only, is given by

sin β = ± sin i cos δ + cos i sin δ = sin δ ± i (2.1.30) where i is the inclination (deg) and δ the declination at a given time. β varies with time and is not constant during a year.[25]

For the dawn-dusk orbit (τAN = 06:00 or τAN = 18:00), the orbital plane is parallel to the terminator (separation between day-lit side and the dark night side) and ∆te = 0 during most of the year. Eclipses only occur during the winter solstice or summer solstice and are short (≈ 19 min). In the case of a SSO with τAN = 13 : 30, the one derived from the constraints on the crossing time (cf. Sect. 2.1.1), eclipses occur at each orbit and the duration is around 34 min. Fig 2.1.20a represents the eclipse duration evolution during one year for this orbit at 500 km. Fig 2.1.20b is the same curve at an altitude of 700 km. The diﬀerence is on the order of 1 min, which is negligible.

Eq. 2.1.30 shows that in the case of closed inclinations, which is the case for SSO, results will be quite similar. For indication, the eclipse duration for the ISS orbit is available in Fig 2.1.20c. The mean duration is closed to the SSO ones but variations are far more important during the year. With this orbit, the thermal environment/budget is more complex.

2.1.6 Lifetime Knowing the lifetime of the orbit is important. It constraints the mission duration and some sub-systems as the power (number of cycles of the battery). Moreover, to avoid the accumulation of non-functional satellites in orbit, it is recommended by ESA, via its guidelines based on the 2011 ISO standard 24113 primary debris mitigation requirements, that a satellite in LEO (< 2000 km) reenters Earth’s atmosphere within 25 years of mission completion.[29]

To obtain this value, Semi-analytic Tool for End of Life Analysis (STELA) from CNES was used. Three models are available: US 76 (1976 Standard), Jacchia 77 and NRLMSIS-00. The last one is the most recent and the most accurate. It is based on an empirical model of the atmosphere developed by the US Naval Research Laboratory. It takes into account most of the atmosphere components (N, N2, O, O2, He, Ar and H) and the "anomalous oxygen". It is valid up to 1000 km. Its name comes from "NRL" for US Naval Research Laboratory, "MSIS" for Mass Spectrometer and Incoherent Scatter radar and "E" for the model that extends from Earth ground through exosphere.[30]

For the propagation, STELA uses most of the existing perturbations: Earth’s gravity ﬁeld, solar and lunar gravity, atmospheric drag, solar radiation pressure and Earth’s shadow for SRP. Some information is needed for the atmospheric drag such as solar activity. A good indicator is the solar ﬂux at 10.7 cm (2800 MHz) or F10.7. The solar activity presents an 11-year cycle but since the date of the launch is unknown, a mean value of 147.66 s.f.u (solar

CHAPTER 2. NOMINAL SCENARIOS 32 2.1. Orbits

Time spent in Earth shadow Time spent in Earth shadow

Initial MLTAN (h) Initial MLTAN (h)

13.5 35 13.5 35.5

34.5 35

34.5 Duration (min) Duration (min)

33.5

34 33

050100 150 200 250 300 350 050100 150 200 250 300 350 Days from January 1st (2018) Days from January 1st (2018)

(a) SSO at 500 km (τAN = 13:30) (b) SSO at 700 km (τAN = 13:30)

Time spent in Earth shadow

35 Initial MLTAN (h) 0 30

15 Duration (min)

0 050100 150 200 250 300 350 Days from January 1st (2018) (c) International Space Station (ISS)

Fig. 2.1.20: Time spent in Earth shadow over a year (2018). Made with Celestlab.

flux units with 1 s.f.u = 10−22 W m−2 Hz−1) is considered. The AP index, which defines the geomagnetic activity, is set to 15. It means an unsettled magnetic condition. These are the default parameters of the software. Information about the satellite is also needed. The mass is set to 4 kg, which is the maximum for a 3U CubeSat. For the mean cross sectional area, it depends on the OUFTI-Next’s configuration. Theses ones will be discussed in Chapt. 3. The fact is that there are three possible configurations. The main difference is the solar panels position. In each case, the area can be computed with the help of a STELA tool. A fixed orientation and a random tumbling configuration can be considered. For the first situation, it is chosen to maximize the area and so the drag. A coefficient of drag is also needed. For 3U CubeSats, CD = 2.2 is a classical value.[15] The first configuration has body-mounted solar panels. It is called the "standard" configuration. The area with a fixed orientation is simply the surface of one long face (0.03 m2). In the case of a random tumbling, it is a little higher with 0.04 m2. The second configuration is the "table" one. Solar panels are deployed on the long edge on both sides. In fine, a surface of 0.01 m2 is presented to the remaining atmosphere. The "cross" configuration is the last configuration. Four solar panels are deployed on short edges of the Z face. It is the configuration with the biggest surface, A = 0.15 m2. Three SSO are considered. The recurrence is not a requirement for the demonstrator.

CHAPTER 2. NOMINAL SCENARIOS 33 2.1. Orbits

Although the discussion about this particularity was interesting, typical SSO are now considered in the following of this document to be more general. One at 500 km, one at 600 km and one at 700 km. τAN = 13:30 is kept since this value is directly related to a requirement. This parameter is important for the calculation since it will change the relative orientation of the satellite with respect to the sun. It has an impact on the SRP as well as on the atmospheric drag (diurnal bulge). The ISS orbit at 400 km and the Cygnus orbit at 500 km are also kept.

Results are available in Tab. 2.1.4. For the "table" and "cross" configuration, two cases are considered for attitude: a random tumbling and a maximum area facing. This second case will give the minimum lifetime of the satellite. This is unfortunately not a realistic scenario but STELA does not allow a variable area depending on the attitude. The lifetime of the ISS orbit is short and depends on initial parameters. The difference between the "Standard" and the "Cross" configurations is significant. If this orbit is considered in the following phase of this project, a more accurate propagation with STELA needs to be done (iterative process). Some parameters need also to be watched as the area, the CD, the exact mass of the satellite and the solar activity. This latter depends on the launch date. One must keep in mind that STELA is based on empirical atmospheric model and it exists some uncertainties. For higher orbits, whether it is 4 or 5 years of life, this does not change drastically the mission. For lower orbits, each day is crucial. The difference between 48 days of lifetime and 168 days is important. This leads to completely different mission strategies. This clearly why a special focus is necessary on this topic if the ISS is chosen. As expected, the launch from the Cygnus at 500 km increases of 2 years (standard configuration) the lifetime of the satellite. One can also see that with an altitude of 600 km, the lifetime is below 25 years for all configurations. At 700 km, OUFTI-Next will stay in orbit more than 25 years with some configurations. A solution is the utilization of an "End of Life Deorbit System" like an aerobrake sail (Fig. 2.1.21). The major problem is its no-negligible size in the structure (0.4 U for the AEOLDOS from Clydespace). Such a high orbit for a CubeSat is very rare for this reason.

ISS Cygnus SSO SSO SSO Conﬁgurations Area 400 km 500 km 500 km 600 km 700 km "Standard" 0.04 m2 5.5 m (168 d) 2.58 y 2.31 y 11.04 y 45.52 y "Table" 0.06 m2 3.6 m (110 d) 1.7 y 1.52 y 7.05 y 29.29 y 0.1 m2 2.28 m (70 d) 0.98 y 0.9 y 4.01 y 16.81 y "Cross" 0.1 m2 2.28 m (70 d) 0.98 y 0.9 y 4.01 y 16.81 y 0.15 m2 1.56 m (48 d) 0.67 y 0.61 y 2.61 y 10.73 y

Table 2.1.4: Lifetime for three SSO with τAN = 13:30 (500, 600 and 700 km), the ISS orbit (400 km) and the Cygnus cargo orbit (500 km). Computed with STELA (NRLMSIS 00 model for the atmospheric drag, mean solar activity and CD = 2.2).

CHAPTER 2. NOMINAL SCENARIOS 34 2.1. Orbits

Fig. 2.1.21: Aerobrake sail from Clydespace (AEOLDOS). Size after deployment: 1.5 m2. Module size: 0.4 U.

2.1.7 Conclusion In this section, much information about orbits were addressed: the crossing time, the recurrence, the eclipse duration and the lifetime of diﬀerent orbits.

First important information, the cross time over a specific latitude changes at every passage with the ISS orbit. Moreover, some tests on recurrence can not be done since the revisit time is high (100 days). It is the same conclusion for a launch from the Cygnus cargo at higher altitude (500 km). The only difference between both orbits is the lifetime of the satellite. As stated by Nanoracks and proved by STELA, the gain of lifetime can be up to 2 years. To be able to conduct some tests on recurrence and also to increase the latitude window by orbit, a SSO is required. A τAN = 13:30 is well designated since the South and North hemispheres are almost entirely covered between 12:00 and 14:00 LMT. Recurrent orbit can also be envisaged. It is independent of the crossing time. If a minimum of 10 days of revisit time is considered, 43 orbits are possible. With a satellite tilt up to 20°, the revisit time can be slightly decreased. For perturbations, the drift in local time is small during the first two years of operation and even the third year, all the North hemisphere can be imaged. If a recurrent orbit is chosen, ground tracks will shift but in a reasonable way, less than 80 km after 1 year. The major problem for SSO is their high lifetimes. OUFTI-Next is a demonstrator and it does not need to stay in orbit during several years. Only a few months are necessary to conduct tests and acquire usable data with the MWIR detector.

The ﬁnal choice of the orbit will be made in the following phase of development of this CubeSat project. It depends on the parameters described in this section but also on launch costs or launch opportunities. At this stage, no orbit is discarded and the basic requirements can be fulﬁlled.

Let’s mention that all the discussions were made on speciﬁc requirements for the orbit but other subsystems, like the optical part, depend on the altitude chosen. Thermal aspects are also not taken into account at this stage.

CHAPTER 2. NOMINAL SCENARIOS 35 2.2. Communication strategy

2.2 Communication strategy

2.2.1 Frequency bands and data rate Contrary to OUFTI-1, OUFTI-Next needs to download acquired data. The UHF frequency band is used for commands (uplink) and the VHF band for telemetry (downlink). The S band is used to download images (downlink).[15] These are typical frequency bands for remote sensing satellites.

Last year, according to [15], a data rate of 100 kbit/s was needed to close the link budget of the S band antenna. However, according to data sheets from COTS S band transceivers/transmitters, a data rate of 1 Mbps (Tab 2.2.1) can be achieved. Therefore, there is probably an error, or some oversized factors in the link budget of [15]. A data rate of 1 Mpbs seems reasonable and is used in the following.

Company Name Data rate Frequency RF Power Power ClydeSpace STX Up to 2 Mbps 2200 - 2450 MHz 1 W (30 dBm) <5 W (CPUT) Endurosat / 20 Mbps 2200 - 2290 MHz 2 W (33 dBm) <9W GOMspace SR2000 Up to 2 Mbps 1980 - 2290 MHz / 4 W Nanoavionics HiSPiCO Up to 1.6 Mbps 2200 - 2290 MHz 0.5 W (27 dBm) <5 W (IQ Wireless) ISIS / Up to 3.4 Mbps 2200 - 2290 MHz 2 W (33 dBm) 9.2W

Table 2.2.1: COTS S band transceivers/transmitters.

For the UHF/VHF, if ISIS transceivers is considered, 9.6 kbps can be achieved in transmission and 1.2 kpbs in reception.[31] Tab. 2.2.2 gives the frequency bands and the corresponding wavelengths for the three channels used. VHF (downlink) UHF (uplink) S Band (downlink) Frequency [GHz] 0.03-0.3 0.3 - 3 2-4 Wavelength [m] 10 - 1 1 - 0.1 0.15 - 0.075 Data rate [kbit/s] 9.6 1.2 1000

Table 2.2.2: Frequency bands with corresponding wavelengths and typical data rate. Theses values are used in the following.

The ground station in Liège is already equipped in UHF and VHF but not in S band. As stated in [15], a receiver (3 m mesh dish) is available at ISIS for €52,500.5 A combined kit, with UHF/VHF and S band is also available for €64,500.6

For the command and the telemetry, there is nothing special to say at this stage of the development. For S band antenna, it is diﬀerent since this is a discriminating factor through the number of images that can be downloaded. 5https://www.cubesatshop.com/product/full-ground-station-kit-s-band/ 6https://www.cubesatshop.com/product/full-ground-station-kit-vhfuhfs-band/

CHAPTER 2. NOMINAL SCENARIOS 36 2.2. Communication strategy

2.2.2 Data budget Typical MWIR detectors have a matrix of 640 × 512 px. Only the Hercules from SCD has a matrix of 1280 x 1024 px. The bit depth (or color depth) is the number of bits per pixel and it is between 8 and 14 depending on the detector and the temperature precision required. The way of information is internally written is also important. Is a 10-bit coding really coded on 10 bits or is it rather on 16 bits (2 bytes)? The answer is unknown regarding the information available on detectors. Therefore, this situation is not considered in the following.

For a thermal point of view and according to [19], with a 10-bit coding, a ∆T < 0.5 K @ 290 K can be achieved and with a 8-bit coding, it is closer to ∆T ≈ 1.25 K @290 K. With these data, the size of one image can be computed (Tab. 2.2.3).

8 bits 10 bits 12 bits 14 bits Size [MB] 0.33 0.41 0.49 0.57

Table 2.2.3: Size in MB of one image (640 x 512 px) depending on the bit depth.

A compression ratio can also be applied. For a lossless compression, it is equal to maximum 2. For lossy one, it is beyond 10 and even up to 100. The well-known JPEG compression is around 10.[32][33] This ratio is a parameter that can be adjusted to increase the number of images downloaded. Of course, if a lossy compression is considered, it needs to be chosen carefully to avoid too much loss of information. In the case of OUFTI-Next, the wanted ∆T is around 1-2 K (cf. Sect. 1.3). Therefore, with such detectable ∆T described above, a lossy compression can be envisaged. If this solution is pursued, it will add a load on the OBC’s processor. That needs to be monitored. Speciﬁc payload processors also exist, like the CP400.85 from Hyperion7, but the power consumption is not negligible (around 500 mW).

The number of images to download to Earth depends on the mission proﬁle and the number of acquisitions per day. The duration of a pass over Liege is function of the orbit and more precisely of the altitude and the minimum elevation capability of the ground station. It is 5° according to work done on OUFTI-1.[34]. Fig. 2.2.1 shows the typical duration of a communication pass. It is function of the satellite altitude and the maximum elevation available. An exploitable passage is between 5 and 10 min for an orbit at 600 km. Fig. 2.2.2 represents the visibility from Liège for a SSO at 600 km (τAN = 13:30) on January 1, 2019. From these values and if transmission is activated at each passage, the total amount of downloaded data/images can be computed (Tab 2.2.4). Calculations are also made for the ISS orbit (Fig. 2.2.3). Pay attention that in this case the frequency of passage over the ground station depends on the date. It is, however, quite similar during the year. A passage of 6 min, which is independent of the orbit, is also considered. It gives a minimal bound.

7http://hyperiontechnologies.nl/products/cp400-85-processing-platform/

CHAPTER 2. NOMINAL SCENARIOS 37 2.2. Communication strategy

Visibility duration − non rotating Earth (min elev = 5 deg)

12 Max elevation : 7.5 deg 11 10 deg 15 deg 10 20 deg 30 deg 9 50 deg 90 deg 8 Duration (mn) 7

500 550600 650700 750 800 Altitude (km)

Fig. 2.2.1: Visibility duration over a ground station (non rotating Earth). Made with Celestlab.

Since some information need to be sent before images (protocol, acquisition of the signal, etc.), the visibility duration can be adapted. At this stage, a precise value can not be computed but it is assumed to be reduced by 25%. It can be adapted in Matlab. With the high bit rate of an S band transmitter, recovering images from the satellite is not a problem and compression does not seem necessary.

8 bits 10 bits 12 bits 14 bits SSO (600 km) 716 573 477 409 ISS (400 km) 643 514 429 367 Mean duration (6 min) 102 82 68 58

Table 2.2.4: Number of images that can be downloaded during 1 day (1 January 2019) from a SSO at 600 km (τAN = 13 : 30) and the International Space Station (ISS) or during one pass (6 min) depending on the bit depth

To be more general, one can also compute the time to download one image. It only depends on the detector size, the bit depth and the data rate. It is not anymore function of the orbit. The VHF channel can also be used if a problem arises with the S band. Only one image can be downloaded by pass. The transmission takes only few seconds in S band. Results are available in Tab. 2.2.5. It is interesting to know them because the S band transceiver/transmitter is a very high energy demanding system. The less it needs to be switched on, the better it is.

The presence of visible detector is desired even if it is not a top requirement. If it can be integrated, it will bring many beneﬁts. Its integration is discussed in Chapt. 3 since it is related to the conﬁguration and the optical design.

CHAPTER 2. NOMINAL SCENARIOS 38 2.2. Communication strategy

Visibility passes

10 Ground tracks

80 8

70 6 60

GS1 4 50 Latitude [deg]

40 2 Time from beginning of pass [mn] 30

0 20 0 2 4 6 810 12 14 16 1820 22 24 −60 −40 −200 20 40 60 80 100 Time from beginning of simulation [hours] Longitude [deg] (a) Visibility passes over Liège [min] (b) Ground tracks. Red lines represent the visibility from Liège.

Fig. 2.2.2: Visibility over the ground station (Liège) with SSO at 655 km (τAN = 13 : 30). Minimum elevation = 5°. Made with Celestlab, from CNES.

Visibility passes

8 Ground tracks 80

70 6 60

GS1 50 4

40 Latitude [deg]

2 30 Time from beginning of pass [mn] 20

0 10 0 2 4 6 810 12 14 16 1820 22 24 −60 −40 −200 20 40 60 80 Time from beginning of simulation [hours] Longitude [deg] (a) Visibility passes over Liège [min] (b) Ground tracks. Red lines represent the visibility from Liège.

Fig. 2.2.3: Visibility over the ground station (Liège) with the orbit of the International Space Station (ISS). Minimum elevation = 5°. Made with Celestlab, from CNES.

CHAPTER 2. NOMINAL SCENARIOS 39 2.3. Acquisition strategy

8 bits 10 bits 12 bits 14 bits S band (1 Mpbs) 2.6 s 3.3 s 3.9 s 4.6 s VHF (9.6 kbps) 273 s 341 s 410 s 478 s

Table 2.2.5: Time to download 1 image in S band (1 Mbps) or VHF (9.6 kbps) depending on the bit depth

At this stage, no study was done on this detector. To give an order of magnitude, let’s just consider the CMOS detector used by GOMspace in its "High performing Camera- system for Earth Observation Projects"8, the Aptina MT9T0319. The pixel size is only 3.2 µm and the matrix size is 2048 × 1536 px. Images are coded in 10 bits. With theses values, one can compute the time to download one image in S band. It is, without compression, 31.4 s. This is 10 times slower than with the MWIR detector. In case of trouble, it is unthinkable to do it with the VHF. It would take around 54 min. In ﬁne, with the S band, the visible detector does not pose a problem but it adds a charge on the COM.

2.3 Acquisition strategy

The goal of OUFTI-Next is to acquire data from agricultural ﬁelds in Mid-Wavelength InfraRed and visible. It will be single pictures and not a linear scan, a Time Delay Integration (TDI) scan or an Attitude and Orbit Control System (AOCS) scan analyzed last year.[19] Detectors matrices are rectangular. A discussion about the GSD and the orbit is done in the following.

One major diﬃculty with MWIR detectors is their working temperature. They must be indeed cool down to very low temperature, 90 K or 150 K depending on the technology used.[35] The idea is to decrease the Signal to Noise Ratio (SNR). At local temperature (25°C), the detector is blinded by its own thermal radiation. Therefore a cooling system is needed and it has an impact on the acquisition strategy. The detector needs to be cool down before acquisition and then kept at low temperature. A speciﬁc master thesis is dedicated to this problematic.[5] The number of acquisitions per orbit depends on this problematic and also on the orbit.

2.3.1 Acquisition possibilities The latitude window, the range of latitude between 12:00 - 14:00 LMT, is not constant. Slightly mentioned in Sect. 2.1.1, it is smaller for the ISS orbit than for a SSO one. For the ﬁrst one, the duration of a pass is variable in time. The mean pass per orbit is 467 s over 80 days while it is 1873 s (31.2 min) for a SSO τAN = 13:30 at 600 km.

Let’s consider arbitrarily the 112th orbit from January 1, 2019 (Fig. 2.3.1). For the ISS, the latitude window is 35°S - 7°S and the duration is 600 s. It is one of the longest pass available since it is near the equator. For more polar latitudes, the duration is around

8https://gomspace.com/Shop/payloads/earth-observation.aspx 9http://uk.rs-online.com/webdocs/0d2f/0900766b80d2f066.pdf

CHAPTER 2. NOMINAL SCENARIOS 40 2.3. Acquisition strategy

300 s. In the case of the SSO, two latitude windows are present in the same orbit. Their duration is 1860 s (31 min) and 1920 s (32 min).

If several acquisitions with spaced latitudes are envisaged, the cooling system needs to be designed for. Three solutions were considered, a full passive system, an active system with a Peltier module and an active system with a cryocooler. The first two ones should not reach the temperatures considered, as will be explained in Chapt. 3 in the thermal budget. This conclusion is directly linked to the different configurations. That is why it is not discussed in this chapter.

Orbit 112 Orbit 112 90 90 Sea Sea 60 Land 60 Land Coast Coast

30 30

0 0

Latitude [deg] -30 Latitude [deg] -30

-60 -60

-90 -90 -180 -120 -60 0 60 120 180 -180 -120 -60 0 60 120 180 Longitude [deg] Longitude [deg]

(a) ISS orbit (400 km) (b) SSO τAN = 13 : 30 at 600 km

Fig. 2.3.1: Ground tracks where highlighted zones are between 12:00 and 14:00 LMT. 112th orbit with epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

With a cryocooler, two solutions exist. The ﬁrst one is to maintain the detector cold during the waiting phase. It is the easiest solution but this cooling system is a high energy demanding subsystem. A second solution is to acquire data at the beginning of a pass, switch oﬀ the cooling system and turn it back before a second acquisition. However, it can only work with the SSO orbit. The cooling time of the detector is typically between 3 min and 10 min depending on the power supplied. This duration is closed to the overall duration of an ISS pass (< 10 min).[5] Of course, these are preliminary values and precise computations need to be made with a transient model. Nevertheless, the detector should not heat up considerably during a few minutes unless the radiator faces directly the sun (cf. Sect. 3.4). With 31 min by pass, this solution is more viable for the SSO.

As shown in Sect.2.1.1, one image a day is clearly feasible even on the ISS orbit. With a SSO, it can be up to one image per orbit. This choice is also linked to the quality of the picture and the interest in acquiring countless images where there is no scientiﬁc feedback from them.

CHAPTER 2. NOMINAL SCENARIOS 41 2.3. Acquisition strategy

2.3.2 MWIR detector The question of the quality is important. By quality, it means a good spatial resolution and a good thermal resolution. For the first one, simple calculation can be made but for the second, it depends on many parameters and was done last year in a specific master thesis. According to it, ∆T is between 0.3 K and 1.24 K depending on inputs (diameter of the pupil, bit depth, ground temperature, etc.).[19] For the spatial resolution, the Ground Sampling Distance is directly linked to the altitude of the orbit, the pixel size of the detector and the Effective Focal Length (EFL). Theses are specific parameters of subsystems. However, these are typical parameters and are not subject to change significantly. The pixel size of detectors are 15 µm and the EFL is limited to 100 mm (1U of CubeSat). The GSD is simply given by ps GSD = H (2.3.1) EFL where ps is the pixel size and H the altitude. The swath is also an interesting value to know. The matrix of MWIR detectors are not squared as explained in Sect. 2.2.2. Therefore, there are two swaths, one along the trajectory of the satellite and one perpendicular to it. In one direction, in km, it is equal to n × GSD SWn = (2.3.2) 1000 with n the number of pixels in this direction. For the other one, n is replaced by m. One can also compute the Field Of View (FOV) of the detector. From the pixel size and the EFL, the Instantaneous Field Of View (iFOV) is available. The FOV in one direction is directly related to it by ps FOVn = n × iF ov = n × arctan . (2.3.3) EFL

From these equations, values can be computed for several altitudes. Results are available in Tab. 2.3.1. One can see that the GSD is below the requirements of 100 m for typical LEO, whether it is a SSO at 600 km or the ISS orbit at 400 km. The altitude limit is around 666 km. The ISS orbit, with its low altitude, offers the best spatial resolution. Of course the swath is reduced but the total area captured is still ≈ 1189 km2. This should encompass a large number of agricultural fields. The curvature of Earth were neglected for all theses calculations. For a swath of 67.2 km, the maximum one, the difference is only 31 cm, which is three orders of magnitude smaller than the related GSD (105 m). The requirements on the MWIR detector, especially the spatial resolution, are fulfilled. It is not the case only if an orbit above 650 km is chosen, which is an unlikely situation. With actual parameters, 60 m is the best achievable spatial resolution. To go smaller, a solution would be to increase the EFL. Unfortunately, the payload volume in an 3U CubeSat is too limited (1.5U for payload, cf. Chapt. 3). The pixel size is also related to the diffraction limit and the wavelength considered (3 - 5 µm). More information and discussions about optical design are available in three dedicated master thesis (reflective and refractive design) about OUFTI-Next.[1][2][3]

CHAPTER 2. NOMINAL SCENARIOS 42 2.4. Attitude strategy

EFL = 100 mm FOVn = 5.5° FOVn = 4.4° H [km] GSD [m] SWn [km] SWm [km] 400 60 38.4 30.72 500 75 48 38.4 600 90 57.6 46.08 700 105 67.2 53.76

Table 2.3.1: GSD, FOV and swath of the MWIR detector in function of the satellite altitude. Detector matrix = n × m = 640 × 512 px. EFL = 100 mm. Earth curvature neglected.

2.3.3 Visible detector As already stated in the communication strategy (Sect. 2.2.2), the presence of one visible detector is not sure. If the MT9T031 is once again considered, one can say that the GSD will be shorter than 15 m at 400 km. This is 4 times smaller than the MWIR detector one. One of the main reason is the size of the pixels which is 10 times smaller (3 µm to compare to 15 µm). If the goal is to superimpose images, they will need to be processed to match the spatial resolution.

2.4 Attitude strategy

2.4.1 Global Navigation Satellite System (GNSS) Since OUFTI-Next is an Earth observation satellite and the strategy is based on the area scan of a chosen target (cf. Sect. 2.3), the state vector of the satellite needs to be known precisely in its ECEF frame.

A solution is to determine the position of the satellite with the Doppler eﬀect. With this technique, an accuracy between 2 and 20 m can be obtained.[36] However, CubeSats are considered here and ground antennas with high diameter (15 m) are out of reach of a university. Furthermore, a very precise propagation of the S/C needs to be performed on Earth and sent to it. The required accuracy is on the order of 50-100 ms. Indeed, the FOV of the MWIR detector is ≈ 5° and the swath is ≈ 50 km at an altitude of 600 km (cf. Sect. 2.3.2). If the position of the satellite needs to be know to 0.1° of the FOV (0.8 km), the permissible time error is 104 ms.[37]

An on-board Global Navigation Satellite System (GNSS) receiver is therefore the solution. Classical COTS GNSS or NAVSTAR GPS receivers can achieve such an accuracy. More important, position and velocity are known all the time. The diﬀerence between the two is simply the constellation considered. A GPS receiver is logically based on the signal coming from the GPS satellites, so American ones. A GNSS receiver uses American satellites but also other constellations like Galileo (Europe), GLONASS (Russia) or Beidou (China). This distinction will depend on the receiver but also on the chosen antenna. For instance, the GNSS200 from Hyperion, which is a multi-constellation receiver, oﬀers an

CHAPTER 2. NOMINAL SCENARIOS 43 2.4. Attitude strategy in-orbit position accuracy below 8 m10. Antenna can be passive or active and needs a sight of view with the constellations.

Integrate one GNSS receiver in the S/C seems therefore natural. Beneﬁts are far more important than the disadvantages (accurate position/velocity vs. low power consumption w.r.t. the generated power). It can also be pointed out that the time/hour of passage can be extracted from the signal.

More information about these modules are given in Chapt. 3 since it is more related to hardware and conﬁgurations.

2.4.2 Accuracy For OUFTI-Next, an integrated Attitude Determination and Control System (ADCS) module is going to be used and one master thesis will be dedicated to this subject. Nevertheless, it is important to know the requirements of this element. The accuracy of the chosen COTS model should not limit the mission and leads to a degradation of the overall performance of the payload (spatial and thermal precision).

If the pointing accuracy is of course important, the jittering is the crucial parameter for a remote sensing satellite. The attitude jitter is perturbations during the pointing phase, some parasitic movements. It depends directly on the reaction wheels but also on the inertia of the satellite. CubeSats have low inertia compare to classical remote sensing satellite and so are more sensitive to disturbances. One can roughly estimate the pointing accuracy and control. The pointing accuracy in the case of OUFTI-Next is clearly not the main parameter. The swath is large, over 30 km at 400 km. A shift of a 1° at the same altitude gives a ground shift at FOV center of 6.98 km, which is clearly above all ADCS module precision. The shift at the edge is a bit higher with 7.00 km. This difference is negligible since it is imperceptible for the MWIR detector. If the chosen target is centered on the detector area, it will remain in the total acquired area. Even if some side zones of the agricultural fields are lost, this is not a big deal if the MWIR detector can prove its interest. Therefore, to be a little bit more precise and regarding the available specifications (cf. Sect. 3.2.1), 0.1° seems to be a feasible precision. It offers to the satellite a good pointing accuracy. It depends of course on the altitude as shown in Tab. 2.4.1.

H [km] Ground shift [km] 400 0.698 500 0.873 600 1.047 700 1.222

Table 2.4.1: Ground shift at the FOV center of the MWIR detector with an angle shift of 0.1°.

10http://hyperiontechnologies.nl/products/gnss200/

CHAPTER 2. NOMINAL SCENARIOS 44 2.5. Power consumption

The second parameter, the pointing control or pointing stability, is more determinant. If the MWIR detector creates lots of constraints, one of its advantage is its large pixel size. The pointing control is indeed directly related to pixel size since the goal is not to move more than one pixel during the integration time. If it is not the case, the image will be blurred. This is the same phenomenon when you take a picture with a camera. In this situation, the optical system is stabilized but to a certain point. In the satellite, to end this analogy, the stabilization is done by the rotating wheels of the ADCS module. The detector needs also to be isolated from the potential vibration of the structure. Tests on all theses aspects will be done in the following phase of this project. To come back to the attitude jitter, the pixel size of 15 µm can be used or the diﬀerent GSD since it is directly proportional. It gives a precision of 0.0086° or 0.52 arcmin at 600 km. This precision is only required during acquisition. The integration time is a few milliseconds (7 ms at 400 km).[19] Of course, several images can be done during acquisition to cover a large target. Therefore, a pointing control of 0.5 arcmins−1 is suggested.

In the case of the visible detector, due to its smaller pixel size, 3.2 µm for the MT9T031, the visible detector needs at least a pointing control of 0.0018° or 0.11 arcmin at 600 km. A solution is to relax this constraint is to consider a group of 4 pixels for instance as one big pixel. It has of course impact on the GSD and other optical values.

All values given in this section are preliminary estimations and dedicated master thesis on this subject are more detailed.[1][2]

2.5 Power consumption

If the power received depends on the conﬁguration and is analyzed in Chapt. 3, this is not the case for the power consumption. The nominal scenario determines entirely the need in terms of power for the CubeSat during the diﬀerent modes.

The orbit can be decomposed into two parts, the full illumination and eclipse. During full illumination, solar arrays of OUFTI-Next point to the sun unless it is in acquisition or in communication. The need of each sub-system will be diﬀerent. During eclipses, the satellite can be in idle mode waiting illumination or in communication. The second case depends on the available power since it is a high energy demanding mode. Fig. 2.5.1 summarizes theses modes and the sub-systems that are operational or not. One may keep in mind that the satellite will not encounter all these cases during one orbit. A power budget, with attitude taken into account, is also available in Sect. 3.3. In this section, the possibility of a communication mode during eclipse is addressed.

For subsystems like EPS or OBC, typical COTS modules were considered. It is impossible to know precisely the exact components that will be used at this stage of the development. Values introduced here as therefore subject to change with the development progress. Nevertheless, they can be considered as close to reality. The principal unknown is the cooling system and its real consumption as it depends on many parameters (orbit, attitude of the satellite, period of the year, etc.). A Peltier module of 4.5 W (1 A @ 4.5 V) was considered to cool down and regulate the detector temperature. It is unfortunately showed in a dedicated master thesis that it is not suﬃcient.[5] If it is

CHAPTER 2. NOMINAL SCENARIOS 45 2.5. Power consumption not considered in the following, it will be mentioned at the end to have a rough estimation of its impact on the power budget. More details about it are available in the thermal budget (Sect. 3.4). To replace it, a cryocooler is used. Its power consumption depends on the encountered cases.

Fully operationnal Orbit Partially operational Non operational

Illumination Eclipse

Sun-pointing Acquisition Communication Idle Communication

ADCS ADCS ADCS ADCS ADCS Integrated ADCS Integrated ADCS Integrated ADCS Integrated ADCS Integrated ADCS GNSS GNSS GNSS GNSS GNSS

COM COM COM COM COM UHF UHF UHF UHF UHF VHF VHF VHF VHF VHF S-Band S-Band S-Band S-Band S-Band Beacon Beacon Beacon Beacon Beacon

EPS EPS EPS EPS EPS

OBC OBC OBC OBC OBC

PAY PAY PAY PAY PAY

MWIR Dectector MWIR Dectector MWIR Dectector MWIR Dectector MWIR Dectector VIS Detector VIS Detector VIS Detector VIS Detector VIS Detector Cooling system Cooling system Cooling system Cooling system Cooling system

Fig. 2.5.1: Operational modes of OUFTI-Next during orbits. Legend: Green = fully operational, orange = partially operational and red = non operational.

2.5.1 Full illumination

The full illumination of the satellite lasts approximately 64 min since Td ≈ 98 min for a SSO at 600 km with τAN = 13:30 (cf. Appendix B). The eclipse varies around 34.5 min for the same orbit (Fig. 2.1.20). For the ISS orbit, the eclipse time is less stable with large changes of illumination pattern over the year. The mean is ≈ 32 min.

Sun-pointing During this mode, the solar arrays points to the Sun with a coarse sun sensors directly integrated in the panels (accuracy of approximately ± 10° with a FOV = 90° [38]). The ADCS is therefore functional in this mode to rotate the S/C. COM is only active in reception and a Beacon (BCN) transmits telemetry in Morse. The payload is non

CHAPTER 2. NOMINAL SCENARIOS 46 2.5. Power consumption operational during this time. The detector is never completely switched oﬀ but its power consumption is on the order of the mW. For the cooling system, it can be switched oﬀ.[5] Tab. 2.5.1 summarizes the power consumption during this Sun-pointing mode. This mode is the least energy-consuming.

Acquisition In this mode, the satellite points nadir or near-nadir with a tilt angle (cf. discussion in Sect. 2.1.3). The MWIR detector and the VIS detector are switched on. Since the ﬁrst one needs to be cool down, an active cooling system is considered. The cryocooler is envisaged since data are available. It is used to cool down the payload to the right temperature (95 K) and after that to maintain it at this temperature. The cooling is the most demanding energy system in this mode.

For instance, the Sofradir RM2 consumes 12.2 W during 3 min to cool down the detector.[39] This is high but it can be reduced if a longer cooling time is considered. Time is not a discriminating factor in this mission. If 15 min are needed to cool down the detector and reduce consumption, it can be envisaged. There are 15/16 orbits a day, and lost one possible pass is not problematic. OUFTI-Next is a demonstrator and has no commercial constraints. To maintain the temperature around 95 K, it was estimated that 3 W is suﬃcient.[5] To cool it down, the 12 W were considered. This is the worst case. Since a mean value is necessary to model a full cycle, 4 min seems reasonable to take several images of a target: 3 min of cool down and 1 min of acquisition. It leads to a consumption of 9.75 W only for the cooling system.

It is unfortunately impossible to give more precise values since tests need to be down on the detector, the cryocooler and the complete satellite to determine them. At this stage, there are too many unknowns: materials, geometry of the payload, etc.[5] A Peltier module can also be envisaged. Its nominal consumption is around 5 W during acquisition but it varies along the cycle since it is used as a regulator in other modes. It is never shut down. Its impact is discussed in a rough way in the following and mostly in the thermal design and the power budget in Chapt. 3. The power consumption for the acquisition mode, with a crycooler, is available in Tab. 2.5.1.

Communication Communication is a high energy-consuming mode due to the transmission of data. ADCS is used to orient the S band antenna to the ground station. The power consumption of the S band transmitter depends on output power and the data rate as shown in the communication strategy (cf. Sect.2.2). If 1-2 Mbps is considered, the power is 4-5 W depending on the model. The duration to download one image with the S band is a few seconds. The S band transmitter must therefore not be switched on during the whole pass. This is interesting because it reduces the mean consumption. Consequently and as an assumption, one can consider that this transmitter is only active during half of the window. This is around 2.5 min to 5 min depending on the pass and the altitude of the orbit. In ﬁne, only 2.5 W are consumed on average (Tab. 2.5.1).

CHAPTER 2. NOMINAL SCENARIOS 47 2.5. Power consumption

SUN POINTING ACQUISITION COMMUNICATION 20% 20% 20% Sub-Systems Nominal Nominal Nominal Margin Margin Margin ADCS iADCS100 (Hyperion) mW 1400 1680 1400 1680 1400 1680 GNSS (Hyperion) mW 157 188 157 188 157 188

COM COM Rx (UHF) mW 240 288 240 288 240 288 COM Tx (VHF) mW 0 0 0 0 1740 2088 S-Band Tx mW 0 0 0 0 2500 3000 BNC (Beacon) mW 250 300 250 300 250 300

EPS Picasso S/C mW 200 240 200 240 200 240 (Clydespace)

OBC iOBC (ISIS) mW 400 480 400 480 400 480

PAY Cooling system (cryo) mW 0 0 9750 11700 0 0 MWIR detector mW 1 1.2 100 120 1 1.2 VIS detector mW 1 1.2 244 292.8 1 1.2 (E2V Dector)

TOTAL POWER mW 2649 3179 12741 15289 6889 8267

Table 2.5.1: Power consumption during full illumination. Modes: sun-pointing, acquisition and communication.

2.5.2 Eclipses During eclipses, no power is received. It is therefore not necessary to orientate the satellite. As indicated just above, the duration of eclipses is around 34.5 min for a SSO at 600 km and τAN = 13:30. It is 32 min for the ISS orbit. The satellite will be in idle mode most of the time. It is also possible to communicate with Earth if the power budget allows it.

Idle In this mode, the only difference with the Sun-pointing is the utilization of the ADCS. However, it can not be switched off and has its own idle mode. In the case of the iADCS-100 from Hyperion, the difference is minimal regarding the nominal mode (Tab. 2.5.2).

Communication It is exactly the same as during full illumination. The fact that the satellite is in eclipse does not change anything (Tab. 2.5.2). It is still an energy-consuming mode and its possibility during eclipse is directly related to the power generated.

CHAPTER 2. NOMINAL SCENARIOS 48 2.5. Power consumption

IDLE COMMUNICATION 20% 20% Sub-Systems Nominal Nominal Margin Margin ADCS iADCS100 (Hyperion) mW 1150 1380 1400 1680 GNSS (Hyperion) mW 157 188.4 157 188.4

COM COM Rx (UHF) mW 240 288 240 288 COM Tx (VHF) mW 0 0 1740 2040 S-Band Tx mW 0 0 2500 3000 BNC (Beacon) mW 250 300 250 300

EPS Picasso S/C mW 200 240 200 240 (Clydespace)

OBC iOBC (ISIS) mW 400 480 400 480

PAY Cooling system (cryo) mW 0 0 0 0 MWIR detector mW 1 1.2 1 1.2 VIS detector mW 1 1.2 1 1.2 (E2V Dector)

TOTAL POWER mW 2399 2879 6889 8267

Table 2.5.2: Power consumption during eclipse. Modes: idle and communication.

2.5.3 Mean consumption With theses values, the mean consumption for diﬀerent scenarios can be computed. The SSO at 600 km with τAN = 13:30 and the ISS orbit are still considered. These scenarios are:

1. Sun pointing during full illumination and idle in eclipse, 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse, 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse, 4. Sun pointing + acquisition (4 min) during full illumination and idle + communication (8 min) in eclipse;

Results for both orbits, with a cry-cooler, are given in Tab. 2.5.3. They will be used in Chapt. 3 for the power budget. One can see that even with high consumption modes,

CHAPTER 2. NOMINAL SCENARIOS 49 2.5. Power consumption their impacts are very limited on consumption. It must be said that duration is relatively short and represents a small portion of the total period. However, these are assumptions and the components consumption are approximations. That is the reason for the 20% margin.

ISS (400 km) SSO (600 km) Case 0% margin 20% margin 0% margin 20% margin 1. 2.6 W 3.1 W 2.6 W 3.1 W 2. 3.0 W 3.6 W 3.0 W 3.6 W 3. 3.4 W 4.0 W 3.3 W 4.0 W 4. 3.4 W 4.1 W 3.3 W 4.0 W

Table 2.5.3: Mean consumption (cryocooler) for diﬀerent scenarios. Two orbits considered: SSO at 600 km with τAN = 13:30 and the ISS orbit. Scenarios: 1. Sun pointing during full illumination and idle in eclipse. 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse. 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse. 4. Sun pointing + acquisition (4 min) and idle + communication (8 min) in eclipse.

Now, a Peltier module can be considered in a very rough way. Instead of the cry-cooler and its 9.75 W during acquisition, 5 W are used in this mode. In full illumination, it is 2 W for thermal regulation. Results are given in Tab. 2.5.4.

ISS (400 km) SSO (600 km) Case 0% margin 20% margin 0% margin 20% margin 1. 3.9 W 4.6 W 3.9 W 4.6 W 2. 4.0 W 4.8 W 4.0 W 4.8 W 3. 4.4 W 5.3 W 4.3 W 5.2 W 4. 4.4 W 5.3 W 4.4 W 5.2 W

Table 2.5.4: Mean consumption (Peltier) for diﬀerent scenarios. Two orbits considered: SSO at 600 km with τAN = 13:30 and the ISS orbit. Scenarios: 1. Sun pointing during full illumination and idle in eclipse. 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse. 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse. 4. Sun pointing + acquisition (4 min) and idle + communication (8 min) in eclipse.

CHAPTER 2. NOMINAL SCENARIOS 50 3| Cubesat conﬁgurations comparison

Many conﬁgurations of OUFTI-Next exist to achieve nominal scenarios introduced in Chapt. 2. The objective of this chapter is to describe theses conﬁgurations and presents the most promising ones.

The goal is to ﬁt the platform and the payload in a 3U structure. For recall, Cubesats are decomposed in units. One unit is typically 10 cm × 10 cm × 10 cm. In the case of a 3U, it is a little more than 3 real units. Fig. 3.0.1 shows the geometric constraints of such a satellite and the typical basis used with the origin at the geometrical center of the structure.

One may therefore understand that it does not exist many possibilities. The principal difference between configurations is the position of the solar arrays. The first one, and the most obvious, is with body-mounted panels. It will be called "standard" configuration in the rest of this chapter. The two others possibilities have deployable solar panels. The "table" configuration has hinges along the long edge, so parallel to the Z-axis. For the "cross" configuration, hinges are located on the small edge, parallel to the X or Y -axes depending on the panel. Fig. 3.0.2 shows 3D model of theses possible configurations. These are typical solutions. They can vary depending of the case analyzed. For instance, for thermal aspect around the detector, the cross may be shifted from the top to the bottom of the satellite (from +Z to -Z). Chapt. 4 is dedicated to summarize all the modifications introduce here and find the best configuration for OUFTI-Next at this stage of the development.

In the following, all sub-systems of the S/C are reviewed and diﬀerences between conﬁgurations are assessed.

51 HPE .CBSTCNIUAIN OPRSN52 COMPARISON CONFIGURATIONS CUBESAT 3. CHAPTER

Fig. 3.0.1: Speciﬁcation drawings for a 3U CubeSat. From Polytech CubeSat standard.[40] 3.1. Payload

(a) "Standard" conﬁguration (body-mounted (b) "Table" conﬁguration (deployable solar pan- solar panels) els along long edges)

Fig. 3.0.2: Diﬀerent conﬁgurations (3U CubeSat) for OUFTI-Next. Made with IDM-CIC from CNES.

3.1 Payload

The payload regroups the MWIR and the possible VIS detectors, the optical part related to them as well as the cooling system.

The optical design will be either a refractive one or either a reflective one. A combination of both is also possible. Master thesis are related to them.[1][2][3] For the whole payload, a minimum of 1.5U is considered. It is situated in the bottom of the structure for all configurations. It exists two possibilities for the detector orientation: an aperture in -Z (small face) or in a long face (X/Y). Fig 3.1.1 represents these two cases. The second case does not add any advantage. In this situation, the size available for the optical design is reduced or light beams need to be bent, which unnecessarily complicates the design. The only advantage is the possibility to accommodate a visible detector with the refractive design. With a reflective system, the optical design is independent of the wavelength. A visible detector can therefore be integrated and shared the same aperture.[2] In the case of a refractive one, the optical design system is designed for the

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 53 3.1. Payload

MWIR frequency band, not the visible one. A second aperture is necessary. If the MWIR detector aperture is on -Z, it is impossible to fit a second aperture for the visible sensor. The aperture for the first one is between 60 mm and 65 mm in diameter on a face size of 100 mm × 100 mm.[1] A solution would be to rotate the whole design and have two apertures on a long face. It will of course have an impact on the Effective Focal Length (EFL) and so on the GSD as described in Sect. 2.3. This design is also less stable since the gain due to the gravity gradient passive stabilization is lost. A 3U CubeSat aligns naturally with the nadir direction due to this torque.

1.5 U

1.5 U PAYLOAD 1 U

PAYLOAD 1 U

(a) MWIR detector aperture in X/Y face (long (b) MWIR detector aperture in -Z face (short face) face)

Fig. 3.1.1: Two conﬁgurations for the detector aperture in the available payload volume (1.5U).

The MWIR needs also to be cool down and so a cooling system is envisaged. A full passive module, as initially thought, is not eﬃcient enough to reach 100 K. A cryocooler is therefore considered. A radiator is needed to evacuate the heat from the detector. Ii is an aluminum plate, to increase thermal conduction, with a high-emissivity coating. It is on a long face of the satellite (3U).[5] Radiators are common on satellites and allow to evacuate the heat easily. For instance, on the ISS, deployable radiators are used. Of course, they are imposing. One set of deployed radiators is composed of 7 panels of 1.8 mby × 3.6 m. Just to give an indication, Fig. 3.1.2 shows two deployed radiators on the space station.[41] For CubeSat, it is less common since only small surfaces are available but it works in the same way.

The crycooler is based on a Stirling engine located near the MWIR detector. In most common design, Fig. 3.1.3a, the engine is behind the detector. It is the linear design and it is typically 40.0 × L 75 mm. Since the optical system is above it, it is too long (1.5U max). A second solution, proposed by SCD, is to put the engine next to the detector as shown in Fig. 3.1.3b. In this situation, the whole design is reduced and be ﬁtted in the back of the payload.

At this stage, the exact position of each component inside the payload is unknown. The payload is seen as a "black box" of 1.5U with an output oriented in the -Z face. The integration of the optical design system and the cooling system will be done once all the main characteristics are frozen. It has no interest to go further on details.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 54 3.1. Payload

Fig. 3.1.2: Two deployed radiators of the International Space Station. Taken during an extravehicular activity of the STS-128 mission. From [42].

(a) MCT SCORPIO BBMW (Sofradir) (b) InAsSb (XBn) Kinglet (SCD)

Fig. 3.1.3: Typical cryocoolers with MWIR detectors.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 55 3.2. Platform

3.2 Platform

The platform, so all the subsystems dedicated to the operation of the mission, is in the upper part of the satellite. Its maximum size is 1.5U.

3.2.1 ADCS GNSS As stated in Sect. 2.4.1, a GNSS receiver is necessary to precisely know the position of the S/C. It is either a module for the ADCS or either takes the form of a PCB. Clydespace also oﬀers a bundle grouping its OBC and a GPS receiver1.

Four COTS models are displayed in Tab. 3.2.1 and some receivers are very promising for their size or their power consumption.

Name GNSS200 GPSRM 1 piNAV-NG SGR-05P Company Hyperion Pumpkin/Novatel SkyFox Labs Surrey Mass 1.5 g 109 g 24 g 60 g Size 20x15x2mm 96x90x16 mm 71.1x45.7x11 mm 103x64x11 mm Position accuracy 8 m 1.5 m (RMS) 10 m (2σ) 10 m (2σ) Velocity accuracy 0.03 m/s (RMS) 0.10 m/s (2σ) 0.15 m/s (2σ) Time accuracy 20 ns (RMS) 100 ns (2σ) 500 ns (2σ) 120 s Time-to-ﬁrst-ﬁx 50 s 90 s 90 s (passive antenna) Typical operating 3.3 V 5 V 3.3 V 3.3 V voltage Typical power 125 mW 1 W 157 mW 1.3 W consumption (passive antenna) (active antena) Operating -45°C to +85°C -40°C to +85°C -40°C to +85°C -20ºC to +50ºC temperature Operating Multi GPS GPS GPS constellation constellation GLONASS Cost 7980$ 6900 € Integrates GOMspace seamlessly with also proposes Remarks ADCS from a model from Hyperion Novatel

Table 3.2.1: Technical speciﬁcations of COTS GNSS receivers. All the data comes from manufacturer online data sheets.

To receive the signal, an antenna is needed. A passive antenna is suﬃcient in this case. Some companies, like SkyFox Labs, Surrey or GOMspace via Inventek can provide patch antennas (Fig. 3.2.1) but they are active antennas. If considered, a power consumption on the order of 50 mW needs to be added. "It is also recommended to keep the antenna facing the Zenith. However after the position ﬁx the antenna can be swapped or rotated or

1https://www.clyde.space/products/7-nanosatellite-on-board-computer-gps-bundle

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 56 3.2. Platform periodically rotated in attitude to Nadir position and back to Zenith, whilst the tracking of the satellites is kept".[43]. Let’s mention that GOMspace places the small antenna (15.2 mm × 15.2 mm) on the interstage to get a clear line of sight (Fig.3.2.2).[44]

Fig. 3.2.1: Patch antenna from Fig. 3.2.2: Gomspace/Inventek GNSS antenna posi- SkyFox Labs (active). tion.[44]

Integrated ADCS module To reduce the development cost and not to reinvent the wheel, an integrated ADCS module is going to be used. With such a payload and precision required (cf. Sect. 2.4), OUFTI-Next needs active control systems like reaction wheels. Magnetorquers can also be present to help the orientation. To know the attitude, diﬀerent sensors are available. The most common are star trackers, sun sensors, magnetometer or simply gyroscopes. The GNSS receiver describes above only gives the position and the velocity of the satellite. To determine the attitude with it, several antennas in diﬀerent faces are needed. There is no interest to do it here.

Major constraints on the ADCS is the precision and its size. The volume is very limited with only 0.5 U available for it. It is located below the platform and above the payload. A little market survey is available in Tab. 3.2.2. These are only integrated modules but some companies propose diﬀerent actuators and sensors individually and it is the customer who integrate them in its platform. Data come from data sheets or from the small market survey done last year in [15].

The pointing accuracy requirement of 0.1° is achievable by all the selected COTS modules. For the pointing control or stability, it is diﬃcult to estimate it because it is inertia dependent. The CubeADCS is the most promising model but its size disqualiﬁes it. XACT from BlueCanyon or iADCS100 are also good solutions even if some information is missing.

The choice is not made at this stage of the development but it shows that the precision sought is possible to ﬁnd.

The ADCS is also used to detumble the satellite after deployment. This phase is crucial and will need to be studied. If the "cross" platform is chosen, the star tracker will be

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 57 3.2. Platform hidden and the ADCS must be able to detumble itself without it. The position of the star tracker is not arbitrary. It may face most of the time the space. It can not be on the same face as the S band patch antenna, nor on the opposite side. For instance, if the antenna is on +X face, the star tracker needs to be on +/- Y. Its position is always ﬁx on the design of the ADCS. In the case of the iADCS from Hyperion, as shown in Fig. 3.2.3, the star tracker is in the opposite side of the subsystem interface connector. The bus on CubeSat is typically on X face behind access doors.[40] It can not be rotated because the PCB ﬁxing bars in the structure are not symmetrical. Its positions constraints all other components. It is not a insoluble problem since the CubeSat is symmetrical.

Fig. 3.2.3: iADCS100 from Hyperion/Berlin Space Technologies. Size: 0.3 U.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 58 3.2. Platform C ° ° /s ° 470 g 0.3 U <<1 1.4 W >1.5 $75 000 C to +40 30 arcsec Hyperion ° iADCS100 Berlin Space Technologies -45 - Magnetometers - Gyroscope - Star Tracker - Reaction wheels - Magnetorquers C ° /s ° (2 axes) (3 axes) ° ° 910 g 0.5 U XACT >10 <3.0 W C to +50 $125 000 ° BlueCanyon Technologies 0.003 0.007 -30 - Magnetometers - Gyroscopes - Star Tracker - Reaction wheels - Magnetorquers ° ° 0.5 0.055 ADCS (Picasso) Clydespace High-Precision - Magnetometers -Sun Sensor - Star Tracker - Reaction wheels - Magnetorquers C ° ° ° 0.1 MAI 694 g 0.5 U 0.013 $66 920 C to +80 ADACS MAI-400 ° 1.13 Nadir 2.05 W max -40 - Magnetometers - Gyroscopes - Star Tracker - Reaction wheels - Magnetorquers C ° (ST) (ST) ° ° 617 g 3 axis 0.75 U $56 000 C to +70 850 mW ° CubeSpace <0.1 CubeADCS <0.06 -10 - Magnetometers - Sun Sensor - Star Tracker - Gyroscopes - Ferrite Core torquers - Air core coil - Reaction wheels - Magnetorquers C ° ° ° € ° /s ° <2 642 g 1.5 0.75 U 2.05 W C to +40 ° 130 000 GOMspace and 0.1320 2U/3U Fine (simulation) 3 axis control Between 0.12 ADCS solution -20 - Magnetometers - Sun Sensor - Star tracker - Reaction wheels - Magnetorquers Table 3.2.2: Some available COTS ADCS module. All data come from data sheets or from [15]. Name Company Mass Size Pointing accuracy Pointing control/stability Slewing rate Sensors Actuators Operating temperature Power Cost

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 59 3.2. Platform

3.2.2 COM As described in Sect. 2.2, three communication channels are needed: UHF, VHF and S band. Transceivers/transmitters are necessary but also antennas. Transceivers/transmitters are just PCB. For instance, ISIS offers a UHF/VHF transceivers in one single card2. The S band transceiver is on its own PCB. Some COTS models were introduced in Sect. 2.2 to justify the bit rate. The three models with a bit rate close to 1 - 2 Mbsp offer similar characteristics. For the antennas, a deployable system is needed for the UHF/VHF. Once again, ISIS offers different possibilities (turnstile, dipole, monopole) that meet the requirements.3 These are omnidirectionnal antennas. They radiate around them, in a torus way. Therefore, the antenna axis must not directly point Liège. This is an unlikely situation, especially since there are four antennas arranged in a cross (Fig. 3.2.4).

(a) General radiation pattern of an (b) Deployable antenna system of ISIS.[31] omnidirectional antenna (in the middle). From [45]

Fig. 3.2.4: VHF/UHF antennas.

The position of antennas will depend on the configuration. If the ISIS structure is chosen, there are four possible positions: top, 4 × middle and bottom (Fig. 3.2.5). For the "standard" configuration, due to the presence of body mounted solar panels, a top position deployment (+Z face) is considered. It is the same solution for the "table" configuration for identical reasons. Depending on the panels’ height and the related deployment mechanism, a top position can be impossible. It must be watched if this configuration is chosen. In the case of the "cross" configuration, a top deployment is impossible since there are hinges there and even if it was possible, antennas will be over the solar panels once deployed. A solution is a deployment in the middle of the structure. This is the only possible solution but a dangerous one. If solar panels do not open, communication with Earth will not be possible. 2https://www.isispace.nl/product/vhf-downlink-uhf-uplink-full-duplex-transceiver/ 3https://www.isispace.nl/product-category/cubesat-products/cubesat-antenna-systems/

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 60 3.2. Platform

Fig. 3.2.5: Four possible positions for the deployable antenna system of ISIS. [31]

The case of the S band antenna is different. A patch antenna is recommended. It is usually attached to a 1U panel (10 cm × 10 cm). Its position is important since it is directional. A patch antenna is defined by its beamwidth which represents the angular separation between two identical points on opposite side of the maximum pattern of the lobe (Fig. 3.2.6).[46] For instance, the beamwidth of the S Band patch antenna of Nanoavionics is 40° horizontal and 40° vertical. It is a squared antenna.4 Clydespace proposes a antenna with a beamwidth of 60° (circular antenna) In fine, the antenna is directional and Liège needs to be clearly visible to communicate. Fig. 3.2.7 represents the attitude of OUFTI-Next and the cone of visibility over Liège with the antenna on the side of the satellite.

Beamwidth -3 dB

Fig. 3.2.6: Beamwidth of an antenna. Remade from [46]

4https://n-avionics.com/cubesat-components/communication-systems/ cubesat-s-band-patch-antenna/

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 61 3.2. Platform

(a) Direct view to Liège (b) View of the S band patch antenna

Fig. 3.2.7: Views of OUFTI-Next in communication mode. Beamwidth of 60°. Made with VTS from CNES

For its location, the easiest and most likely solution is one long face of the satellite, at the opposite of the radiator. Indeed, the antenna needs to point to the ground station. If it is on the same face as the radiator, the latter will face the Earth and so receive its albedo, which is to be avoided for thermal considerations (cf. Sect 3.4). One can also consider the antenna on the -Z face, either with a deployable system or with a hole in the middle to still have an aperture for detectors. In the first solution, the S Band patch antenna is on the payload’s aperture door (Fig. 3.2.8). After the deployment from the launch dispenser, the door is opened and the antenna can be used. With this solution, the ADCS is less solicited since rotations are less important. It is also potentially possible to communicate and acquire data at the same time. The payload aperture and the antenna are on the same face of the satellite. Nevertheless this situation is very demanding in energy. The major problem is the addition of a single point of failure. If the door does not open, there is no acquisition and the mission is compromised and can not be fulfilled. In the case of a patch antenna on the side of the CubeSat, there is no need of an aperture door. Even if a problem arises for the S band module, the VHF module is still there as an emergency backup (cf. Sect. 2.2). Moreover, a deployable door means the development of a mechanism and all tests related. In the case of the "table" or "cross" configuration, the mechanisms will not have to interfere, which adds constraints and potential failures. The second solution takes advantage of the first one but delete this single point of failure. The idea is to have a hole of the size of the detector aperture in the patch antenna. Fig. 3.2.9 represents this situation. Instead of one antenna, there are four small antennas around the hole. Some research has been done on the subject and performances are similar to classical patch antennas. Unfortunately, it was only used once

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 62 3.2. Platform with the Tigrisat CubeSat mission, a 3U satellite developed by Iraqi students with the collaboration of the Sapienza University of Rome and launched successfully in 2014.[47][48] In contrary to classical COTS module, this antenna needs to be built, developed and tested by the university.

Fig. 3.2.8: S band patch antenna on the payload’s aperture door. From [15]

(a) S band patch antenna. (b) Dimension of the S band patch antenna.

Fig. 3.2.9: Four small S band patch antennas. The payload’s aperture is ﬁtted in the middle. From [47][48]

If the side location is retained, the thickness of the S patch antenna needs to be watched. This is not a problem for the "standard" and "table" conﬁgurations but for the "cross" one. Solar panels need to go over the antenna and the total width of the satellite must remain in the speciﬁcations of the deployers POD. It depends on the S band patch chosen. Some are directly integrated in a 1U panel whereas some are screwed on the panel, adding a thickness. This is the case of the Clydespace’s one5.

Once again, with the cross configuration, if solar panels do not deploy, communication is impossible with Earth or at least difficult. The signal can be strong enough to pass through the disruptive element that is the non-deployed solar panel. This situation, if the "cross" configuration is chosen, needs to be analyzed and tested.

5https://www.clyde.space/products/13-cput-sband-patch-antenna

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 63 3.2. Platform

3.2.3 OBC The On-Board Computer (OBC) is the conductor of the satellite. Its role and its reliability are vital. Nevertheless, it is impossible to choose one speciﬁc model now. For the power consumption (sect. 2.5), the ISIS one, the IOBC, was used arbitrarily to have a value closed to the reality.6

3.2.4 PWR For the EPS, COTS are envisaged, without at this stage a speciﬁc model in mind. It is the size of one PCB and it is located in the top part of the structure. Let’s mention that some companies, like Clyde Space, proposes an EPS coupled with the battery (20 Whr or 40 Whr). It reduces the overall size and there is a thermal control integrated. The capacity of the battery will be computed in Sect. 3.3 regarding the power budget.

The solar panels have typically a 28.7% or 30% (AzurSpace) eﬃciency at BOL depending on the provider. According to ISIS, 1U panels produce approximately 2.3 W in LEO and 6.9 W for 3U panels (X/Y) with 30% eﬃciency.

In the case of deployable solar panels, a thermal knife is used to cut a wire and the spring loaded mechanisms is released. Fig 3.2.10 represents swept panels hinges from Nanoavionics.

Fig. 3.2.10: Backward swept panels hinges (spring loaded mechanisms) made by Nanoavion- ics

If the "cross" configuration is quite well defined for the deployement (90° from the face), the table configuration can be opened at 90° or at 135°. Blue Canyon Tech has a 3U spacecraft bus, the XB3 spacecraft, with an opening on the edges (Fig 3.2.11).[49] It increases the total solar panels area since two faces of the body are covered with them. On the other side, it also increases the thermal conduction to the structure, and so the overall temperature radiated to the MWIR detector.

6https://www.isispace.nl/product/on-board-computer/

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 64 3.2. Platform

Fig. 3.2.11: XB3 spacecraft (spacecraft bus) from Blue Canyon. Solar panels are deployed with a 135° angle.

Deployment is always risky and are avoided if possible in space applications. A failure of the mechanism here is quite problematic. It will of course decrease drastically the generated power but it will also affect the good behavior of other subsystems. For the "table" configuration, the star tracker of the ADCS will be hidden as well as the radiators. The overall mission will be affected but the satellite will be functional. The COM is not impacted since the S band patch antenna is on the 4th side, as well as the GNSS antenna. In the case of the "cross" configuration, since all faces are covered by the panels, it will affect the ADCS (star tracker and the GNSS antenna), the COM as already explained in its dedicated section and the payload via the radiators. In this case, the mission can not be fulfilled since no communication channel with the satellite, or at least very limited, is available.

3.2.5 STR COTS structures are quite identical since the CubeSat acceptance checklists are precise on the material used and the geometry. The structure is directly related to the chosen configuration. The "table" configuration is the more problematic one since hinges are placed on the side panels, which is quite rare. However it exists as shown just above with the XB3 spacecraft (Fig. 3.2.11). The structure needs also to be compliant with the VHF/UHF antenna system. As explained in the COM part, the system is not at the top of the structure but in the middle of the "cross" configuration. A specific structure needs to be chosen. For instance, the Clydespace’s one has reinforcements that prevent a priori this deployment (Fig. 3.2.12).7

7https://www.clyde.space/products/1-cs-3u-cubesat-structure

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 65 3.3. Power budget

Fig. 3.2.12: 3U structure from Clydespace with its reinforcements.

3.3 Power budget

3.3.1 Power generation The power generation depends on the conﬁguration and so on the solar cells available surface. Deployable solar panels are envisaged because it increases this parameter and therefore the overall production. To maximize it, the ADCS module will point the S/C towards the sun. It is done thanks to the sun sensors directly integrated in panels between solar cells. Solar arrays surfaces and related maximum productions are available in Tab. 3.3.1.

"Standard" "Table" "Cross" configuration configuration configuration Surface of solar 4 × 3U 1 × 3U 3 × 3U arrays + 1 × 1U Maximum power 6.9 W 20.7 W 29.9 W produced

Table 3.3.1: Solar arrays surfaces (conﬁgurations) and the related maximum power produced.

For the "standard" configuration, one may think, why only used one 3U panel knowing that the final configuration will probably have 2 × 3U panels on a long face as well as on 1U panel on +Z. Indeed, this configuration can increase the power generated up to 10 W but the satellite needs to be oriented correctly to the sun. The optimum is a rotation of -13° around X or Y to see the top face and 45° around Z to present the corner between two long faces. Fig. 3.3.1 represents this situation. The view is from the sun. This is a very specific orientation and the satellite needs to know the sun position to orientate itself. Sun sensors are usually integrated in solar panels and they are coarse ones. As already stated in Sect. 2.5, the precision is ≈ 10° with FOV = 90°.[38] Therefore, fine sun sensors with a wider FOV are needed on each panel. Some companies can include

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 66 3.3. Power budget them in their integrated ADCS module. For instance, GOMspace has a ﬁne sun sensor with a half-FOV of 60° and precision of 2° at the edge 8. If these sensors are included on each face, the satellite should be able to orientate itself adequately to maximize the production. This situation is however not considered in the following. Such an orientation is based on assumptions that may not be met. Moreover, Simu-CIC is used to compute the attitude and the sun pointing is always related to one surface, not a combination of several ones.

Fig. 3.3.1: Optimal orientation for the sun pointing mode. View from the sun to the satellite. Rotation: -13° around X/Y and 45° around Z. 3D model made with IDM-CIC.

Let’s come back to the main discussion about the attitude and the power production and more specially on the acquisition mode. In this mode, the satellite will point the target (nadir or with a tilt angle) and the power received will decrease, same during communication mode. This attitude is computed with SimuCIC and processed in Matlab. The software from CNES gives the angle between the normal of the solar arrays and the direction of the sun. The power generation is therefore given by

P = −εbolACsunV cos α (3.3.1) where εbol is the solar panel eﬃciency at Beginning Of Life (30%), A the solar arrays 2 −2 surface (m ), Csun the solar constant (1361 W m ), V the visibility from the sun (from 0 to 100%) and α the angle between the normal of the solar arrays and the direction of the sun (deg). Maximum values presented in Tab. 3.3.1 are obtained by considering α = 180. The normal of the solar arrays points outward. It explains the minus sign in the equation. With theses values in hands, it is interesting to know if the attitude has a real impact on the power generation or not.

Let’s consider the "cross" conﬁguration for a propagation of 15 days on a SSO at 600 km with τAN = 13:30 as well as on the ISS orbit. Two cases are considered for both orbits: a full sun pointing and a full nadir pointing. Results for 1 day, for the sake of clarity, are represented in Fig. 3.3.2 and Fig. 3.3.3. Same information for the "standard" and "table" conﬁgurations are available in Appendix C.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 67 3.3. Power budget

(a) Sun pointing mode. (b) Nadir pointing mode.

Fig. 3.3.2: Power production on a SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. "Cross" conﬁguration.

(a) Sun pointing mode. (b) Nadir pointing mode.

Fig. 3.3.3: Power production on the ISS orbit. Epoch: January 1, 2019. "Cross" conﬁgura- tion.

Theses are two extreme cases but they are interesting to analyze. The ﬁrst mode corresponds to the maximization of the production. It will be, if everything works, the basic attitude mode for OUFTI-Next. It will stay in that mode until it points nadir to acquire data. The power produced will decrease during this phase. That is why a full nadir pointing simulation is done.

With the SSO, the position of the sun is constant over time and it explains the repetition of the pattern. Let’s mention that at 12:00 Local Mean Time the sun is at the zenith. In the case of the "cross" conﬁguration, the solar arrays are on the top and if the satellite points nadir, a maximum production is achieved at this moment. These are the peaks in Fig. 3.3.2b. They are not equal in amplitude to the value obtained with the sun pointing mode due to the inclination of the orbit.

8https://gomspace.com/UserFiles/Subsystems/datasheet/gs-ds-nanosense-fss-22.pdf

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 68 3.3. Power budget

For the "standard" and "table" conﬁgurations, this phenomenon does not happen at the same moment. Peaks are at the beginning of the illumination phase when the satellite is in very low latitude (around 90°S) and shows its long face to the sun.

In the case of the ISS, peaks are moving since the LMT changes at every orbit as explained in Chapt. 2 (cf. Sect. 2.1.1). The amplitude of the peaks is also changing over time. It is related to the angle α. To see clearly this phenomenon, a propagation of 1 year for both orbits was done and is represented in Fig. 3.3.4. The pattern for the ISS orbit is not surprising. This is very close to the eclipse duration shown in Fig 2.1.20c in the dedicated section (Sect. 2.1.5). It is the same for the SSO but it is less visible.

(a) Sun-Synchronous Orbit (SSO) (b) International Space Station (ISS)

Fig. 3.3.4: Power production with in nadir pointing mode. Epoch: January 1, 2019. "Cross" conﬁguration.

The goal is to quantify the impact done by a nadir pointing on a full sun pointing mode. The mean power produced can be computed in both cases and compare for a duration of 15 days. Values are available in Tab. 3.3.2. A full nadir pointing is a bit extreme but it shows that the power produced is drastically reduced. Only 15 days are considered even if over a year, as shown above, variations for the ISS orbit can be important. The reason is simply that if the satellite is launched on this orbit, its best lifetime is 5.5 months (cf. Sect. 2.1.6). OUFTI-Next will therefore never encounter all these variations. Taking a short interval of time is more representative of the reality. At the end, the point is to show that a full nadir pointing is the worst case in a qualitative way and not to extract exact values.

In SimuCIC, it is possible to combine different attitude modes. Unfortunately, it is impossible to select a specific target and point nadir during the overflown. To overcome this limitation, one can create a "false" ground station at the same place and impose an attitude change. The station generates a zone of influence but its size can not be directly controlled and is too large. It tends to increase the visibility and so the number of passes. Nevertheless, a scenario with OUFTI-Next pointing nadir over the Tadla plain (Morocco), Liege during communication and the sun otherwise is possible. It was done and results are represented in Fig. 3.3.5 for the SSO. It can not be made with the ISS orbit since the crossing time window is not an available input in SimuCIC. For the SSO, as shown in

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 69 3.3. Power budget

Sun pointing Nadir pointing ISS (400 km) SSO (600 km) ISS (400 km) SSO (600 km) "Standard" 4.2 W 4.5 W 1.4 W 1.5 W configuration "Table" 12.7 W 13.6 W 4.3 W 4.4 W configuration "Cross" 18.4 W 19.3 W 9.1 W 8.8 W configuration

Table 3.3.2: Mean power produced during 15 days with a sun pointing mode and a nadir pointing mode. Epoch: January 1, 2019. "Cross" configuration. the acquisition strategy, Sect. 2.3, the Tadla plain is on the constant latitude window. If results are analyzed, one can see that the nadir pointing and the communication phase have almost no impact on the overall scheme. The mean power produced is indeed 4.4 W for the "standard" configuration, 13.1 W for the "table" and 19.2 W for the "cross" one during that day. It is less than 1.5% of difference with a full sun pointing mode.

To conclude, if only one acquisition per day is done, it is totally transparent regarding the power produced. Of course, if more acquisitions are done, it can drastically decrease.

Fig. 3.3.5: Power production with a per default sun pointing mode, a nadir pointing over the Tadla plain in Morocco and a station pointing over Liege. SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. "Cross" conﬁguration.

3.3.2 Power margin For the power consumption, the idea is to compare the value obtained in Sect. 2.5 and the ones just above. Four typical scenarios were introduced.

As summarizes in Tab. 3.3.3, values are closed for the "standard" conﬁgurations. For the "table" and the "cross" conﬁguration, there is no problem as the margin is over 8 W. All four cases have a positive margin. Case 1. and 2. are the most common scenario. The case 1. is not a interesting one since nothing happens in contrary to case 2. For this

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 70 3.3. Power budget

ISS (400 km) SSO (600 km) Case Production Consumption Margin Production Consumption Margin 1. 4.2 W 3.1 W 1.1 W 26.2% 4.5 W 3.1 W 1.4 W 31.1% 2. 4.2 W 3.6 W 0.6 W 14.3 % 4.5 W 3.6 W 0.9 W 20 % 3. 4.2 W 4.0 W 0.2 W 4.7 % 4.5 W 4.0 W 0.5 W 11.1 % 4. 4.2 W 4.1 W 0.1 W 2.4 % 4.5 W 4.0 W 0.5 W 11.1 %

Table 3.3.3: Power budget (cryocooler) on two orbits (mean power and 20% margin on the consumption). Two orbits considered: SSO at 600 km with τAN = 13:30 and the ISS orbit. Scenarios: 1. Sun pointing during full illumination and idle in eclipse. 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse. 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse. 4. Sun pointing + acquisition (4 min) during full illumination and idle + communication (8 min) in eclipse. one, the margin is almost 15%. Moreover, a 20% margin was already considered for the consumption. It means that one image per orbit is clearly feasible. One orbit can be fully dedicated to download data but it can also be done on the same orbit (case 3.). Let’s mention that the sun pointing mean power was considered for the production as the attitude has almost no impact. The same table without the 20% margin is available in Appendix C.

Same calculation can be made with the rough estimation done about a Peltier module. Results are available in Tab. 3.3.4. One can conclude that the Peltier can not be fitted on "standard" configuration. Here, as discussed at the beginning of this section, only a 3U solar panel was considered. If the optimal orientation is chosen, 10 W are available in sun pointing mode. It gives a production of 6.4 W on average on a orbit. Margins will be positive for all cases with the "standard" configuration. Of course, as explained, it is based on assumptions. They deserve to be deepened to conclude.

ISS (400 km) SSO (600 km) Case Production Consumption Margin Production Consumption Margin 1. 4.2 W 4.6 W -0.4 W -9.5% 4.5 W 4.6 W -0.1 W -2.2% 2. 4.2 W 4.8 W -0.6 W -14.3 % 4.5 W 4.8 W -0.3 W -6.7 % 3. 4.2 W 5.3 W -1.1 W -26.2 % 4.5 W 5.2 W -0.7 W -15.6 % 4. 4.2 W 5.3 W -1.1 W -26.2 % 4.5 W 5.2 W -0.7 W -15.6 %

Table 3.3.4: Power budget (Peltier) on two orbits (mean power and 20% margin on the consumption). Two orbits considered: SSO at 600 km with τAN = 13:30 and the ISS orbit. Scenarios: 1. Sun pointing during full illumination and idle in eclipse. 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse. 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse. 4. Sun pointing + acquisition (4 min) during full illumination and idle + communication (8 min) in eclipse.

To avoid this optimum configuration, one can also only deployed one long 3U panel instead of two on the "table" configuration. The production would be 13.8 W in sun pointing and 8.9 W in average. It is sufficient but it will affect the center of gravity as well

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 71 3.3. Power budget as the rotational inertia around the Z-axis. The mass is not more almost symmetrically distributed. Fig. 3.3.6 represents this conﬁguration. The deployable mechanism adds a risk. If it does not work, the situation goes back to the "standard" conﬁguration with body mounted solar panels.

Fig. 3.3.6: "Table" conﬁguration with only one 3U deployable solar panel. 3D model made with IDM-CIC.

The main problem with the Peltier module, as it will be explained in the thermal budget (cf. Sect. 3.4) is the radiator. The "standard" conﬁguration is, even with positive margins, not the perfect one. The "table" and the "cross", with their high-power production (> 12.5 W on average) and the shadows created by the panels are more appropriate.

3.3.3 Battery capacity From the power production and the power consumption, battery can be sized. Only values with the cryocooler are considered in the following. The battery capacity depends directly on the maximum duration of the eclipse and the power consumed during this phase. The energy used during this phase is given by

Eecl = Pecl × teclMAX = 2.4 W × 35 min = 1.4 Wh (3.3.2) for the SSO considered in this section and if idle is the only mode taken into account. It is not the installed capacity since the eﬃciency of the battery (output vs. input eﬃciency) needs to be added as well as the Depth Of Discharge (DOD). This value is directly related to the battery’s useful life and the number of cycles that the battery endures. There are typically between 14 and 15 eclipses a day for a satellite in LEO. During one year, it leads to around 5500 cycles. Fig. 3.3.7 represents a typical lithium battery life with respect to the DOD. The life cycle is directly related to the orbit lifetime and it is not necessary to design a battery with a lifetime of 5 years if the satellite goes back to Earth after only 1 year. 30% of DOD seems reasonable regarding the lifetime computed in Sect. 2.1.6. It gives around 4 years of life.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 72 3.3. Power budget

1000000

100000 10 yr life

5 yr life Cycle Life

10000 2 yr life 1 yr life

1000 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Depth Of Discharge (DOD) %

Fig. 3.3.7: Typical lithium battery life with respect to the Depth Of Discharge (DOD). Data from [50].

The installed capacity can be computed by 100 100 Einst = Eecl × × × (1 + Margin/100) = 6.9 Wh (3.3.3) Eﬀ DoD with Eﬀ = 85%, DOD = 30% and the margin = 25%. This last value is a margin in case of thermal degradation of battery, solar cell capacity, etc.[50]

One can also compute this battery size if communication is enable. Unfortunately, the number of communication phases during eclipses is unknown. The worst case, a link with Liege at each eclipse is considered. It gives 9.8 Whr. The consumption is taken without margin since there is a margin here. There is no reason to consider both.

Even if it is no problem on average, the battery will discharge during acquisition and communication in full illumination with the "standard" configuration. The instantaneous consumption (Tab. 2.5.1) is indeed superior to the power produced (Tab. 3.3.2). It will influence the DOD. On both orbits, SSO and ISS, OUFTI-Next enters in eclipse after communication. It means that the battery will not be fully charged at this moment. That is why it is interesting to look at the battery cycle over a large propagation to see if everything goes well. For this simulation, only the SSO can be modeled with SimuCIC as explained above. For the capacity, 9.8 Whr can be used but typical battery capacities for CubeSats are 10 Wh, 30 Wh, 40 Wh and 80 Wh. Therefore 10 Whr seems more appropriate. This problematic of the discharge during full illumination only arises with the "standard" configuration. Results for the "table" and "cross" configuration are available in Appendix C. The propagation lasts 1 year. Fig 3.3.8 shows that a 3U solar panel and a battery capacity of 10 Whr are sufficient. It proves that the mean computation is correct for the "standard"

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 73 3.4. Thermal budget conﬁguration. It only takes a few hours (≈ 5 h) to fully charge the battery (Fig 3.3.8b). With the margin, one can also note that the DOD is never below 75% after the ﬁrst charge. This is due to the 25% margin on the capacity. In this computation, no aging of the battery was considered.

100

60 Battery charge [%] 50

40 0 30 60 90 120 150 180 210 240 270 300 330 360 Time [day] (a) 1 year (b) 1 day

Fig. 3.3.8: Battery cycle (10 Whr) for the "standard" conﬁguration. Orbit: SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. Acquisition: Tadla plain, Morocco. Communication: Liege.

It was an unknown during all the project but theses computations tend to prove that the standard conﬁguration can fulﬁll the mission in terms of power with the crycooler. Of course, there are several assumptions behind. Fortunately, its impact is very localized since the acquisition duration is short and it is switched one only in that mode.

3.4 Thermal budget

The principal challenge for the thermal design is the cooling of the MWIR detector. As already mentioned, it must be at 90K or 150K (-183°C or -123°C) depending on the technology.[35]

This section gives several details on the cooling system as well as more configuration related parameters. More detailed information is available in a dedicated master thesis.[5] A master thesis is also dedicated to the whole thermal design of the satellite. Its conclusion should also lead to the optimal configuration of the satellite and the arrangement of subsystems in the platform. Batteries should, for instance, be kept in a specific range of temperature (from 0°C to 45°C in charge and -20°C to 60°C during discharge).[4] This section is however only dedicated to the detector and the impact of the cooling system on the satellite configuration.

To cool it, three methods are possible: a full passive solution, a full active one and a mix of both. The main factor is the achievable ∆T . Power aspects were considered in Sect. 2.5.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 74 3.4. Thermal budget

3.4.1 Full passive solution With a passive solution, a radiator is used, combined with a thermal strap that connects it to the detector. The ﬂux is directly related to the radiator temperature and what it can radiate to space. For instance, it must absolutely not see the sun. The solar constant is indeed 1361 W m−2 and it will warm up considerably the detector. This can be avoided if the radiator is on one long face on the satellite.

On the "standard" conﬁguration, the satellite should turn around Z-axis in acquisition mode. During communication, it can not be done if the S band antenna is on one long face. In sun pointing mode, the radiator does not see the sun. For "table" and "cross" conﬁgurations, the radiator is in the shadow of the solar panels. In this case, the radiator will "see" the back of the solar arrays and a radiative exchange exists between both surfaces. It has an non-negligible impact on the performances and the optimal size of the radiator. For the "cross", the precision of the sun sensor is crucial. A shift can potentially let some solar rays reached the radiator. A simple ray tracing code was developed on Matlab to determine the critical angle and detect an illumination of the structure. Fig. 3.4.1 represents the "cross" with a shift of 10° around X-axis and 10° around Y -axis. This is the typical accuracy of coarse sun sensors. One part of the structure is no more shadowed by the panels. This is the worst case. 10° of precision is for one coarse sun sensors. With 4 sun sensors on each panel, this case should not happen.

As mentioned in [5], -45°C to -20°C can be reached with a passive system. It is considerably too hot. The Earth’s albedo is the problem as the radiator receives it. A solution is to use a sun shield as CryoCube 1, a CubeSat developed by NASA Kennedy Space Center to perform cryogenic fluid management experiments.[51] It is impossible for the "standard" and "table" configurations. It requires a specific deployment system. On the "cross", the shield can be opened between the solar panels as shown in Fig. 3.4.2. However the panels need to be on -Z face and no more on +Z face. With this configuration, Fig. 3.4.3, the sun becomes a problem again. The solar panels no longer shade the structure and the radiator can be illuminated if there is a misalignment with the sun. OUFTI-Next, as before, will have to rotate around the Z-axis to orientate the radiator to cold space. A second solution is to keep the solar panels on +Z but reduced their size to 2U. The satellite will still produce 20.7 W in sun pointing mode (29.9 W before) and the radiator will be in the shadow. On -Z, a small sun shield can be deployed with 1U panels. Once folded, it makes a 3U panel. This configuration is shown in Fig. 3.4.4. The problem is the triple radiative exchange: the sun shield with the radiator and with the solar panels. Theses two solutions, although attractive, leads to several constraints. The principal is the management of a sun shield, its development and its integration. For a demonstrator and a CubeSat, it would lead to a growing complexity of the satellite just to keep a full passive system. Let’s also mention that in the first solution, if the solar panels do not deployed, the mission is a failure. They are indeed oriented to the structure once folded.

It was computed that with a heat shield, temperature can reached -75°C to -35°C.[5]

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 75 3.4. Thermal budget

40 Z

0 20 -40 -20 0 0 20 -20 X 40 Y

Fig. 3.4.1: Impact (red) of sun rays on the "cross" Fig. 3.4.2: Sun shield of the Cube- conﬁguration. Green arrow = sun direction. 10° Sat CryoCube 1. From [51]. rotation around X axis and 10° around Y axis.

Fig. 3.4.3: "Cross" conﬁguration with solar Fig. 3.4.4: "Cross" conﬁguration with 2U panels in -Z and a sun shield. Made with solar panels in +Z and a sun shield -Z. 3D IDM-CIC. model made with IDM-CIC.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 76 3.4. Thermal budget

3.4.2 Mixed solution A solution to increase the cooling is the combination of a passive system and a Peltier module. It will add a ∆T . Another advantage of this system is the temperature regulation by adjusting the power sent to the module.

Unfortunately, the Coeﬃcient Of Performance (COP) of a Peltier is low and the ∆T is related to its operational temperature. For a typical Peltier used in CubeSat (5 W), at 300 K, ∆T ≈ 100K while at 150 K, ∆T ≈ 15K. Due to rejected power, the hot side reaches too high temperatures and the detector can not reach its operating temperature.[5] However, the SNR of the detector can be potentially increased. It will of course degrade the results. At this stage, some technical information about detectors are unknown to determine if this approach is feasible. No heat shield was considered. If it is used, the ∆T can be higher but this is a very restrictive conﬁguration. This is the reason why it was not discarded.

3.4.3 Full active solution The last solution is a crycooler. This is a full active system. As explained before, it is based on a Stirling engine (one piston) that will cool down the detector and reject the heat to the radiator. It is completely independent of the satellite attitude. The Earth’s albedo will not saturate the radiator. Of course, a full illumination of it still needs to be avoided. The solar ﬂux is too high.

As mentioned in [5], around 12 W are needed to cool down the detector. The exact value depends on the initial condition and also on the wanted cooling time. With less power, it will increase and conversely with high power, the duration will decrease. As used in Sect. 2.5 for the power consumption, 3 min is a typical value.

With this system, the MWIR detector can be cooled down to 150 K. It is, according to [5], the only possible solution available at this stage of the development without a performance degradation.

Cryocooler are however not perfect and can lead to several problems. The ﬁrst one is the presence of mobile parts. Fortunately, this type of system is used in military applications. They are, for instance, used to cool down MWIR detector on missiles or on helicopters. They are therefore designed to survive to severe vibrations. So, it should not be a problem for the launch. The second problem is vibrations created by the Stirling engine. It could lead to performance deterioration of the ADCS, especially the pointing control. If this happens, some information, like the warm-up time of the detector if the cryocooler is switched oﬀ during acquisition , will have to be known.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 77 3.5. Mass budget

3.5 Mass budget

In this section, a rough estimation of the satellite mass is given. As the power budget, there are unknown on each subsystem. They are even larger here because almost all the components of the payload are unknown.

The maximum weight for a 3U CubeSat is 4 kg but it is not a strict limit.[40] Tab. 3.5.2 summarizes all the components and their mass. Some masses are unknown and diﬃcult to estimate.

One related problematic is the position of the center of gravity. The satellite needs to be well balanced on the X-axis and Y-axis. It means that this center "shall be located within 2 cm from its geometric center in the X and Y direction". In the Z direction, specifications are less strict since it is 7 cm from the geometric center.[40] With platform above and payload below, the satellite is relatively well balanced. A first estimation of the center of gravity along Z can be done for each configuration. Every subsystems of the platform are located at +10 cm except the ADCS at +5 cm. All the payload is located at -7.5 cm. It is the solar arrays that will modify the center of gravity. For the "standard" configuration, only the small 1U panel on +Z has an impact on it. For the "table", they don’t play a role since they are uniformly distributed along Z. For the "cross", all the weight is located at the top of the structure. Results are available in Tab.3.5.1. The platform counterbalances the payload and the center of gravity stays close to the geometric center. Since exact position and models of each subsystem are partially unknown, it is complicated to give a better estimate. IDM-CIC, from CNES, is the perfect tool to estimate its position in the following phase of the project.

"Standard" "Table" "Cross" configuration configuration configuration CG location +1.6 cm +1.3 cm +4.2 cm

Table 3.5.1: Estimation of the position of the center of gravity along Z-axis. Origin at the geometric center of the satellite.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 78 3.5. Mass budget

"Standard" "Table" "Cross" Sub-Systems configuration configuration configuration ADCS iADCS100 g 400 400 400 (Hyperion) GNSS g 1.5 1.5 1.5 (Hyperion) GNSS antenna g 25 25 25

COM UHF/VHF transceiver g 85 85 85 UH/VHF antennas g 85 85 85 S band transmitter g 75 75 75 (Nanoavionics) S band antenna g 50 50 50

EPS 3U EPS g 86 86 86 (Clydespace) Batteries g 250 250 250

OBC iOBC (ISIS) g 94 94 94

PWR Solar arrays g 350 450 650

STR ISIS 3U g 303 303 303

PAY Crycooler + MWIR detector g 400 400 400 (Sofradir) VIS detector g 100 100 100 Optical system g 150 150 150 Interface g 200 200 200 payload/platform Radiator g 125 125 125

TOTAL POWER g 2780.5 2976.5 3176.5

Table 3.5.2: Mass of each subsystem

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 79 3.6. 6U structure

3.6 6U structure

If a 3U CubeSat is the size intended for OUFTI-Next, it is interesting to look at a 6U structure.

With a 6U (2 × 3U or 30 cm × 20 cm × 10 cm), the payload is generally located on one side of the structure (30 cm × 10 cm × 10 cm) and the platform on the other side. Fig. 3.6.1 shows a 6U structure from ISIS with 3U imager9. The available volume for the payload is clearly the main advantage of a 6U. The Effective Focal Length can be longer and so the GSD reduced. One can also fit secondary payloads. For instance with a Effective Focal Length (EFL) of 0.2 m, a GSD of 30 m can be achieved at 400 km (ISS orbit). Unfortunately, an increase of the EFL leads to diffraction problems. One way to cope this problem is to increase the pupil size but it can not be done since the 6U is 10 cm deep.

Fig. 3.6.1: Typical 6U structure from ISIS. Payload (3U imager) on one half and platform on the other one.

If a cryocooler is used, it does not change anything. For the mixed solution with a Peltier module (cf. the thermal budget in Sect. 3.4), the radiator size can not be increased. It will stay on the long face of the satellite. One of the wide face will see the Earth and the other one provide energy with solar panels. Compared to the "standard" configuration, the surface of solar panels is doubled (2 × 3U in body mounted). It leads to 13.8 W during sun pointing mode and 8.9 W in average. It is sufficient for a Peltier module. For the platform, a bigger ADCS module is necessary. It needs to compensate the increase in mass and inertia. Its power consumption is a bit higher. For instance, between the iADCS100 and the iADCS400, both from Hyperion, the second one needs 2 W instead of 1.4 W in nominal mode for the first one. For the size, the difference is 0.4U (0.3U for the iADCS100 and 0.7U for the iADCS400).

9https://www.isispace.nl/product/6-unit-cubesat-structure/

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 80 3.6. 6U structure

The lifetime of a 6U is also diﬀerent. The atmospheric drag depends directly on the area A and the mass m according to

1 A 2 vr FD = − CD ρvr (3.6.1) 2 m vr where CD is the drag coeﬃcient and vr the relative velocity of the satellite. One can see that if both A and m are doubled the force remains unchanged. On a 6U, the mass can go up to 12 kg, so 3 times higher than a typical 3U CubeSat.[40] The drag is therefore less important. According to STELA, the lifetime on the ISS is 0.95 years with A = 0.06 m2 and m = 12 kg. If the mass is reduced to 8 kg, the lifetime is 0.65 years.

In ﬁne, a 6U structure will not change fundamentally the mission and it will not lead to a performance gap.

CHAPTER 3. CUBESAT CONFIGURATIONS COMPARISON 81 4| Optimal conﬁguration & scenario

This chapter connects the previous ones. It makes the link between the requirements, the nominal scenarios derived from them and the different configurations. It is an iterative process that leads to the suitable configuration for the mission. It also summarizes a typical scenario that can be realized with the chosen configuration.

4.1 Conﬁguration

Three conﬁgurations are available, the "standard" with body mounted panels, the "table" with two deployable solar panels on the long side and the "cross" with 4 deployable solar panels on the small side. The "standard" is the easiest one and the less dangerous. There is no deployable mechanism unless the UVH/VHF antenna system. It is also the cheapest one.

4.1.1 Payload orientation To decrease the GSD thanks to longer Eﬀective Focal Length and proposes an easier optical design, the aperture is on the -Z face of the satellite. The total available size for the payload is 1.5U. This decision does not disqualify any of the conﬁgurations.

4.1.2 Power & cooling system The main parameter for choosing the conﬁguration is clearly the generated power with respect to the power consumption. The latter depends directly on the cooling system of the MWIR detector.

As shown in the power budget (Sect. 3.3), the "standard" configuration can deal with a crycooler and have a margin on all possible modes (sun-pointing, acquisition, communication). The body mounted 3U solar panel is sufficient. If a Peltier module is chosen, with rough estimations, the power generated is no sufficient. A solution to keep the "standard" configuration would be to use fine sun sensors and more solar arrays surfaces (2 × 3U and 1U on +Z). The "table" configuration with only one deployable solar panel (3U) is a good compro- mise. It offers good margins and small risks. The classical "table" and "cross" configurations produce much more energy but only a small part is consumed. It is clearly not efficient. The management of this excess energy may be a problem. Either it is not produced or simply dissipated in heat. This is an important problematic to consider in the further development of the satellite.

82 4.1. Conﬁguration

If the "standard" conﬁguration is used with the cryocooler, a 10 Wh battery is suﬃcient.

4.1.3 Radiator & cooling system The radiator is the second parameter that needs to be watched carefully. Since the working temperature (90 K or 150 K depending on the detector) can be reached with the passive solution, a Peltier module or a cryocooler can be used.

According to [5], the temperature is too high with the Peltier. A small performance degradation could be envisaged using it. It needs to be discussed with the detector manufacturers. The thermal precision requirement may be carefully watched. It is to be smaller than the temperature increase of the plant. One of the advantages of a Peltier module is that there is has no moving part. It is therefore more robust than a cryocooler. If the cryocooler is considered, it needs to be a folded design (cf. Sect. 3.1). The heat shield is not envisaged in this optimal configuration. Of course it will protect the radiator from the Earth’s albedo but it adds to many constraints. The "cross" needs to be consider and a specific deployable system needs to be developed. Moreover it is also a big risk and OUFTI-Next is a demonstrator, not the final mission. If the detector needs such a specific system, this strongly constrains its use in a constellation or on another satellite. The KISS1 approach prevails here. The "standard" configuration can be used but a system needs a sensor needs to be integrated in the radiator face to measure the illumination. If it sees the sun, the satellite needs to rotate and points to cold space this face. In the case of the "table" or the "cross" configuration, the radiator is shadowed by the solar panels.

4.1.4 Conclusion From the discussion on the configuration, the "standard" configuration associated with a cryocooler can fulfill the mission. If a Peltier is chosen, one needs to be sure that the ADCS module can position the satellite optimally with respect to the sun.

If one look at the demonstrator requirements (Sect. 1.3), the structure is eﬀectively a 3U and the MWIR detector can be integrated. For the VIS detector, its integration is still an open question. It will depend on the optical design chosen. It was discussed in Sect. 3.1. The thermal precision will depends on the cooling system. With the crycooler, as the detector is at its specify working temperature, it should not be a problem. The GSD depends both on the optical scenario and the orbit. It is below 100 m if the altitude does not go over 666 km. It will be discussed in the next section as well as the temporal resolution and the hour of passage.

This "standard" conﬁguration is represented in Fig. 4.1.1 with an open side panel to see the interior. The exact arrangement of PCB inside the platform is unknown. The ADCS module and the payload are placeholders 3D models.

1Keep It Simple and Stupid

CHAPTER 4. OPTIMAL CONFIGURATION & SCENARIO 83 4.2. Scenario

UHF/VHF antennas Solar planels

Platform (COM, PWR, OBC)

ADCS module Star Tracker

Payload Radiator

Fig. 4.1.1: "Standard" conﬁguration with annotations. Made with IDM-CIC.

4.2 Scenario

The scenario is directly related to the orbit and the attitude of the satellite. The main constraint on the satellite subsystems is the precision of the ADCS module. This parameter was assessed in Sect. 2.4. Some COTS models were introduced but there will be a dedicated master about this topic.

4.2.1 Orbit & acquisition Two types of orbits are typically available for CubeSat, the ISS one and a SSO. The first one offers an easy access to space and the launch window does not depend on another satellite. The CubeSat is brought to the station by a resupply cargo. There are regular launchers, so it’s not a problem. In the case of the SSO, launches are also regular but the hour of passage is really a discriminant factor. OUFTI-Next needs to be over the target between 12:00 and 14:00 in Local Mean Time (LMT). On the ISS orbit, this LMT is completely independent of the latitude and varies with a cycle of ≈ 60 days. For a SSO, it is not the case. The crossing time at the ascending node is the principal information. Only specific values allow the satellite to stay in the window. It also depends on the target, whether they are in the southern or the northern

CHAPTER 4. OPTIMAL CONFIGURATION & SCENARIO 84 4.2. Scenario hemisphere. As shown in Sect. 1.1.3, irrigated ﬁelds are located in all latitude. The North hemisphere regroups however more than 50% of these lands. With the ISS orbit, all theses areas are covered. For the SSO, there is a constraint and it needs absolutely to be a τAN between 13:00 and 14:00. The latter will only cover the North hemisphere in the window and no more the South hemisphere. A τAN = 13:30 is the best suited SSO. With a SSO, one has access to recurrent orbits and it is therefore possible to made some tests on this aspect. One target a day can be even improved to one target per orbit. On the ISS, there is no recurrence. Since the latitude window moves, it can lead to a few days without a suitable target, especially in the South hemisphere.

As a demonstrator, OUFTI-Next does not need to stay in orbit during years. If the "standard" configuration is considered, the lifetime is around 5 months. The lifetime will decrease drastically to less than 70 days with the "cross" configuration. This is an additional reason to disqualify these configurations. In a SSO, the satellite is directly higher in altitude and the lifetime is no more a concern.

The ISS orbit still has advantages. With its low altitude, it oﬀers the best GSD with 60 m. Since pictures of the deployment are made by astronauts, it also leads to a better media impact.

In fine, requirements can be fulfilled with both orbits as long as the "standard" configuration is considered. The ISS orbit is just more restrictive on the acquisition and the attitude strategies (drag and lifetime).

4.2.2 Communication Acquire data is one thing but the satellite needs to download them to Earth. It was shown in Sect. 2.2.2, that it is not a bottleneck with a S band transmitter. The data rate is high enough (1 Mbps) to download one image in less than 5 s. The only constraint is the construction of a S band ground station in Liège. It is not a negligible cost (a few tens of thousands of euros). It can also lead to partnership with others universities around the world.

CHAPTER 4. OPTIMAL CONFIGURATION & SCENARIO 85 Conclusion

After feasibility studies done last year, this thesis was focused on the continuity of theses works and on a more precise analysis of the scenarios and available conﬁgurations. The contours of this 3U CubeSat are more precise. This work will enable future students to focus in detail on some more speciﬁc elements.

Requirements were first recalled for last year’s works and some new were derived as the hour of passage. Some technical information about irrigation as well as the location of irrigated fields were given in this first chapter. OUFTI-Next is above all a demonstrator for a possible constellation. Requirements are therefore different. One CubeSat can not be as effective as several satellites, especially on the temporal resolution. If it were, there would be no point in considering a constellation. OUFTI-Next is intended to be a 3U CubeSat with a Mid-Wavelength InfraRed detector. The main requirements were on the spatial precision and the hour of passage. The GSD needs to be below 100 m to acquire exploitable data. The physics behind evapotranspiration fixes the hour of passage. The satellite needs to be between 12:00 and 14:00 over a target to take a picture. It is the maximum emission period. There is no constraint on the temporal constraint since it is a demonstrator. At least one image a day is the perfect goal.

From these requirements, the Chapt. 2 was dedicated to nominal scenarios. These are typical parameters that are independent of the CubeSat configuration. A strong emphasis was put on the orbit design. It covers many subjects as the crossing time, the orbit lifetime, the eclipse duration. Some concepts as recurrent orbits were also introduced. Even if this type orbit will probably not be chosen, it is interesting since it is not a common discussion in astrodynamic books. Two main orbits were considered regarding the launch opportunities. The first one is the ISS orbit and the second one a SSO. The main differences between both were addressed in specific sections and in the acquisition strategy. They are not on an equal footing regarding the acquisition possibilities. A SSO offers the same large areas at each orbit while it is more restrictive on the ISS orbit. However, for the latter, it varies with time. The spatial resolution depends also on the altitude and since the ISS is at a low altitude (400 km), the GSD is better (60 m). In fine, both orbits can fulfill the requirements but different advantages and disadvantages. The communication strategy, with a data budget, was also introduced in Chapt 2. It shows that the data can be downloaded to Earth without being a bottleneck. From the orbit and the acquisition strategy, it was possible to determine typical constraints for the ADCS module. This information will be used in the future phase of

86 Conclusion this project. It was also show that a GNSS receiver is necessary. It was not obvious at the first point but it adds many advantages (position, velocity and hour). Finally, the power consumption, which is independent of the configuration, were computed. The main parameter was the cooling system. A master thesis is dedicated to this problematic. Several scenarios were introduced since there are many possibilities. In the following phase of this project, the determination of one specific cooling system will help to refine this power consumption analysis. At this stage, only estimations can be done.

In Chapt. 3, three typical 3U configurations were introduced. The main difference between them is the solar panels. One has body mounted panels the two others have deployable ones, either on the long sides or on small sides. The payload and all subsystems were reviewed to perform the nominal scenarios developed in the previous chapter. The location of each of them was discussed as well as their size. A power budget was also realized. From the power consumption derived in Chapt. 2 and the power generation, the margin were deduced. Configurations with deployable solar panels have positive margins. The power generation is very important in theses case with more than 20 W. For the configuration with body-mounted panels, it will depend on the cooling system. With a cryocooler, margins are positive. If a Peltier module is considered, special attitude orientation is needed. This conclusion is very important because this configuration is the cheapest and simplest one. The cooling system is an important system of the satellite. A full passive system is not possible. The idea of the heat shield was introduced but it was discarded. This complicates too much the satellite and it can jeopardized the mission. As a demonstrator, OUFTI-Next needs to be as simple as possible. Finally, the mass budget was estimated. OUFTI-Next stays in the requirements and this should not be a problem in the future unless big change were introduced.

The last chapter, Chapt. 4 makes the link between all parts. It shows that a "standard" configuration, so with body mounted solar panels, fullfills the mission, either on the ISS orbit or on SSO one. One image a day is feasible and there is no specific constraint of the data budget with the ground station.

This thesis permitted to show diﬀerent aspects of a CubeSat, from the orbit to the power generation. It sums up the state of the mission, the possibilities, the constraints and what it can be expected from this nanosatellite. Let’s mention that some software from CNES was used. A small description of them is available in Appendix. A

The main concern at this stage is the detector and its thermal behavior. With data from the manufacturers, the cooling system will be refined as well as the power budget. The determination of the optical design will allow a better management of the payload and the occupied volume. The cooling system will also be designed and the strap positioned in 3D to see if there is no problem. The determination of the ADCS module will also define what can be expected for the final precision and the pointing accuracy. It will also constrain the configuration with the integration of the star tracker, the GNSS receiver and sun sensors, coarse or not.

87 A| Software

A.1 Celestlab

Celestlab is an astrodynamic toolbox developed by the Centre National d’Etudes Spatiales (CNES). It is focused on mission analysis, which is ideal for this master thesis. It contains lots of interesting functions to compute for instance orbits, eclipse duration, changes of coordinates, trajectories, maneuvers and many more. Some graphical demos are available and are very helpful to give relevant information with very few data provided by the user. Very easy to use, it requires Scilab, an open-source software quite close to Matlab. Celestab is distributed with an open-source license. It is available here: https: //logiciels.cnes.fr/fr/node/67?type=desc. Each use of the software is referenced in the master thesis.

A.2 IDM-CIC

IDM-CIC is a plug-in module for Excel developed by the CNES. It is dedicated to all budgets of a CubeSat. For each subsystem, the user can introduce a component, for example a S band transceiver, its main properties, its power consumption, its size, its mass, a 3D model, etc. Once all is encoded, the user builds the satellite as a LEGO® by giving the location of each PCB or element. The mass budget, the center of gravity, the power budget are then computed by IDM-CIC. One of the main advantages of this software is the integrated library with typical CubeSat subsystems. It is therefore very easy to construct a CubeSat and then see it in 3D via SteckUp. The 3D view can be exported to 3ds, the format used by VTS.

A.3 Ixion

Ixion is an online application about orbitography and sampling developed by the "Institut Pierre Simon Laplace" (France). It is available here: http://climserv.ipsl. polytechnique.fr/ixion/. Data from active satellites or from theoretical orbits are available. It was used in this master thesis to extract the Local Mean Time (LMT) over the ground tracks or the sampling of data for the International Space Station (ISS). An English version is available but the translation is incomplete.

88 A.4. Simu-CIC

A.4 Simu-CIC

Simu-CIC is an orbital propagator software in development at Centre National d’Etudes Spatiales (CNES). One of its major advantage is its compatibility with CIC files (Centre d’Ingénierie Concourante). They are text files that contain all the information computed as the attitude of the satellite, its position, its velocity, the mesh type, etc. with the same type step. It offers a full connectivity between software and also the possibility to extract data and read them, for instance, with Matlab. It is directly linked to VTS and so offers the possibility to visualize the orbit/attitude just after the propagation. The attitude control panel of Simu-CIC is quite complete with station pointing, specific orientation, sun-pointing, etc. Logical relations allow to superpose or to set the order of attitude changes. Simu-CIC is not yet available from the CNES website but it will be soon. As Celestlab, Scilab is required.

A.5 STELA

Semi-analytic Tool for End of Life Analysis (STELA) is an orbital propagator dedicated to end-of-life of satellites in LEO,GTO or GEO. It is developed by CNES and available here: https://logiciels.cnes.fr/fr/content/stela Long propagation can be done in few minutes thanks to semi-analytical models and statistical analysis. One of the main information given by STELA is the lifetime of the satellite. For LEO, as it was used for this master thesis, some information as the mass of the satellite, the atmospheric drag model (NRLMSISE-00, US76 or Jacchia 77) or the value of solar activity (fixed or variable) needs to be provided as well as the reflecting area. For a CubeSat, it is easy to compute but not for bigger satellites. A dedicated tool is therefore available with basic 3D model. STELA can also be used to determine the location of reentry with iterative models and maneuvers to avoid specific populated areas during reentry. This module was not used since it is irrelevant for this master thesis.

A.6 VTS

Visualisation Tool for Space data (VTS) is a visualize tool developed by Spacebel for the CNES. It does not compute anything but shows important information to the user. From a simple 3D model and CIC configuration files (position, velocity and attitude), the satellite can be represented. All the solar system is available in 3D, via Celestia, with a special focus on the Earth. VTS plays the role of a clock and the different views (3D, 2D, Zenith, etc) are synchronized. It is also possible to show detector opening, ground station, etc. VTS is available here: http://timeloop.fr/vts/.

APPENDIX A. SOFTWARE 89 B| Orbit

Between Day 1-5 90 Sea Between Day 1-5 60 Land 70 Coast Sea 60 Land 30 Coast 50 0 40

30 Latitude [deg] -30

Percentage % 20 -60 10 -90 0 1 2 3 4 5 -180 -120 -60 0 60 120 180 Day number Longitude [deg] (a) Percentage over 6 days (b) Ground tracks where highlighted zones are between 12:00 and 14:00 LMT

Fig. B.0.1: SSO (600 km) with τAN = 10:30. Epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

Between Day 1-5 90 Sea Between Day 1-5 60 Land 70 Coast Sea 60 Land 30 Coast 50 0 40

30 Latitude [deg] -30

Percentage % 20 -60 10 -90 0 1 2 3 4 5 -180 -120 -60 0 60 120 180 Day number Longitude [deg] (a) Percentage over 6 days (b) Ground tracks where highlighted zones are between 12:00 and 14:00 LMT

Fig. B.0.2: SSO (600 km) with τAN = 22:30. Epoch: January 1, 2019. Data obtained with Simu-CIC and processed in Matlab.

90 PEDXB RI 91 ORBIT B. APPENDIX

a [km] h [km] i [deg] ν0 [rev/day] DT0 [day] CT0 [day] NT0 [day] Td [min] δ [deg] α1 [deg] Smin [day] Smax [day] 6883.50 505.50 97.42 15.00 2.00 11.00 167.00 94.85 2.16 24.78 5.00 5.00 6888.09 510.09 97.44 15.00 1.00 6.00 91.00 94.95 3.96 39.42 1.00 5.00 6895.32 517.32 97.47 15.00 1.00 7.00 106.00 95.09 3.40 35.04 1.00 6.00 6900.76 522.76 97.49 15.00 1.00 8.00 121.00 95.21 2.98 31.43 1.00 7.00 6905.00 527.00 97.50 15.00 1.00 9.00 136.00 95.29 2.65 28.42 1.00 8.00 6908.39 530.39 97.52 15.00 1.00 10.00 151.00 95.36 2.38 25.90 1.00 9.00 6911.17 533.17 97.53 15.00 1.00 11.00 166.00 95.42 2.17 23.76 1.00 10.00 6913.49 535.49 97.54 15.00 1.00 12.00 181.00 95.47 1.99 21.93 1.00 11.00 6939.13 561.13 97.64 15.00 0.00 1.00 15.00 96.00 24.00 66.37 0.00 0.00 6965.00 587.00 97.74 14.00 11.00 12.00 179.00 96.54 2.01 20.36 1.00 1.00 6967.37 589.37 97.75 14.00 10.00 11.00 164.00 96.59 2.20 21.95 1.00 1.00 6970.21 592.21 97.76 14.00 9.00 10.00 149.00 96.64 2.42 23.78 1.00 1.00 6973.68 595.68 97.77 14.00 8.00 9.00 134.00 96.72 2.69 25.92 1.00 1.00 6978.03 600.03 97.79 14.00 7.00 8.00 119.00 96.81 3.03 28.44 1.00 1.00 6983.63 605.63 97.81 14.00 6.00 7.00 104.00 96.92 3.46 31.43 1.00 1.00 6991.12 613.12 97.84 14.00 5.00 6.00 89.00 97.08 4.04 35.01 1.00 1.00 6995.90 617.90 97.86 14.00 9.00 11.00 163.00 97.18 2.21 21.14 5.00 6.00 7001.64 623.64 97.88 14.00 4.00 5.00 74.00 97.30 4.86 39.32 1.00 1.00 7008.67 630.67 97.91 14.00 7.00 9.00 133.00 97.44 2.71 24.82 4.00 5.00 7017.49 639.49 97.94 14.00 3.00 4.00 59.00 97.63 6.10 44.49 1.00 1.00 7024.72 646.72 97.97 14.00 8.00 11.00 162.00 97.78 2.22 20.38 4.00 4.00 7028.86 650.86 97.99 14.00 5.00 7.00 103.00 97.86 3.50 29.87 3.00 4.00 7033.42 655.42 98.01 14.00 7.00 10.00 147.00 97.96 2.45 21.97 3.00 7.00 7044.10 666.10 98.05 14.00 2.00 3.00 44.00 98.18 8.18 50.55 1.00 1.00 7053.84 675.84 98.09 14.00 7.00 11.00 161.00 98.39 2.24 19.68 3.00 3.00 7057.50 679.50 98.10 14.00 5.00 8.00 117.00 98.46 3.08 25.94 3.00 3.00 7065.57 687.57 98.14 14.00 3.00 5.00 73.00 98.63 4.93 37.02 2.00 3.00 7070.96 692.96 98.16 14.00 7.00 12.00 175.00 98.74 2.06 17.81 5.00 5.00 PEDXB RI 92 ORBIT B. APPENDIX

7074.82 696.82 98.17 14.00 4.00 7.00 102.00 98.82 3.53 28.44 2.00 5.00 7079.98 701.98 98.20 14.00 5.00 9.00 131.00 98.93 2.75 22.86 2.00 7.00 7083.26 705.26 98.21 14.00 6.00 11.00 160.00 99.00 2.25 19.02 2.00 9.00 7098.09 720.09 98.27 14.00 1.00 2.00 29.00 99.31 12.41 57.04 1.00 1.00 7112.99 734.99 98.33 14.00 5.00 11.00 159.00 99.62 2.26 18.41 2.00 2.00 7116.32 738.32 98.34 14.00 4.00 9.00 130.00 99.69 2.77 21.99 2.00 2.00 7121.54 743.54 98.37 14.00 3.00 7.00 101.00 99.80 3.56 27.14 2.00 2.00 7125.47 747.47 98.38 14.00 5.00 12.00 173.00 99.88 2.08 16.76 5.00 7.00 7130.98 752.98 98.41 14.00 2.00 5.00 72.00 100.00 5.00 34.95 2.00 2.00 7139.26 761.26 98.44 14.00 3.00 8.00 115.00 100.17 3.13 23.82 3.00 5.00 7143.04 765.04 98.46 14.00 4.00 11.00 158.00 100.25 2.28 17.83 3.00 8.00 7153.12 775.12 98.50 14.00 1.00 3.00 43.00 100.47 8.37 47.09 1.00 2.00 7164.26 786.26 98.54 14.00 3.00 10.00 143.00 100.70 2.52 19.05 3.00 3.00 7169.04 791.04 98.56 14.00 2.00 7.00 100.00 100.80 3.60 25.95 3.00 3.00 7173.40 795.40 98.58 14.00 3.00 11.00 157.00 100.89 2.29 17.29 4.00 7.00

Table B.0.1: Characteristics of repeat ground track orbits for an altitude between 500 and 800 km (cf. Fig. 2.1.11). Discussion about these values in Sect. 2.1.2. Computed with Celestlab. C| Power Budget

(a) Sun pointing mode. (b) Nadir pointing mode.

Fig. C.0.1: Power production on a SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. "Standard" conﬁguration.

(a) Sun pointing mode. (b) Nadir pointing mode.

Fig. C.0.2: Power production on a SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. "Table" conﬁguration.

93 (a) Sun pointing mode. (b) Nadir pointing mode.

Fig. C.0.3: Power production on the ISS orbit. Epoch: January 1, 2019. "Standard" conﬁguration.

(a) Sun pointing mode. (b) Nadir pointing mode.

Fig. C.0.4: Power production on the ISS orbit. Epoch: January 1, 2019. "Table" conﬁgu- ration.

ISS (400 km) SSO (600 km) Case Production Consumption Margin Production Consumption Margin 1. 4.2 W 2.6 W 1.6 W 38.1% 4.5 W 2.6 W 1.9 W 42.2% 2. 4.2 W 3.0 W 1.2 W 28.6% 4.5 W 3.0 W 1.5 W 33.3% 3. 4.2 W 3.4 W 0.8 W 19.0% 4.5 W 3.3 W 1.2 W 26.7% 4. 4.2 W 3.4 W 0.8 W 19.0% 4.5 W 3.3 W 1.2 W 22.7%

Table C.0.1: Power budget on two orbits (mean power and without margin on the consumption). Two orbits considered: SSO at 600 km with τAN = 13:30 and the ISS orbit. Scenarios: 1. Sun pointing during full illumination and idle in eclipse. 2. Sun pointing + acquisition (4 min) during full illumination and idle in eclipse. 3. Sun pointing + acquisition (4 min) + communication (8 min) during full illumination and idle in eclipse. 4. Sun pointing + acquisition (4 min) during full illumination and idle + communication (8 min) in eclipse.

APPENDIX C. POWER BUDGET 94 100

70 Battery charge [%] 60

50 0 30 60 90 120 150 180 210 240 270 300 330 360 Time [day] (a) 1 year (b) 1 day

Fig. C.0.5: Battery cycle (10 Whr) for the "table" conﬁguration. Orbit: SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. Acquisition: Tadla plain, Morocco. Communication: Liege.

100

70 Battery charge [%] 60

50 0 30 60 90 120 150 180 210 240 270 300 330 360 Time [day] (a) 1 year (b) 1 day

Fig. C.0.6: Battery cycle (10 Whr) for the "cross" conﬁguration. Orbit: SSO at 600 km, τAN = 13:30. Epoch: January 1, 2019. Acquisition: Tadla plain, Morocco. Communication: Liege.

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