DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018

Detecting minimoons in the Earth- Moon system with microsatellite compatible technologies

MATIAS KIDRON

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Detecting minimoons in the Earth-Moon system with microsatellite compatible technologies

November 23, 2018

Author: Matias Kidron

Supervisor: Nickolay Ivchenko Examiner: Tomas Karlsson

EF233X Degree Project in Space Technology

Athesissubmittedinfulfillmentoftherequirementsforthedegreeof Master in Aerospace Engineering in the Department of Space and Plasma Physics School of Electrical Engineering and Computer Science KTH Royal Institute of Technology

Abstract

Minimoons, Earth’s temporarily-captured orbiters, are excellent candidates for asteroid mining technology demonstrations and general asteroid studies because of their relatively long stay in the vicinity of Earth. In this thesis, microsatellite compatible surveillance technologies are discussed and the suitability of various locations in the Earth-Moon sys- tem for minimoon surveillance is examined. This is done to acquire knowledge on which type of an orbit a minimoon-surveying-microsatellite could be placed on. The instantaneous visible fraction of the minimoon steady-state population is the figure of merit when comparing surveillance systems and locations. The visible fraction is esti- mated by simulating the distribution of visible minimoons in the sky-plane. The objects in the simulated sky-plane are synthetic minimoons, which are generated in large numbers according to the geocentric 6-dimensional-residence-time-distribution of minimoons, and thus, the bin values of the sky-plane distribution can be thought of as instantaneous prob- abilities for containing a detectable minimoon within certain ecliptic latitude-longitude range. The visible fractions are estimated for various locations with given surveillance system performance. Multiple microsatellite compatible surveillance technology configurations are examined as well as the e↵ect of limiting magnitude and maximum angular velocity. Minimoons are faint and fast moving objects and thus the use of synthetic tracking algo- rithm is beneficial and considered. Only visual band surveillance systems with aperture sizes less than 0.30 m and minimoons with diameter sizes larger than 0.50 m are considered in the simulations.

i Sammanfattning

Minim˚anar, jordens tempor¨art f˚angade satelliter, ¨arutm¨arkta kandidater f¨ordemonstra- tioner av asteroidbrytningteknologi och f¨orallm¨anna asteroidstudier p˚agrund av deras rel- ativt l˚anga vistelse i n¨arheten av jorden. I den h¨aravhandlingen, diskuteras mikrosatellit kompatibla ¨overvakningsteknologier och d¨artill unders¨okes l¨ampligheten av olika platser i jord-m˚ane-systemet f¨or¨overvakning av minim˚anar. Det h¨arg¨ors f¨oratt ska↵a kunskap om vilken typ av omloppsbana en mikrosatellit f¨orminim˚ane¨overvakning kunde placeras p˚a. Den momentana synliga fraktionen av den j¨amviktstillst˚and minim˚anepopulationen ¨ar den merit som anv¨ands vid j¨amf¨orelse av ¨overvakningssystem och platser i rymden. Den synliga fraktionen uppskattas genom att simulera f¨ordelningen av synliga minim˚anar i skyplanet. F¨orem˚alen i det simulerade skyplanet ¨arsyntetiska minim˚anar, vilka gener- eras i stort antal enligt den geocentriska 6-dimensionella-uppeh˚allstid-distributionen av minim˚anarna, och s˚alunda kan v¨ardena i den diskretiserade skyplanf¨ordelningen betrak- tas som momentana sannolikheter f¨oratt inneh˚alla en observerbar minim˚ane inom det specifiserade ecliptiska latitudinella-longitudinella omr˚adet. De synliga fraktionerna ber¨aknas f¨orolika platser med det givna ¨overvakningssys- temets parametrar. Flera mikrosatellit-kompatibla ¨overvakningsteknologikonfigurationer unders¨oks, s˚av¨alsom e↵ekterna av begr¨ansande magnitud och maximal vinkelhastighet. Minim˚anar ¨ardunkla och snabba r¨orliga f¨orem˚al, och s˚aledes ¨aranv¨andningen av synthetic tracking f¨ordelaktig och ¨overv¨agd. Endast ¨overvakningssystem som fungerar i visuellt band med en bl¨andarstorlek mindre ¨an0,30 m och minim˚anar med en diameter st¨orre ¨an0,50 m beaktas i simuleringarna.

ii Acknowledgements

I have had amazing and inspiring teachers since the very first grade in the elementary school. Thank you. I would especially like to thank Mikael Granvik and Grigori Fedorets for their scientific advice and help during this thesis project. In addition, I would like to thank my family, girlfriend, LTU and KTH for their support.

iii Contents

Abstract i

Acknowledgements iii

Contents iv

List of Figures vi

List of Tables vii

Nomenclature viii

1 Introduction 1

2 Theory 3 2.1 Brightnessofobjects...... 3 2.2 Cameras and telescopes ...... 5 2.3 Detectionandtracking...... 9 2.4 Shift-and-addtechnique ...... 11 2.5 Advantages of space-based surveillance ...... 13

3 Earth’s temporarily-captured natural satellites 15 3.1 Definitions...... 15 3.2 The creation of the population model ...... 16 3.3 Steady-state population ...... 16 3.4 Earlier 6D-geocentric-residence-time-distribution ...... 17 3.5 Sky-planedistributions...... 18 3.6 Rate-of-motion ...... 19 3.7 Rotation rates ...... 20 3.8 Summary of the observational challenges with TCAs ...... 20

4 MicroSat asteroid surveillance technologies 21 4.1 Earlier and proposed missions ...... 21 4.2 Other available and researched technologies ...... 25 4.2.1 Telescope technologies ...... 25 4.2.2 Sensor technologies ...... 27 4.2.3 Other technologies ...... 27 4.3 Alternatives...... 27 4.4 Summary of MicroSat compatible technologies ...... 28

iv 5 Simulation 29 5.1 6D-geocentric-residence-time-distribution ...... 30 5.2 Scaled-up minimoon population ...... 31 5.3 Observatories ...... 34 5.4 Observations ...... 35 5.5 Post-processing ...... 36 5.5.1 The e↵ects of Earth and the Moon on observing ...... 36 5.5.2 Examined surveillance system cases and their parameters ...... 36

6 Results 38 6.1 CaseS17...... 39 6.2 CaseS18...... 40 6.3 CaseNS...... 45 6.4 CaseTS...... 46 6.5 General comments on the examined cases ...... 47 6.6 Performance on speculated orbits ...... 48 6.7 Summaryofresults...... 52

7 Discussion 53

8 Conclusions 54

Bibliography 55

Appendices 60 A Observatory-fileformat ...... 60 B Objects-fileformat ...... 60

v List of Figures

2.1 Definition of phase- and solar elongation angle...... 4 2.2 Airypattern...... 7 2.3 Angular resolution as a function of aperture diameter and wavelength. . . . 8 2.4 Decreasing minimoon orbit uncertainty with more observations...... 10 2.5 Shift-and-addtechnique...... 11 2.6 Computational load of synthetic tracking...... 12 2.7 The improvement in the peak signal with synthetic tracking...... 13 2.8 Atmospheric electromagnetic opacity as a function of wavelength...... 14

3.1 Size of the TCO and TCA steady-state populations as a function of absolute magnitude...... 17 3.2 a, e, i-residence-timedistributionofminimoons...... 18 3.3 Constrained sky-plane distribution of minimoons from Earth...... 19 3.4 GeocentricvelocitiesofTCAs...... 19 3.5 Rotation rates of small asteroids...... 20

4.1 Computer rendering of NEOSSat...... 22 4.2 ASTERIApriortolaunch...... 22 4.3 A CAD model of a synthetic tracking telescope...... 23 4.4 Deployableopticsdesign...... 26 4.5 SpaceFab’s Waypoint MicroSat...... 26

5.1 Absolute magnitude distribution of synthetic minimoon population. . . . . 31 5.2 Distribution of minimoons in (a, e, i)-orbital element phase space...... 32 5.3 Distribution of minimoons in (!,M0, ⌦,a)-orbital element phase space. . . . 33 5.4 Observatory locations...... 35

6.1 Case S17: Sky-plane distribution at highest vf location...... 40 6.2 Case S18: Visible fractions at observatory locations...... 41 6.3 Case S18: The sky-plane distribution at highest vf location...... 42 6.4 Case S18: The sky-plane distribution of angular velocity at highest vfd location...... 42 6.5 Case S18 with decreased velocity search range at di↵erent observatory lo- cations...... 44 6.6 Case S18: x- and y-coordinates of visible synthetic minimoons...... 45 6.7 Case TS: The sky-plane distribution at highest vf location...... 47 6.8 Case S18: Earth’s decreasing e↵ect on visible fraction...... 48 6.9 Limiting magnitude as a function of aperture diameter...... 50 6.10 Visible fraction as a function of limiting magnitude at speculated orbits. . . 50 6.11 Visible fraction as a function of maximum angular velocity at speculated orbits...... 51 6.12 Distribution of vf in the EMS with less capable S18...... 51

vi List of Tables

2.1 Values of basis functions...... 5 2.2 Geometric albedos and G1 and G2 constants for three main asteroid types. 5

4.1 The parameters used in Shao et al. (2017) to estimate system performance. 23

5.1 Bin widths and ranges used in the 6DGRTD...... 30 5.2 Observatory coordinates...... 34 5.3 Surveillancesystemparametersusedintestcases...... 37

6.1 S17results...... 39 6.2 S18results...... 41 6.3 NSresults...... 46 6.4 TSresults...... 46 6.5 Case S18: Averaged results for speculated spacecraft orbits...... 49 6.6 Resultssummaryforcases...... 52

A.1 .gaia3 format...... 61 B.1 .desformat...... 62

vii Nomenclature

Acronyms

6DGRTD 6-dimensional-geocentric-residence-time-distribution

ASTERIA Arcsecond Space Telescope Enabling Research in Astrophysics

CANYVAL-X CubeSat Astronomy by NASA and Yonsei using Virtual Telescope Align- ment eXperiment

CCD Charge-coupled-device

CDST Collapsible-tube Deployable Space Telescope

CMOS Complementary metal–oxide–semiconductor

COTS Commercial-o↵-the-shelf

DPT Deployable Petal Telescope

EMS Earth-Moon system

FPGA Field programmable gate array

GEO Geosynchronous equatorial orbit

GPU Graphics Processing Unit

HSC Hyper Suprime-Cam

L Lagrange point

LEO Low Earth orbit

LSST Large Synoptic Survey Telescope

NEA Near-Earth asteroid

NEO Near-Earth object

NEOSSat Near Earth Object Surveillance Satellite

NES Natural Earth satellite

PHO Potentially hazardous object

TCA Temporarily-captured-asteroid

TCF Temporarily-captured-flyby

TCO Temporarily-captured-orbiter

viii Symbols

↵ Phase angle

e Ecliptic longitude v Delta-v

Asteroid to observer distance

✏ Obscuration factor

⌘ Specific energy

Solar elongation

Wavelength

e Ecliptic latitude µ Standard gravitational parameter

DC Dark current Heliocentric - used as a sub-index ⌦ Longitude of ascending node

! Argument of perihelion

!r Rate of rotation Phase function

⌧ Transmittance

⇥ Di↵raction limited angular resolution

✓ Angle away from the Sun in the ecliptic

⇣ Topocentric angular velocity a Semi-major axis

C Computational load

D Asteroid diameter d Wavelength range

Da Aperture diameter de Geocentric distance e Eccentricity f Focal length

F/N Focal ratio fb Flux from an object FOV Field-of-view

ix G Shape function constant H Absolute magnitude i Inclination k Straddle factor m Apparent magnitude

M0 Mean anomaly

N0 Flux from a zero magnitude star nf Number of frames npx Number of pixels

NBG Background noise

NRN Read noise pv Geometric albedo QE Quantum eciency R Angular resolution r Relative distance

Re Earth’s radius ras Asteroid to the Sun distance ros Observer to the Sun distance S Signal S/N Signal-to-noise ratio spx Pixel scale T Rotation period ts Slew time tSE Single exposure length tTE Total exposure length V Apparent visual magnitude v Relative velocity vfd Visible fraction in the field-of-view per day vf Visible fraction vgrid Velocity grid size

Vlim Limiting apparent magnitude

Vref Visual apparent magnitude of reference object wpx Pixel width

x

1 Introduction

In 2006 a few meter asteroid 2006 RH120, entered Earth’s Hill sphere and was observed to orbit Earth for a year until its return to a heliocentric orbit. Unlike quasi-satellites which are on Earth-like heliocentric orbits, 2006 RH120 was captured by Earth on a geocentric orbit. It was the first verified Earth’s temporarily-captured natural satellite (Kwiatkowski et al., 2009). Granvik et al. (2012) predicted that Earth has a steady population of temporarily-captured asteroids, which originate from the near-Earth asteroid population. According to the latest estimate by Fedorets et al. (2017), there is an 80 cm diameter asteroid captured on a geocentric orbit at any time. These temporarily-captured asteroids, also known as minimoons and drifters, provide excellent opportunities for asteroid studies and they are also the natural first step in asteroid resource utilisation (Granvik et al., 2013). Minimoons are too small for profitable asteroid mining, but due to their relatively long time in the proximity of Earth, they would be excellent testbeds for technology demon- strations and scientific studies. For example, asteroid de-spinning, anchoring, automated navigation and redirection technologies could be demonstrated with them. Bringing an entire minimoon in a capsule to Earth would be scientifically valuable. A mineralogical analysis would help scientists to calibrate their remote-prospecting cameras and theories about the internal structure of asteroids could be tested. Furthermore, information about the formation of our solar system could be gained. Studies about rendezvous missions to minimoons have already been made by Chyba et al. (2014) and Brelsford et al. (2016). Ideally, a spacecraft would be waiting on a parking orbit, at the Earth-Moon L1 or L2, and get activated for rendezvous maneuver in case of a suitable detection. Brelsford et al. (2016) calculated that most of the minimoons would be accessible with a couple of hundreds of v in such case. Detecting minimoons with existing ground-based observatories is challenging as min- imoons are often too faint to be detected when they are beyond the Moon and too fast when they are closer to Earth. Bolin et al. (2014) studied the discoverability of minimoons with current and near future ground- and space-based surveillance systems. They found that an infrared surveillance system at L1 could be an e↵ective solution for detecting min- imoons. In a study by Near-Earth Object Science Definition Team - NASA (2017), this type of spacecraft mission, with a 0.5 m mirror, was estimated to cost about half a billion US dollars. Subaru telescope with Hyper Suprime-Cam (HSC) was estimated to have a 90% chance of detecting a minimoon in 5 nights. Jedicke et al. (2017) are currently further studying HSC’s capabilities in detecting minimoons. Bolin et al. (2014) also estimated that the Large Synoptic Survey Telescope (LSST) will start detecting minimoons on monthly basis when it starts operating in the 2020s. LSST’s performance in detecting minimoons was further studied by Fedorets et al. (2015). When the simulation was later run with the latest Fedorets et al. (2017) minimoon model, it was estimated that LSST should be able to discover all larger minimoons if minimoons can be extracted from LSST’s data flow and the detections can be linked. It is currently being studied whether this is possible or not. Despite promising estimates, it is uncertain if HSC and LSST could provide a steady stream of detections for follow-up. In addition, the operation costs of HSC and

1 LSST are high, 17 million $/ (University of Hawaii, 2016) and 37 million $/year (Kahn, 2014), respectively. Thus, having them dedicated for dedicated minimoon surveillance is unlikely and it is viable to consider other platforms for this purpose. Jedicke et al. (2018) concluded in their holistic overview of minimoon studies that “the real future for mining asteroids awaits an a↵ordable space-based detection system”. Space-based surveillance systems have many advantages over ground-based systems. For instance, they are not disturbed by the presence of atmosphere and they can cover the whole sky. Using microsatellites (MicroSats) or CubeSats, a subcategory of MicroSats, is a lucrative option for asteroid surveillance. A surveillance system built on CubeSat platform mostly from commercial-o↵-the-shelf (COTS) components could cost an order of magnitude less than current systems such as NEOWISE, Mainzer et al. (2011), or its proposed successor NEOCam. CubeSat and sCMOS technologies have vastly improved in the 21st century and this has opened new possibilities for scientific space-based mis- sions (Poghosyan and Golkar, 2017). University of Melbourne (2018) is working on the first infrared space telescope CubeSat, SkyHopper, which is to be launched in 2021-2022. ASTERIA, a CubeSat developed by Jet Propulsion Lab, was launched in 2017 to demon- strate the capabilities of CubeSats in astronomy in the visible spectrum (NASA, 2017). The capabilities of MicroSats in finding asteroids have been recently demonstrated by NEOSSat mission (Wallace et al., 2014) and studied by Shao et al. (2017) and Shao et al. (2018). In both studies, the small telescope aperture sizes were compensated with the use of synthetic tracking algorithm. This thesis looks into the feasibility of using MicroSat compatible surveillance technolo- gies in discovering minimoons and the suitability of di↵erent locations in the Earth-Moon system for this purpose. The analysis is limited to telescopes working in the visible band- width with aperture diameters < 30 cm with a focus on COTS technologies, but also other technologies are investigated and discussed. The system requirements set by suciently powerful radars and sensitive infrared telescopes are challenging and expensive to meet with a MicroSat. Radars require high power and infrared telescopes very precise thermal control and their compatibility with synthetic tracking algorithm is not well known. After looking into the available technologies, the instantaneous visible fraction of the minimoon steady-state population is estimated for di↵erent MicroSat-based surveillance systems at multiple locations in the Earth-Moon system. This is done to acquire knowledge on which type of orbit a surveillance system should be placed on. The visible fractions are calculated from simulated minimoon sky-plane distributions. A scaled-up minimoon population is used in the simulation to have a large number of objects in the sky-plane. The objects, synthetic minimoons, are generated according to the geocentric 6D-residence-time- distribution which is based on the latest minimoon model by Grigori Fedorets (University of Helsinki). When the scaling is considered, a bin count in the sky-plane distribution can be thought of as a probability that there is a visible minimoon in the ecliptic latitude- longitude range defined by the bin. The size distribution of the synthetic minimoon population follows Brown et al. (2002) model. Only minimoons that have a larger diameter than 0.5 m are considered in the simulation. Because minimoons are faint and fast moving objects, the use of shift-and-add algorithm is considered, namely synthetic tracking, which was presented in Shao et al. (2014). The purpose of Section 2 is to familiarize the reader with the most important theoretical and technological concepts in asteroid surveillance. Section 3 is an overview of the research done on Earth’s temporarily-captured natural satellites, after which the available MicroSat compatible surveillance technologies are discussed in Section 4. Section 5 describes the methods used to estimate the visible fractions at di↵erent locations in Earth-Moon system and the results are presented in Section 6.

2 2 Theory

This section describes the theory and terminology which are crucial for the understanding the content presented in later sections. The equations presented in this section are used in the simulation to calculate properties for the asteroids and to estimate surveillance system performance. In addition, the advantages of space-based surveillance are briefly discussed.

2.1 Brightness of objects

Apparent magnitude (m) is the measure of astronomical body’s brightness [mag]. It is a logarithmic measure in which a smaller value corresponds to a brighter object and each 1 magnitude is 100 5 2.5 times brighter than the next one as defined by the following ⇡ relation: fb1 m1 m2 = 2.5 log10 , (2.1) fb2 2 where fb stands for flux [Wm ]. Nowadays, magnitudes are mostly measured with CCD cameras through ultraviolet, blue or visual filters. For example, visual filter’s average wavelength and bandwidth are 545 nm and 88 nm, respectively (Karttunen et al., 2017). In order to determine the brightness of a body, the magnitude of another body and the fluxes must be known. Therefore, there must be a reference flux which corresponds to zero magnitude. In visual band, this flux is 3,640 Jy or 3, 640 10 26Wm 2. ⇥ Absolute magnitude (H) describes the intrinsic brightness of a body. For an asteroid, the absolute magnitude is defined as its apparent visual magnitude if it would be observed from Earth at 0°phase angle (↵) and the asteroid would be 1 AU away from both Earth and the Sun, a geometrically impossible situation. The phase angle is illustrated in Figure 2.1. The absolute magnitude is a↵ected by the diameter (D) and the geometric albedo (pv) of the asteroid, as shown in Equation 2.2. D H(D, p ) = 15.618 5 log 2.5 log p (2.2) v 10 1000 10 v Geometric albedo describes the intrinsic reflectance of a body. It is defined as the ratio of body’s reflected flux at zero phase angle to reflected flux from a Lambertian disk with the same cross-section. Geometric albedo depends on the composition and texture of the body’s surface. Due to absolute magnitude’s size dependence, it is often used as a proxy for asteroid’s size. The apparent visual magnitude (V ) of the Sun is -26.74 when observed from Earth (Williams, 2016). If the observer would move closer to the Sun, the object would ap- pear brighter and the apparent magnitude would decrease. Using the IAU 2012 standard HG1G2 system by Muinonen et al. (2010), an asteroid’s apparent visual magnitude can be estimated by using Equation 2.3 when the geometry is defined by Equations 2.4 and 2.5.

V = H + 5 log (r ) 2.5 log (2.3) 10 as 10 2 2 2 1 ras + ros ↵ = cos (2.4) 2ras ⇣ ⌘ 3 1 ras sin ↵ =sin . (2.5) ros ⇣ ⌘

In Equations 2.3, 2.4 and 2.5, ras [AU] is the distance between the asteroid and the Sun, [AU] is the distance between the asteroid and the observer, ros [AU] is the distance between the observer and the Sun, is a phase function and is the solar elongation angle. The geometry is clarified in Figure 2.1.

Figure 2.1: The geometrical parameters of Equations 2.4 and 2.5 (Myhrvold, 2016).

The phase function in Equation 2.3 describes how the phase angle a↵ects the asteroid’s apparent visual magnitude. The phase function

(↵,G ,G )=G (↵)+G (↵)+(1 G G ) (↵) (2.6) 1 2 1 1 2 2 1 2 3 has an opposition-e↵ect basis function 3(↵) and two other basis functions 1(↵) and 2(↵). The constants G1 and G2 define the shape of the phase function. Some values of the basis functions are presented in Table 2.1. The rest of the values can be acquired by fitting a cubic spline to the data points presented in the table. The reason for the opposition-e↵ect, a rapid increase of brightness when ↵<10°, is not well known. However, it is mainly caused by coherent backscattering and the absence of shadows (Karttunen et al., 2017). The values of constants G1 and G2 are listed in Table 2.2 for three main asteroid types.

In this thesis, the three-parameter HG12 system by Muinonen et al. (2010) is used instead of the IAU 2012 standard HG1G2 system with G12 =0.5 and pv =0.14 if not otherwise stated. The relation between constants G12, G1 and G2 is presented in Muinonen et al. (2010). Conversions between asteroid diameters (D) and absolute magnitudes can be performed by using the relation by Fowler and Chillemi (1992):

1329 H/5 D = 10 . (2.7) 1000 ppv ⇥ 4 Table 2.1: Values of basis functions for several phase angles and two first derivatives for each function (Muinonen et al., 2010).

↵ [ °] 1 2 0.0 1.0 1.0 7.5 0.75 0.925 30.0 0.33486016 0.62884169 60.0 0.13410560 0.31755495 90.0 0.05110476 0.12716367 120.0 0.02146569 0.02237390 150.0 0.00363970 0.000165506

↵ [ °] 3 0.0 1.0 0.3 0.83381185 1.0 0.57735424 2.0 0.42144772 4.0 0.23174230 8.0 0.10348178 12.0 0.06173347 20.0 0.01610701 30.0 0.0

(7.5°)= 1.90986 (7.5°)= 0.57330 (0°)= 0.10630 10 20 30 (150°)= 0.09133 (150°)= 8.657 10 8 (30°)=0 10 20 ⇥ 30

Table 2.2: Geometric albedos, G1 and G2 constants for three main asteroid types (Shevchenko et al., 2016).

Type pv G1 G2

C 0.061 0.017 0.82 +0.02 0.02 +0.02 ± 0.02 0.01 S 0.22 0.05 0.26 +0.01 0.38 +0.01 ± 0.01 0.01 M 0.17 0.07 0.27 +0.03 0.35 +0.01 ± 0.02 0.01

2.2 Cameras and telescopes

Charge coupled devices (CCD) and complementary metal-oxide-semiconductors (CMOS) are the most common modern image sensors. They both consist of numerous detectors, pixels. To put it simple, these devices measure how many photons fall on each pixel and as outputs, give digital images, which are matrices of photon counts. The measuring time interval is called integration time or exposure time. The longer the exposure time, the larger the photon counts can build up. In addition to this, there are also other parameters a↵ecting the sensitivity, limiting magnitude Vlim, of the surveillance system and they will be discussed in this section.

5 In this thesis, Schroeder (1999) is followed for estimating the limiting magnitude of a surveillance system, the combination of a telescope and a sensor. The signal from the object to the sensor is ⇡ 2 2 0.4V S = N ⌧ (1 ✏ )D d10 ref , (2.8) 0 4 a 2 1 1 where N0 [photons m s nm ] is the flux from a zero-magnitude star at 550 nm, ⌧ is the optical transmittance of the system, ⌘ is the obscuration factor, Da is the telescope’s aperture diameter, d is the bandpass and Vref is the visual apparent magnitude of the object. It is clear from this equation that the received signal is highly dependent on the aperture size. The noise from the background to the detector is

⇡ 2 2 0.4V 2 N = N ⌧ (1 ✏ )D d10 sky s , (2.9) BG 0 4 a px where Vsky is the background brightness [mag] and spx is the pixel scale [”/pixel], the angle covered by a pixel. Background brightness has multiple sources such as the light reflected from interplanetary dust, Earth and distant galaxies. Other noise sources that are considered in this thesis are read noise (NRN ) and dark current (NDC). After each exposure, the data must be read out from the pixels, which causes noise. Read noise 1 1 1 depends on the sensor and is usually few electrons per pixel [e ]. Dark current [e s ]is noise due to thermal excitation of electrons in the sensor and it can be decreased with cooling. Signal-to-noise ratio (S/N) describes the ratio between desired signal from the object and noise. If it is assumed that the exposures are short enough so that the signal is not spread over multiple pixels, the S/N equation can be written as kSQEn t S/N = f SE , (2.10) 2 (kS + NBG)QEnf tSE +(NDCnf tSE)+NRN nf q where k is the straddle factor which describes the fraction of photons falling on the best pixel, QE is the quantum eciency, nf is the number of frames and tSE is the length of single exposure. The total exposure time is the product of frame count and single exposure length. The reason for the short exposure assumption is clarified later. Not every photon hitting the sensor liberates an electron, photo-electron, and thus, some photons might stay undetected. Quantum eciency describes the fraction of detected photons from all the photons falling on the sensor. Quantum eciency depends on the wavelength and the sensor. The S/N can be understood as the relative error of the measurement so that S/N = 5 corresponds to 20% error and S/N = 100 to 1% error. ± ± Having decided a required S/N, the limiting apparent magnitude of the surveillance system can be solved from Equation 2.10 by setting Vlim = Vref as presented in Schroeder (1999). After solving for Vlim, the relation can be written as follows:

(S/N)2 Vlim = 2.5 log10 2 2 "0.5⇡(1 ✏ )N0k⌧dDaQEnf tSE ⇥ (2.11) 2 4(NBGQEtSEnf + NDCnf tSE + NRN nf ) 1+ 1+ 2 . s (S/N) !# The angular resolution (R) of a telescope describes the minimum angular separation needed between two point sources for them to remain resolvable (Schroeder, 1999). A point source is an object with an angular size smaller than the angular resolution of the telescope. However, due to di↵raction caused by the lens of a telescope, a point source does not come across as a single dot but as a ring-shaped di↵raction patter, Airy pattern, which is illustrated in Figure 2.2.

6 Figure 2.2: Airy patterns from two point sources. From top to bottom: clearly resolvable point sources, point sources at Lord Rayleigh’s limit and not resolvable point sources (Bliven, 2014).

According to Lord Rayleigh’s criterion, two equally bright point sources are just re- solvable when the peak of the other Airy pattern falls on the first dark ring of the other, as in the middle image in Figure 2.2. Therefore, the radius of the first dark ring defines the angular resolution. The di↵raction limited angular resolution, in arcseconds, can be calculated by using the relation: 1.22 ⇥= 206265 . (2.12) Da ⇥ The angular resolution of a ground-based telescope is limited by atmospheric e↵ects rather

7 than the di↵raction limit. The angular resolution can also be limited by aberrations, imperfections due to defects in the optical system that cause the light to not focus properly on point. However, high quality space-based telescopes are di↵raction limited. Equation 2.12 is illustrated in Figure 2.3 when considering various surveillance systems.

Figure 2.3: Log-log graph illustrating the relation between di↵raction limited angular resolution R =⇥, aperture diameter Da and wavelength (Cmglee, 2012).

It is to be noted that the numeric multiplier in Equation 2.12 depends on the obscu- ration factor, which is further explained in (Schroeder, 1999). A large number of stars are visible in the background when imaging asteroids with high sensitivity cameras. With low angular resolution, or too high pixel scale, there is a risk that a star is within the di↵raction limit or that a star would occupy the same pixel as the asteroid and leave the asteroid unnoticed. The resolution in the digital images taken through the telescope is also limited by the pixel scale, which depends on the focal length (f) and pixel size (wpx). Focal length is the distance between the lens and the image plane where the sensor is placed. Pixel scale is defined as 206265 w s = ⇥ px . (2.13) px f

Increasing focal length strengthens magnification, but as it can be inferred from Equation 2.13, it will also reduce the field-of-view (FOV), the covered angular sky area [(°)2]. In addition to the focal length, the FOV depends on sensor size, which is defined by the

8 number and size of the pixels. The FOV is defined as

2 spx FOV = pnpx , (2.14) 60 60 ⇥ ✓ ⇥ ◆ where npx is the total number of pixels in the sensor. Sometimes the unit of FOV is given in degrees instead of square degrees. In that case it means the diameter of the FOV. Another common parameter is the focal ratio (F/N), which describes the ratio of focal length and aperture diameter.

2.3 Detection and tracking

In optical asteroid surveys, CCD and CMOS sensors are used to take multiple images of the same region in sky over a period of time and then software is used to compare the images and detect which objects have moved in the images. The direction, rate of motion and apparent magnitude of the object in the images can be used to create preliminary estimates of the object’s size, distance and orbital characteristics (Jedicke, Granvik, Micheli, Ryan, Spahr and Yeomans, 2015). The orbit uncertainties of minimoons decrease rapidly as the number of detections and observing time span are increased. Figure 2.4 illustrates how the accuracy of orbit determination improves in just three days of observations. Suciently small pixel scale is crucial to get accurate enough astrometry for orbit determination. In this thesis, a pixel scale of 3” is used unless otherwise stated. It is a similar value to what NEOSSat had, (Wallace et al., 2014), and the systems suggested by Shao et al. (2017) and Mainzer et al. (2015).

9 Figure 2.4: The orbit of minimoon converges as the number of detections and observational time span increases Granvik et al. (2013). Top left, 3 detections spanning one hour; top right, 6 detections spanning 25 hours; bottom left, 9 detections spanning 49 hours and bottom right, 12 detections spanning 72 hours. The true orbit of the minimoon in black and the orbital uncertainty in gray in a geocentric rotating reference frame where the Sun is at (1,0,0). The black dots represent the location of the minimoon at the moment of observation.

10 2.4 Shift-and-add technique

The total signal from a faint object can be increased by increasing the exposure time. However, a fast moving object becomes streaked in a long exposure image because as it moves, the photons emitted by the object are spread over multiple pixels in the sensor and thus, the signal from the object might not be distinguishable. This spread of signal is known as a trailing loss. Trailing loss can be avoided with shift-and-add technique, which was first presented by Tyson et al. (1992). In this thesis, it is also referred to as synthetic tracking (Shao et al., 2014). Instead of using a single long exposure, shift-and-add technique relies on taking multiple short exposures. For example, instead of a single 30 s exposure, one would take 60 frames with 0.5 s exposure. For this to be beneficial, the read noise must be small and the single exposures must be short enough to ensure that the photons from the object do not spread over multiple pixels. Faint objects are not visible in one frame but the algorithm can add the consequent images so that all the photons from the asteroid end up in the same pixel in the synthetic image. This shift-and-add concept is illustrated in Figure 2.5. The object is searched from a three-dimensional data cube in (x,y,vx,vy) space. The number of di↵erent velocity vectors to be tried depends on the pixel count of the sensor, which defines the possible starting points for the vector, the velocity range to be searched, which defines the size of the velocity grid, and velocity grid spacing.

Figure 2.5: Shifting and adding the frames by the right amount creates a synthetic image in which the photons are in a single pixel which results in a higher S/N Shao et al. (2014).

The computational load (C) of the synthetic tracking search [FLOPS] can be estimated by using the following equation: n n v C = px ⇥ f ⇥ grid , (2.15) tTE + ts where npx is the total number of pixels in the sensor, nf the number of frames taken, vgrid the size of the velocity grid in 2 dimensions, tTE total exposure time and ts the slew time (Shao et al., 2017). The size of the velocity grid is the velocity search range [ °/day] in ± two dimensions divided by the velocity grid spacing. In this thesis, 2spx/tTE is used as the velocity grid spacing as in Shao et al. (2017).

11 As an example, if we set the total exposure and slew time as 800 s and 10 s, respectively, and set the length of a single exposure so that a maximum angular velocity object cannot move more than half a pixel width per exposure, then the maximum angular velocity range to be searched and the sensor size ultimately define the computational load. Figure 2.6 illustrates how the computational load increases as the velocity search range is increased. As it can be inferred from Equation 2.15, with n = 4096 4096 sensor the computational px ⇥ load would be four times higher compared to the illustrated n = 2048 2048 case. px ⇥ Conveniently synthetic tracking process gives quickly an estimate of the object’s ve- locity which helps to perform follow-up observations required for orbit determination. In addition, synthetic tracking has other advantages such as decreased sensitivity for false positives and the ability to increase the S/N by just increasing the number of frames. The result of the technique is illustrated in Figure 2.7.

Figure 2.6: The computational load and required single exposure as a function of angular velocity search range, when s = 3” and n = 2048 2048. px px ⇥

12 Figure 2.7: The peak signal from the asteroid is weak in the left image due to trailing losses. After shifting and adding multiple frames with synthetic tracking, a stronger peak signal is achieved for the asteroid and stars are streaked instead (Zhai et al., n.d.). The horizontal color bar describes the signal intensity. Pixel numbers on horizontal and vertical axes.

2.5 Advantages of space-based surveillance

Building a space-based telescope is more challenging than building an equal size ground- based telescope. In addition, performing maintenance is often impossible. However, space- based telescopes have multiple advantages over ground-based ones. Space-based telescopes do not su↵er from the presence of atmosphere. Earth’s atmosphere not only limits the observable wavelengths, as illustrated in Figure 2.8, but the atmosphere also blurs astro- nomical objects and shifts them. The blur, often called seeing, is caused by turbulence in Earth’s atmosphere. Seeing limits the maximum angular resolution of ground-based tele- scopes. The shifts of astronomical objects are due to atmospheric refraction. Nowadays, atmospheric distortions can be reduced to some extent with adaptive optics, a technique which creates counter acting distortions with deformable mirrors. Space-based systems are also not limited by geographical coordinates. They can cover the whole sky, and in addition, there is less background brightness in space. Ground-based observatories are usually built far away from cities to minimize the e↵ect of light pollution but even the best sites cannot reach as low background sky brightness as telescopes placed in space. Low background brightness is especially important when surveying extremely faint objects such as minimoons.

13 Figure 2.8: Atmospheric electromagnetic opacity as a function of wavelength (NASA, 2008).

14 3 Earth’s temporarily-captured natural satellites

In this section, fundamental characteristics of Earth’s temporarily-captured natural satel- lites are described as well as how the models have been created. The model used in this thesis is based-on the latest work of Grigori Fedorets (University of Helsinki), which is presented in Section 5. The latest model has di↵erences to the earlier models and thus, less attention is given to earlier minimoon survey studies. A more holistic overview of the Earth’s temporarily-captured natural satellites is given in Jedicke et al. (2018). Regard- ing the detectability of minimoons with existing and proposed ground- and space-based surveillance systems when an older model is used, Bolin et al. (2014) have given the most extensive overview.

3.1 Definitions

A near-Earth object (NEO) is an asteroid, comet or artificial body, which closest approach to the Sun is less than 1.3 AU. As of early 2018, from around 17 000 near-Earth asteroids (NEA) that have been discovered, over 8 000 of them have diameters larger than 140 meters (NASA, 2018b). Earth’s temporarily-captured natural satellites are NEAs, which get captured in the Earth-Moon system. An asteroid is considered to be captured, when its specific energy v2 µ ✏ = (3.1) 2 r with respect to the Earth-Moon barycenter is negative. In Equation 3.1, v and r are the relative velocity and distance to the Earth-Moon barycenter and µ is the standard gravitational parameter. Gravity is the dominating reason for the capture of meter-sized bodies. Only a small fraction of captures are due to aerobraking (Moorhead and Cooke, 2014). Permanent captures do not occur without external perturbation. Following the definition presented by Fedorets et al. (2017), a natural-Earth satellite (NES), in this context a temporarily-captured asteroid (TCA), is an object on a geocentric pseudo-elliptic orbit within 0.03 AU and must make at least one approach inside Earth’s Hill radius, 0.01 AU, during the capture. The TCA population can be further divided into temporarily- captured orbiters (TCO) and temporarily-captured flybys (TCF). Hereafter, TCOs are called minimoons and TCFs are called drifters as suggested by Jedicke, Bolin, Bottke, Chyba, Fedorets, Granvik and Patterson (2015). Minimoons are TCAs, which make at least one revolution around Earth in geocentric rotating frame, and drifters are TCAs which make less than one revolution around Earth in the geocentric rotating frame. Quasi- satellites appear to revolve around Earth in this reference frame but they are not TCAs because they are gravitationally bound to the Sun instead of the Earth-Moon system (Fedorets et al., 2017).

15 3.2 The creation of the population model

Granvik et al. (2012) created the first TCA population model. An improved model was later created by Fedorets et al. (2017). In this thesis, the latest minimoon model by Grigori Fedorets (University of Helsinki) is used. The creation of the model follows same principles as the creation of 2017 model which is briefly explained in this subsection. More thorough explanations can be found from Granvik et al. (2012) and Fedorets et al. (2017). A large number of capturable NEOs, test particles, were created by assigning them random combinations of orbital parameters which could lead to a capture. The Keplerian elements were drawn from a uniform distribution of Earth-like values: 0.87 AU Pluto, and the Moon were all considered. Non-gravitational forces, such as the Yarkovsky e↵ect, were not included in the simulation. A rotating asteroid emits momentum carrying photons anisotropically, which has an e↵ect on the asteroid’s trajectory. Out of the 12.5 million particles, which trajectories were integrated through the Earth-Moon system, 20,272 test particles fulfilled the conditions to be categorized as minimoons and 31,385 as drifters. On average, minimoons stayed captured for 276 days and made 3.19 revolutions around Earth, whereas drifters stayed captured for 73 days and made 0.55 revolutions around Earth.

3.3 Steady-state population

Fedorets et al. (2017) estimated the size of TCA steady-state population using their simu- lation results and multiple di↵erent NEO population models. The predicted steady-state populations with di↵erent NEO models are presented in Figure 3.1. If the conservative NEO model by Brown et al. (2002) is used, the largest member of the TCA steady-state 7 population should have a diameter of 80 cm. In total, approximately 10 of the NEO population gets captured in the Earth-Moon system each year (Granvik et al., 2012).

16 Figure 3.1: The size of minimoon (left) and minimoon and drifter (right) steady-state populations as a function of absolute magnitude, estimated by Fedorets et al. (2017), using the NEO population models by Rabinowitz et al. (2000), Brown et al. (2002), Granvik et al. (2016) and Harris and D’Abramo (2015).

In 2016, Catalina Sky Survey made the first confirmed minimoon discovery. The 2-6 meter-sized minimoon 2016 RH120 fits well in the predicted minimoon population, but it is important to remember that this does not confirm the correctness of the model. In this thesis, the conservative NEO model by Brown et al. (2002) is used, which sets the number of 0.5 m and larger minimoons to around 23 with the latest minimoon model.

3.4 Earlier 6D-geocentric-residence-time-distribution

Residence-time-distributions can be acquired for minimoons by recording how much time they spend in various orbital-element configurations during their capture. The distri- butions presented in this subsection are based on the orbital integrations presented in Fedorets et al. (2017). In this thesis, a newer distribution is used which di↵erences are discussed in Section 5. The most notable di↵erences are in the way residence time is distributed in the (a, e, i) -orbital element space. The Fedorets et al. (2017) distribution is presented in 3.2, the newer distribution in Section 5.

17 Figure 3.2: Minimoon residence-time distribution in a, e, i orbital element phase space (Fedorets et al., 2017). The path of 2006 RH120 is marked with dashed line.

3.5 Sky-plane distributions

The instantaneous visible fractions can be calculated from the sky-plane distributions. Sky-plane distributions describe how objects are distributed along ecliptic longitude and latitude given some reference direction such as the opposition. The sum of objects in the sky-plane relative to the total number of objects is the visible fraction. The approach used in this thesis is inspired by Bolin et al. (2014). In their work, minimoon sky-plane distributions were calculated for an observatory at Earth using the Granvik et al. (2012) model. As an example, if apparent visual magnitude is limited to V<20, absolute magnitude to H<38 and the rate of motion to < 15°/day, the most minimoons that are visible are close to the opposition, as Figure 3.3 shows. The advantage of low phase angle is strong as there are more visible objects in higher latitudes close to opposition than in the ecliptic plane at east and west quadratures, which have higher numbers of minimoons if no constraints are considered. This is shown in Bolin et al. (2014). The advantage of low phase angle is also expected to be clearly present with the latest model.

18 Figure 3.3: Number density of minimoons on the sky-plane with the following constraints: V< 20, H< 38 and rate of motion < 15°/day (Bolin et al., 2014).

3.6 Rate-of-motion

The speed of TCAs increases as they come to the proximity of Earth, as illustrated in Figure 3.4. This is especially problematic for their ground-based observing, because the angular velocity of TCAs grows very high when they are close. As a consequence, if a long exposure is used, the flux from a TCA spreads over many pixels which decreases the peak signal-to-noise ratio. Despite the model used, the velocities are higher at lower orbits. The fast TCAs closer to Earth should be visible to space-based surveillance systems which are further away.

Figure 3.4: Geocentric velocities of minimoons (left) and drifters (right) Fedorets et al. (2017).

19 3.7 Rotation rates

The rotation rates of small, D<1 m, asteroids are fairly unknown. Based on meteor observations, the rotation period (T ) and diameter could be connected by relation T ⇡ 0.0001 D 60 60 [s] by Beech and Brown (2000). For a one meter asteroid this gives ⇥ ⇥ ⇥ T = 0.4 s, which corresponds to a rotation rate !r = 17.5 rad/s. If the relation T = 0.005 D 60 60 [s] by Farinella et al. (1998) is used, the rotation period T and rate ! ⇥ ⇥ ⇥ r are 18 s and 0.3491 rad/s respectively (Farinella et al., 1998). The latter model is used for kilometer-seized objects and thus, estimating rotation periods of sub-meter-sized objects with it is questionable. However, its results agree well with Light Curve Database’s median values in the 1-100 m range (Warner et al., 2009). Bolin et al. (2014) assumed that the median rotation rate follows the latter relation in 1-10 m range and that small asteroids’ spin-rate distribution is Maxwellian. All four of these models are illustrated in Figure 3.5. The only known minimoon, 2016 RH120, had T =165 s, which would not be that rare of an occasion with these models (Bolin et al., 2014). The high rotation rates do not a↵ect their detection in visual bandpass but it a↵ects their detectability in infrared. One meter-sized or smaller TCAs can be assumed to be in thermal equilibrium because they are small, rotate fast and their distance to the Sun is fairly constant while being captured. Therefore their attitude wouldn’t a↵ect their brightness. The sky-plane distributions of visible minimoons could be very di↵erent for infrared surveillance systems since their brightness wouldn’t depend on the phase angle.

Figure 3.5: Rotation rates as a function of diameter for small asteroids (Bolin et al., 2014). Note that the unit is revolutions per hour instead of per second .

3.8 Summary of the observational challenges with TCAs

Considering the steady-state population and the geocentric velocity distribution, it can be said that TCAs are generally faint, fast and few in the Earth-Moon system in meter- class. When observed from Earth, they are the brightest when they are the fastest and contrariwise. Therefore, it is worth considering other locations for observing them. Space- based surveillance systems located away from Earth in the Sun direction could contribute especially in the detection of TCAs which are close to Earth or in the space between the spacecraft and Earth.

20 4 MicroSat asteroid surveillance technologies

Earlier missions and existing asteroid surveillance technologies are presented to give the reader a good picture of the current capabilities in asteroid and TCA surveillance. The surveillance system specifications used in the simulation are based on the findings of this literature review. This section begins by reviewing earlier and proposed space-based Mi- croSat asteroid surveillance missions and related technologies. After that, other available and researched technologies are reviewed. In addition, competing technologies in asteroid and TCA surveillance are discussed.

4.1 Earlier and proposed missions

A microsatellite, MicroSat, is a satellite which wet mass is 10-100 kg. As of mid-2018, there has been only one MicroSat asteroid surveillance mission. The Near Earth Ob- ject Surveillance Satellite (NEOSSat), by the Canadian Space Agency and Defence Re- search and Development Canada, was launched to low-Earth-orbit in 2013 (Wallace et al., 2014). The objective of the mission is to detect and track potentially hazardous asteroids (PHO) inside Earth’s orbit. Other mission goals are to demonstrate the capabilities of the Multi-Mission Microsatellite Bus and the capabilities of MicroSat platform for military. NEOSSat, in Figure 4.1, is a 74 kg MicroSat measuring approximately 0.9 m 0.65 m ⇥ 0.35 m. Its ba✏e extends 0.5 m from the body where the Near Earth Space Surveil- ⇥ lance Imager (NESSI) is rooted. NESSI works in the visual bandpass and compromises of a combination of a 15 cm diameter aperture F/6 Maksutov Cassegrain telescope and a 1,024 1,024 scientific CCD with 13 µm pixels. Each pixel covering 3”, NESSI has a FOV ⇥ of 0.85 0.85. Its estimated limiting magnitude is 19.5 mag with 100 s exposure, but ⇥ during its operation noise has occurred in the images which has degraded the performance. NEOSSat’s custom ba✏e has allowed it to search for NEAs along ecliptic plane between 45°-55° solar elongation. Using even smaller satellites for astronomy has become of interest in the 21st cen- tury. CubeSats, a sub-class of MicroSats, are small satellites usually built from COTS components. Their weights and volumes range from 0.2 kg to 40 kg and 0.25 U - 27 U respectively. One CubeSat unit (U) is 10 cm 10 cm 10 cm. Over 850 CubeSats have ⇥ ⇥ been launched as of mid-2018 Kulu (2018). In addition to educational and technology demonstration missions, CubeSat platform has proven to be a viable option for low-cost science missions (Poghosyan and Golkar, 2017). ASTERIA, Arcsecond Space Telescope Enabling Research in Astrophysics, a 6 U CubeSat developed by NASA, is a good rep- resentative of the latest CubeSat technology. ASTERIA, in Figure 4.2, with its 83 mm diameter aperture is capable of detecting objects in visual bandpass down to V =8inits large 28.6 FOV. It was launched in 2017 to demonstrate CubeSat platform’s capabilities to perform precision photometry, which it has successfully accomplished by repeatedly achieving a pointing accuracy of 0.5” when observing stars (NASA, 2018a).

21 Figure 4.1: A computer rendering of NEOSSat (Micro systems Canada Inc., 2013).

Figure 4.2: ASTERIA prior to its launch in April 2017 (NASA, 2017).

22 Shao et al. (2017) proposed that a constellation of 9U CubeSats, equipped with 10 cm diameter aperture synthetic tracking telescopes, could be used to find NEOs. They showed that a constellation of six CubeSats on heliocentric orbit could detect 90% of PHOs with H 22 in less than 4 years. CubeSats’ interplanetary capabilities have been already  demonstrated by Mars Cube One (MarCO) mission, (NASA, 2018c), and will be further demonstrated in late-2018 by NEA Scout mission (Johnson et al., 2017). The CubeSat design presented in Shao et al. (2017) is a modification of a design study conducted by Zarifian et al. (2014). Shao et al. (2017) estimated that the designed 9U CubeSat could detect asteroids down to V = 20.49 mag with S/N = 7 by taking 80 10 s frames and lim ⇥ using synthetic tracking. The telescope is illustrated in Figure 4.3 and the parameters they used in their estimate are presented in Table 4.1. They also estimated that a similar system with the same total exposure, tTE = 800 s, could achieve a limiting magnitude of 22.15 mag.

Table 4.1: The parameters used in Shao et al. (2017) to estimate the limiting magnitude of the synthetic tracking telescope of their 9U CubeSat. Total QE is the product of optical and sensor QE.

Input values: NEO limiting magnitude 20.49 mag NEO distance 0.362 AU 1 Transverse velocity 12 km s Phase angle 0° Telescope aperture diameter 10 cm Total QE (optical and sensor) 0.64 Pixel scale 3.30”/pixel Detector read noise 1.20 e Frame time 10.00 s Total integration time 800 s Total FOV 14.10 (°)2 Sky background 22 mag/(”)2 Zero apparent magnitude reference 2.48 1010 photons/m2/s ⇥ Derived values: Apparent magnitude 20.49 Flux detected 0.72 e/s Noise/frame variance 83.86 e Signal/frame 7.17 e Total S/N 7.00 in 800 s

Figure 4.3: A CAD model of a 10 cm diameter aperture telescope that could be used with a CubeSat (Shao et al., 2017).

23 Performing synthetic tracking on-board of a CubeSat has become feasible due to the recent advances in technology. Scientific CMOS cameras are nowadays capable of high frame rates with as low readout noises as 1e. Examples such as Andor’s NEO and ZYLA sCMOS sensors, (ANDOR, 2010), were mentioned in Shao et al. (2017). There are also more and more capable CubeSat compatible COTS processing units which can perform synthetic tracking searches in nearly real-time over a certain velocity range. Shao et al. (2017) estimated that the flight-proven Xilinx Virtex-7 field-programmable gate array (FPGA) would have to use only 10% of its arithmetic units and consume less than 7 W to perform 5.7 GFLOPS of synthetic tracking search (Xilinx, 2018). That comes from performing synthetic tracking with 6 velocity search with 2 pixel spacing across 80 4K ± 4K frames. ⇥ Shao et al. (2018) presented a new more capable MicroSat-based NEO surveillance sys- tem. They estimated that a 27.9 cm diameter aperture telescope with synthetic tracking, 50 10 s frames, could achieve V = 22.01 with S/N = 7. With lower focal ratio and ⇥ lim speculated back-illuminated CMOS 12K sensor, a FOV of 17.79 (°)2 could be achieved. They considered that reaching this performance is possible with the latest available hard- ware. TransAstra Corporation is currently developing two MicroSats to demonstrate syn- thetic tracking in asteroid detection. Both missions are done in partnership with NASA and they are part of NASA’s Utilizing Public-Private Partnerships to Advance Tipping Point Technologies programme. Theia mission aims to send a MicroSat equipped with a synthetic tracking telescope to Earth’s orbit to detect small fast moving dim objects such as space debris and NEAs (NASA, 2016a). Sutter Survey would have a compound synthetic tracking telescope system consisting of four 14 cm diameter aperture telescopes and have total FOV of 30 (°)2 Sercel (2017) and still weigh approximately only 60 kg. TransAstra Corporation estimates that a constellation of three Sutter Survey MicroSats could be built with less than 50 million dollars and it could be as good as LSST at finding and tracking small and faint asteroids. Synthetic tracking technique was first demonstrated with CHIMERA camera on Palo- mar 200 inch telescope by Zhai et al. (2014). They were able to detect an asteroid which was moving 6.32°/day with V = 23 at S/N=15. With conventional 30 s single exposure the trailing loss would have degraded the asteroid’s apparent magnitude on the camera to V = 25, which would have been too faint to be detected. Another ground-based syn- thetic tracking test was performed at the Jet Propulsion Lab’s Table Mountain Facility (Zhai et al., n.d.). Synthetic tracking technique has also been demonstrated with the data collected by Planet Labs’s SkySat-3 satellite (Zhai et al., 2018b). The satellite was tem- porarily turned around to find NEOs with its 35 cm diameter aperture Earth-observing telescope. Synthetic tracking improved the performance but they did not reach as high S/N as predicted by the theory. Typically for Earth-observing telescopes, the pixel scale and the FOV were small. It is also to be noted that SkySat-3 weighs a little over 100 kg and does not therefore qualify as a MicroSat. The main challenge with on-board synthetic tracking is computation. The main on- board data processes are data reduction and star removal, synthetic tracking search, can- didate selection and postage-stamp image generation for down-link. From these main processes, the synthetic tracking search requires two magnitudes more computational re- sources than the others and thus, it dictates the required computational resources (Shao et al., 2017). The velocity search range could be increased by keeping the camera idle every once in a while and not performing the synthetic tracking in nearly real-time. In trade, the sky-area covered per day would decrease. The latest GPUs are capable of tens of GFLOPS per watt. Depending on the power budget of the MicroSat this would set the upper boundary for on-board computations at few TFLOPS at best.

24 4.2 Other available and researched technologies

4.2.1 Telescope technologies There are no COTS space-grade wide-field telescopes for astronomy. Small FOV space- grade telescopes mainly for Earth-observing are manufactured (Apertureos, 2018). How- ever, converting COTS ground-based telescopes to space-based telescopes has been stud- ied. As of mid-2018, the only wide-field solution is to have a customized telescope. The most important parameters are aperture size for sensitivity, and FOV for covered sky-area, and as with every space-application, with minimum mass and volume. Ackermann et al. (2010) provide an overview of di↵erent telescope types and their wide-field capabilities in the sub-meter aperture range. Refractor telescopes were considered the most optimal for small survey telescopes. With aperture diameters smaller than 15 cm it was considered nearly ideal. In the 10-40 cm diameter aperture range they are usually used with focal ratios ranging from 4 to 9 to provide a FOV up to 9° equalling 64 (°)2.Itisdicultto estimate how large wide-field telescopes it is possible to accommodate in MicroSats. If the weight of the 3 kg 10 cm aperture telescope illustrated in Figure 4.3 is scaled-up as a function of aperture area, a 30 cm aperture telescope would weigh 27 kg, which is on the upper limit of payload weight suitable for MicroSats. NASA has a team which seeks to develop an inexpensive and lightweight CubeSat telescope which would be sensitive in ultraviolet, visible and infrared wavelength bands (NASA, 2016b). Its carbon nanotube resin mirror would be reproducible and would not require polishing. This technology will still need many years of advancement before it could be installed in CubeSats but the technology can be expected to lower the cost of telescopes in the future if the development program proceeds successfully. Silicone-carbide has also proven to decrease the weight and cost of a space-telescope, (Kasunic et al., 2017), and it has already been started to use in MicroSat compatible telescopes by Apertureos (2018) and SpaceFab (2018). Fitting a relatively large aperture with tens of centimeters of focal length to a CubeSat or MicroSat is challenging. However, new deployable telescope designs have emerged to enable this. Deployable Petal Telescope (DPT) design enables packing a 20 cm aperture and 1400 mm focal length telescope in just 2-3 CubeSat units of space (Champagne et al., 2014). Another design enabling to fit a 20 cm diameter aperture telescope with 414 mm focal length in a CubeSat is the Collapsible-tube Deployable Space Telescope (CDST). A smaller version of it is illustrated in Figure 4.4 Freeman et al. (2010). SpaceFab (2018) is developing a satellite for both space and Earth observing. The Waypoint is a 18 kg 12U CubeSat, to be launched in 2019, with a 21 cm diameter and 48 megapixel sensor. With its deployable secondary mirror, which is illustrated in Figure 4.5, it achieves a focal length of 175 cm.

25 Figure 4.4: A computer model of a 15.24 cm diameter aperture CDST design occupying four CubeSat units of space when collapsed. Agasid et al. (2010)

Figure 4.5: SpaceFab’s Waypoint MicroSat with a deployable secondary mirror (SpaceFab, 2018).

26 4.2.2 Sensor technologies

Small read noise sensors with high frame rates have enabled synthetic tracking. Large format CCDs are usually not considered because they have lower frame rates and might need a mechanical shutter to prevent smearing during read out (Shao et al., 2018). How- ever, the newly developed CCD282 by Teledyne-e2v, is capable of suciently fast frame rates and and has sub-electron level read noise (Gach et al., 2014). Its suitability for syn- thetic tracking should be further examined. Teledyne-e2v has also high quality sCMOSs which are especially designed for space applications Jorden et al. (2017). Teledyne-e2v has supplied over 150 space missions with their sensors. Andor’s latest back-illuminated sCMOS for astronomy, Marana, presents the state-of- the-art sensor technology (ANDOR, 2018). It has a 2,048 2,048, w =11µm sensor, ⇥ px with a maximum QE of 95%. It is capable of 48 frames per second with a read noise of just 1.6 e. Andor’s older model, Zyla, is also suitable for synthetic tracking purpose (ANDOR, 2010). Despite speculations, 4K 4K and larger scientific CMOSs for astronomy have not ⇥ become common yet but are expected to emerge in the near future (Shao et al., 2017)(Shao et al., 2018).

4.2.3 Other technologies

The highest angular resolutions can be achieved with interferometry. Multiple telescopes can be arranged so that they create a single telescope which synthetic aperture is as large as the distance between the telescopes. This is an ecient way to increase the angular resolution, but the amount of gathered light is still limited by the real aperture size. Space- based interferometry is challenging because it would require extremely precise formation flying. Yonsei University’s Astrodynamics and Control Laboratory and NASA’s Goddard Space Flight Center have studied the use of two CubeSats to create a virtual telescope. The main purpose of the CANYVAL-X mission, launched in early-2018, is to demonstrate the core technologies of a virtual telescope system, such as maintaining alignment (Park et al., 2017). A system of two spacecrafts flying in formation, the other carrying the sen- sor and the other the lenses, could achieve very large focal lengths and thus, very large magnifications and resolutions. However, the field-of-view decreases as the focal length increases and therefore, this technology might not be of great use for asteroid surveying. In the future, large space telescopes could be autonomously assembled in space from a large number of CubeSats, each carrying one mirror element (Underwood et al., 2013). This could be a more cost ecient way to build a large aperture space telescope, which could also be used for detecting asteroids.

4.3 Alternatives

There are also competing approaches to MicroSat-based TCA surveillance. In this subsec- tion, the most promising space-based and ground-based alternatives are briefly discussed. The Near-Earth Object Camera (NEOCam) is a proposed asteroid surveying mission by NASA (Mainzer et al., 2006). The primary targets of NEOCam are potentially haz- ardous asteroids, but it could be also be very e↵ective at finding TCAs with its 50 cm diameter aperture infrared telescope. One meter-sized or smaller TCAs can be assumed to be in thermal equilibrium because they are small, rotate fast and their distance to the Sun is fairly constant while being captured. Therefore their visibility in infrared is independent of not only phase angle but also attitude. In addition, NEOCam is planned to be located at L1, which was considered as the best location for such system in Bolin

27 et al. (2014) for finding TCAs. NEOCam could potentially find TCAs, but it is uncertain if this mission will continue receiving funding. The Large Synoptic Survey Telescope (LSST) is a state-of-the-art ground-based tele- scope with an 8.4 m diameter mirror. Its construction began in 2014 in Chile and it is predicted to start surveying the sky in the early-2020s. Its wide-field 3200 megapixel camera can take images of the entire sky in just three nights and detect objects as faint as V = 24.5 with 30 s exposures. A limiting magnitude of Vlim = 27 mag can be reached with added images. It is designed to gain information about dark matter and energy, hazardous asteroids, remote solar system, transient optical sky and the formation and structure of the Milky Way (Corporation, 2018). LSST’s TCA discovering capabilities have been stud- ied by Bolin et al. (2014) and Fedorets et al. (2015). Bolin et al. (2014) concluded that LSST should be able to find 1.5 TCAs per month. Fedorets et al. (2015) looked into the possibility of extracting TCAs from LSST data and how to connect possible detections. It is not yet certain whether it is possible or not. When the synthetic TCA population by Fedorets et al. (2017) was used in LSST survey simulation, it was found out that LSST should eventually find all larger TCAs if linking detections from di↵erent nights is possible. Dedicating LSST to TCA search to provide a steady stream of detections in real-time is unlikely.

4.4 Summary of MicroSat compatible technologies

Detecting and tracking TCAs with MicroSats built from commercial COTS components would radically decrease costs compared to other alternatives. The only custom built component could be the telescope itself. Ideally the telescope would have a large aperture for gathering as many photons as possible to detect faint and small objects. The largest telescope suggested to be used on an asteroid surveying MicroSat mission has a diameter of 28 cm (Shao et al., 2018). Whether it is possible to have significantly larger wide-field telescopes on-board is challenging to estimate. Corrective mirrors are commonly used with wide-field telescopes, and they add to weight. There are lightweight and compact space-grade telescope solutions for narrow-field but not for wide-field. Developing compact solutions to achieve longer focal lengths has been motivated by the interest to perform high resolution Earth-observation with MicroSats. MicroSat-based space surveillance is not yet very developed. The surveillance system presented in Shao et al. (2018) is the most capable of what has been presented. In the simulations of this thesis, the largest aperture diameter considered for a MicroSat compatible survey telescope is 30 cm, slightly more than what has been already suggested. The small aperture size can be compensated with the use of synthetic tracking algorithm to increase sensitivity. Regarding sensors, Andor Marana presents the current state-of- the-art but larger sensors can be expected to emerge in the near future. CCDs are not considered because of the issues mentioned in Subsection 4.2.2. Estimates presented in Shao et al. (2017) can be used to predict the power needed to perfrom synthetic tracking on-board. The major advantages of MicroSat-based surveillance solutions to the existing ones are: lower costs, better availability for dedicated surveillance and that the satellite can be taken into regions in space where TCAs are more abundant and slower. Missions like MarCo have shown that MicroSats, even CubeSats, can be used in interplanetary missions and thus operate also in the whole Earth-Moon system (EMS).

28 5 Simulation

This section describes the methods used to study the suitability of di↵erent locations in the EMS for minimoon surveillance and how di↵erent surveillance system parameters a↵ect the visibility of minimoons. In conventional survey simulations, the apparent brightnesses are calculated for all the asteroids that are in the field-of-view of the satellite-based surveillance system. This is repeated after every time step and therefore requires the propagation of thousands or millions of bodies for many years depending on the asteroid population of interest. This is computationally very expensive and thus, a di↵erent approach was chosen in this thesis. In the chosen method, a synthetic minimoon population is generated based on the 6D-geocentric-residence-time-distribution (6DGRTD) which is created on the basis of the latest minimoon integrations. As explained in Granvik et al. (2012), the residence-time distribution can be thought of as an instantaneous probability distribution of the minimoon population’s orbital elements. Following Brown et al. (2002) size distribution, there are approximately 22.7 minimoons of sizes H<34.26 in the steady-state population. The generated synthetic minimoon population consists of 567,656 bodies, 25,000 times the steady-state population of H<34.26 minimoons. The large number of bodies is necessary to have clear di↵erences in the way the synthetic minimoons are distributed along ecliptic latitude and longitude in the simulated sky-plane distributions. It follows that one visible synthetic minimoon in the simulation corresponds to de- tecting 1/567,656 of the minimoon steady-state population, which corresponds to 0.00004 minimoons. The translation from visible synthetic minimoons to real minimoons can be simply achieved by dividing the visible synthetic minimoon count by the scaling factor, 25,000. The figure of merit is the instantaneous visible fraction (vf ) of the minimoon steady-state population, which is the sum of synthetic minimoons in the sky-plane distri- bution divided by the total number of synthetic minimoons. The advantage of this method is that only 567,656 observations need to be simulated per test observatory location in the EMS. No propagation is required because the synthetic minimoons are generated for the observation epoch. Only H<34.26 minimoons, larger than half a meter, are considered. The method is more thoroughly explained in the following subsections.

29 5.1 6D-geocentric-residence-time-distribution

The 6D-geocentric-residence-time-distribution (6DGRTD) used in this thesis was created by Grigori Fedorets. It was acquired by reading the times minimoons spent in various orbital-element configurations during their capture from the integration logs after which the times were normalized. How the integrations were carried out is explained in the Section 3. The geocentric ecliptic orbital element space was discretized to 29,859,840,000 bins. The bin widths and ranges are presented in Table 5.1. After neglecting bins which had zero residence time, the table representing the 6DGRTD has 14,296,794 rows and seven columns, the first six representing Keplerian elements and the last column representing the fraction of the steady-state population. The distribution is illustrated in Figures 5.2 and 5.3 in the following subsection. The latest model has noticeable di↵erences compared to the Fedorets et al. (2017) minimoon model. There is a visible peak in the residence time in the bins where semi-major axis is 0.000625 AU, 100,000 km. The e↵ects of one extraordinarily long-lived minimoon ⇡ were already eliminated from the distribution because it single-handily raised certain bin values by an order of magnitude. Whether or not this peak is due to the same phenomenon should be investigated. If it is an especially rare occasion that a minimoon ends up on such orbital element configuration, this peak, containing 0.3% of the total residence time, distorts the model since it is describing steady-state population. Therefore, it would skew results when performing the simulation. Other major di↵erences to the earlier model are seen especially in the distribution of eccentricities. In earlier models, there were no high eccentricity orbits further away from Earth as it can be seen from Figure 3.2. In the new distribution, very small semi-major axes are not preferred but because of the preference for high eccentricity some minimoons are distributed closer to Earth than in the earlier models where the border of EMS was more densely populated. The reasons for these changes are currently being investigated.

Table 5.1: Bin widths and ranges used in the 6DGRTD.

Orbital element Bin width Range Semi-major axis (a) 0.00025 AU 0 AU-0.1 AU Eccentricity (e) 0.02 0-1 Inclination (i)5° 0°-180° Longitude of ascending node (⌦) 15° 0°-360° Argument of perigee (!) 15° 0°-360° Mean anomaly (M0)5° 0°-360°

30 5.2 Scaled-up minimoon population

The steady-state H<34.26 minimoon population was scaled-up 25,000 times, which required a generation of 567,656 synthetic minimoons. The synthetic minimoons were as- signed orbital elements according to the 6DGRTD. The absolute magnitudes were drawn from Brown et al. (2002) H-distribution, which was extrapolated to cover smaller objects. The H-distribution for the 567,656 synthetic minimoons is illustrated in Figure 5.1. The synthetic minimoon generator script is work of Mikael Granvik. The scaling factor was de- cided empirically. The distribution of synthetic minimoons stayed similar with more than half a million objects when di↵erent seed numbers were given to the generator. A popula- tion with 1,000,000 synthetic minimoons was also tested and it did not seemingly change the distribution. However, larger synthetic minimoon populations result in clearer pat- terns in simulated sky-plane distributions especially if the limiting magnitude constraint is set lower. The absolute magnitude was limited to 34.26, which corresponds to a minimoon with a 0.5 m diameter. Smaller objects are more plentiful but not as interesting from scientific perspective. Figures 5.2 and 5.3 illustrate how the orbital elements are distributed among synthetic minimoons.

Figure 5.1: Absolute magnitude distribution of the synthetic minimoon population. The bin width in the histogram is 0.01.

31 Figure 5.2: Distribution of minimoons in (a, e, i)-orbital element phase space. These plots also represent the 6DGRTD accurately. The color-scale varies in the plots.

32 Figure 5.3: Distribution of generated minimoons in (!,M0, ⌦,a)-orbital element phase space. These plots also represent the 6DGRTD accurately. The color-scale varies in the plots.

33 5.3 Observatories

Multiple observatory points were created in the space around Earth by varying the geo- centric distance de, ecliptic latitude e and longitude e,wheree = 0 is towards the Sun. The values used for the aforementioned three variables are listed in Table 5.2. The locations are illustrated in Figure 5.4.

Table 5.2: The spherical coordinates of the 154 observatory locations consists of all possible combinations of de, e and e inside each of the three sections in the table.

de e° e° 7,171 km 0 0 8,371 km 15 90 ± ± 42,157 km 180 ± 0.5 LD 1.0 LD 1.5 LD 2.0 LD 2.5 LD 3.0 LD 3.5 LD 4.0 LD 4.5 LD 7,171 km 0 90 ± 8,371 km 15 ± 42,157 km 30 ± 45 ± 60 ± 75 ± 90 ± 4.5 LD 0 15 ± 0 165 ±

More observatories were created in the proximity of Earth to gain more detailed knowl- edge about how Earth’s presence disturbs observing. The radius of the sphere defining the EMS is approximately 4 lunar distances (LD) but observatories were also created out- side the EMS to gain more knowledge about the L1 and L2 regions. Observatories at (4 LD,0,0) and (-4 LD,0,0) are at Lagrange points 1 and 2, respectively. Their results give first estimates of what could be visible from halo orbits around these points. Less interest was given for higher ecliptic latitudes because being o↵the ecliptic plane is not expected to be advantageous as it would only increase phase angle. With the scripts created during the project, generating observatories in any location in the EMS is quick and easy.

34 Figure 5.4: Locations of observatories in Cartesian geocentric ecliptic coordinate system. The sun is at (1 AU,0,0).

5.4 Observations

OpenOrb is a fortran based open-source asteroid orbit computation software (Granvik et al., 2009). It can be used for, for example, detecting linkages between astrometric asteroid observations, statistical ranging and ephemeris calculations. The ephemeris fea- ture of OpenOrb software is used to calculate a selection of properties for each generated synthetic minimoon seen from each observatory location. For this purpose, OpenOrb is given objects- and observatories-files, which formats are explained in Appendices A and B. The properties of main interest are their geocentric ecliptic coordinates, distance, angular velocity, opposition-centric latitude and longitude, phase angle and apparent magnitude. HG12-system is used to calculate the apparent magnitude with G12 =0.5, as in Bolin et al. (2014). Some upper limits for the aforementioned parameters are implemented inside OpenOrb to speed up the calculations and reduce the output data:

• The apparent magnitude of the minimoon at the moment of observation must be less than Vlim = 25.

• The opposition-centric ecliptic longitude must be in the range -135° to 135°to ensures a typical Sun exclusion angle of 45°. ±

• The topocentric angular velocity ⇣ must be less than 20°/day.

35 5.5 Post-processing

All the post-processing is performed with MATLAB by filtering OpenOrb output data. After filtering, sky-plane distributions and visible fractions can be calculated for each case. The total visible fraction and the visible fraction inside the total sky-area covered per day are considered when comparing locations. The number of minimoons that could be detected cannot be simply inferred from the visible fraction because the refresh rate inside a specific sky-area cannot be properly estimated without propagation of the population.

5.5.1 The e↵ects of Earth and the Moon on observing The observations are filtered by neglecting all observations in which the synthetic mini- moon in Earth’s shadow or inside Earth exclusion angle. Earth’s shadow is modelled as a cylinder with a radius of 6,371 km reaching out to 4 LD to the anti-Sun direction. Earth exclusion angle is set so that it is 16°at LEO and then changes with the observers distance so that the same exclusion angle is preserved. The Moon is not taken into consideration in observing because at the observation epoch it would only a↵ect some observatories based on its location in the EMS.

5.5.2 Examined surveillance system cases and their parameters The surveillance systems to be examined are:

• S17: The NEA surveillance spacecraft described in Shao et al. (2017) Appendix B

• S18: The NEA surveillance instrument described in Shao et al. (2018) Table 1

• NS: NEOSSat as it is described in ESA eoPortal Directory (2018)

• TS: TestSat.

S17 is interesting because it has the most detailed design of the proposed missions, whereas S18 has the most capable surveillance system. Case NS is the only existing MicroSat for asteroid surveillance purpose which has been actually built. It is the only one which is not considered to use synthetic tracking. TestSat (TS) is a test case which represents what is considered achievable with current technology, see Section 4. Its sensor values are based on ANDOR Marana (ANDOR, 2018). Detailed system specifications are listed in Table 5.3. In case NS, only a single exposure is taken and its length is limited so that ⇣lim =4 °/day can be captured without trailing losses. This assumption is a clear disadvantage for NS. To be able to better compare the systems, some assumptions and simplifications are made for all cases:

• The limiting magnitude for each surveillance system is recalculated using Equation 2.11, requiring S/N = 7 as in Shao et al. (2017).

• The use of wide-band filter is assumed for each system, d = 450 900 nm. The use of wide-band filter was suggested for minimoon surveillance in Bolin et al. (2014).

• The length of single exposure is defined as t =0.5 s /⇣ . SE ⇥ px lim • The total exposure time is assumed to be 800 s as in Shao et al. (2017) for systems using synthetic tracking.

• The slew time is 10 s as in Shao et al. (2017).

36 Table 5.3: Surveillance system parameters used in test cases.

S17 S18 NS TS

Da [cm] 10.0 27.9 15.7 30.0 f [cm] 40.63 61.72 89.30 75.63 ✏ 0 0 0.33 0 ⌧ 0.8 0.7 0.8 0.8 QE 0.8 0.8 0.8 0.8 spx [”/pixel] 3.30 1.27 3.00 3.00 wpx [µm] 6.5 3.8 13.0 11.0 Number of pixels 4,096 4,096 11,960 11,960 1,024 1,024 2,048 2,048 ⇥ ⇥ ⇥ ⇥ NRN [e] 1.20 1.70 2.0 1.6 NDC [e/pixel/s] 0.006 - - 0.400 FOV [(°)2] 14.1 17.80 0.73 2.91 2 FOVd [(°) /day] 1494 1887 3146 309 tSE[s] 3.30 1.27 10.00 3.00 tTE[s] 800 800 10 800 ⇣lim [°/day] 12 12 3.6 12

Recalculated Vlim [mag] 20.55 22.44 18.36 21.92 C [GFLOPS] 74 11,035 - 25

• The straddle factor (k) is given a typical value of 0.4 (Hejduk et al., 2004).

• Background sky brightness is assumed to be 22 mag/(”)2 (Romanishin, 2006).

• The centre of the total field-of-view is at the median oppositioncentric latitude and longitude of detected minimoons.

In addition to examining the four aforementioned surveillance systems in all of the observatory locations listed earlier in this section, the e↵ects of Vlim and velocity search range on the visible fractions are examined at speculated orbits which would spend time close to favourable observatory locations.

37 6 Results

As of late-2018, the used 6DGRTD is considered to be almost certainly wrong and therefore the results should be taken with great caution. Nonetheless, the section shows how results could be interpreted. The instantaneous visible fraction vf and instantaneous visible fraction in FOV per day, vfd, are calculated for each case at each observatory location. From now on the term visible fraction is used instead of instantaneous visible fraction. Visible fraction describes the fraction of the steady-state population that is visible to the observer. Visible fraction in FOVd describes the fraction of the steady-state population that is visible during one day of observing. High vfd means that the visible population is more dense on some specific area in the sky-plane which would be beneficial when observing. The observed population is based on the latest minimoon model which has not been used in earlier studies and thus, comparing the results with earlier estimates is dicult. In Bolin et al. (2014) it was estimated that LSST would have 0.27 H<38 minimoons in its FOVd. H<38 corresponds to 10 cm diameter and larger objects. This population including also smaller minimoons is many times more larger in the EMS but naturally the smaller minimoons are also many times more dicult to observe. The results presented in this section give direction to the type of orbit that could be considered for a surveillance system to have as many visible minimoons as possible in the sky-plane. The results from di↵erent cases represent what is theoretically visible to the systems. More attention is given to the analysis of better performing systems. The biggest limitation of this analysis is not considering the refresh rate of the minimoons in the sky-plane distribution. This would help to translate the visible fractions to detected minimoons over some observational time period. The average angular velocity of the visible population is the best indicator of how fast the minimoons change in the sky- plane. Nevertheless, the results are clear on which locations and eventually orbits should be further studied. To be able to draw conclusions from the patterns in the sky-plane distributions, the synthetic minimoon counts in the 3° 3° bins of the sky-plane distribution should be in ⇥ the order of tens. It is also to be noted that di↵erent color scales are used in the figures to have more clarity. In addition to presenting the results for the surveillance systems at the observatory locations presented in previous section, results from some speculated orbits are presented and it is shown how the visible fractions change when limiting magnitude and velocity search range are varied.

38 6.1 Case S17

In case S17, the number of synthetic minimoons in the bins of sky-plane distributions range from zero to eight, which is too little to properly draw conclusions from the pat- terns in the sky-plane distributions. The visible fraction is next to zero especially outside 45° opposition-centric ecliptic longitude and latitude even at the best location which is ± illustrated in Figure 6.1. As expected, the highest bin counts in the sky-plane distribution are close to the opposition where the phase angle is the smallest and there is a rapid increase in the apparent brightness. The results from the locations with highest visible fractions are listed in Table 6.1. The average angular velocity is significantly less for visi- ble objects close to Earth-Sun L2 where the visible fraction was the lowest. The median angular velocity is 3.2°/day so the lower average is not due to few extreme velocity objects that would have a significant e↵ect on the average when the number of objects is lesser. The slower average angular velocity is due to the higher geocentric distance of the objects. More attention is given to case S18 where the bin counts are suciently high for proper analysis.

Table 6.1: Results from the ten observatories which had the highest visible fractions and the observatory location where the lowest visible fraction was recorded with S17. The average ⇣ considers only visible minimoons.

de e [ °] e [ °] vf vfd Minimoons Average ⇣ [ °/day] 2.0 LD 0 0 0.002255 0.000921 0.0512 6.0 2.5 LD 0 0 0.002154 0.000971 0.0489 5.7 2.0 LD 0 15 0.002123 0.000863 0.0482 5.8 1.5 LD 0 15 0.002005 0.000682 0.0455 5.8 1.5 LD 0 0 0.001999 0.000680 0.0454 5.9 3.0 LD 0 0 0.001977 0.000897 0.0449 5.0 2.5 LD 0 15 0.001962 0.000831 0.0447 5.4 2.0 LD 0 -15 0.001943 0.000733 0.0441 6.0 1.0 LD 0 15 0.001940 0.000817 0.0440 5.9 2.5 LD 0 -15 0.001864 0.000794 0.0423 5.5 4.5 LD 180 0 0.000253 0.000044 0.0058 3.9

39 Figure 6.1: Sky-plane distribution of visible minimoons at the observatory location with highest visible fraction with S17. At (2 LD,0,0).

6.2 Case S18

In case S18, the bin counts in the sky-plane distributions are an order of magnitude higher than in S17, a result of relatively high Vlim. It is important to remember the logarithmic nature of the brightness unit. The bin counts are high enough to draw conclusions from the sky-plane distributions. Table 6.2 and Figure 6.2 show that the highest visible fractions are in very similar locations to case S17. Also, the highest bin counts are where the phase angle is the lowest as usually with systems working in the visible spectrum. However, as Figure 6.3 shows, the highest values are not exactly at the peak of theoretical maximum apparent brightness but around this, which is partly due to the Earth exclusion which lowers the bin values where the opposition-centric ecliptic longitude and latitude are close to zero. At the locations with the highest visible fractions there is a 50% probability to have a minimoon in the sky-plane and 25% probability to have one inside the FOVd. However, the refresh rate of the sky-plane distribution is not considered and thus it does not trivially translate to actual detections over certain time period.

40 Table 6.2: Results from the ten observatories which had the highest visible fractions and the observatory location where the lowest visible fraction was recorded with S18. The average ⇣ considers only visible minimoons.

de e [ °] e [ °] vf vfd Minimoons Average ⇣ [ °/day] 2.0 LD 0 0 0.027150 0.012182 0.6165 5.8 2.5 LD 0 0 0.026618 0.013646 0.6044 5.4 2.0 LD 0 15 0.026271 0.011769 0.5965 5.7 1.5 LD 0 15 0.025406 0.010311 0.5769 5.8 1.5 LD 0 0 0.025070 0.009782 0.5692 5.7 2.5 LD 0 15 0.024178 0.011926 0.5490 5.3 2.0 LD 0 -15 0.023948 0.010161 0.5438 5.7 3.0 LD 0 0 0.023250 0.012129 0.5279 4.7 1.0 LD 0 0 0.023121 0.008789 0.5250 5.4 2.5 LD 0 -15 0.022792 0.010702 0.5176 5.3 4.5 LD 180 15 0.002760 0.000555 0.0627 3.5

Figure 6.2: Case S18: Visible fractions at observatory locations.

41 Figure 6.3: Sky-plane distribution of visible minimoons at the observatory location with highest visible fraction with S18. At (2 LD,0,0).

Figure 6.4: Sky-plane distribution of the median angular velocity of minimoons at (2.5 LD,0,0). Also the number sky-plane distribution of minimoons is shown.

42 Nevertheless, some estimates can be made. Figure 6.4 shows a trend in the angular velocity distribution. At (2.5 LD,0,0), where the vfd is the highest, the FOVd covers the sky approximately 22 degrees in opposition-centric longitude and latitude around the ± opposition and contains about half of the visible objects. In the FOVd the average angular velocity is 5.9°/day. Considering the direction of the minimoons in sky-plane and the square form of the FOVd, the content of the FOVd updates completely in approximately 10 days if it is assumed that the sky-plane directions and velocities of the minimoons do not change too much during that time. Thus, 40 days of observation should result in a detection. The trajectories of minimoons are fairly chaotic and therefore, to achieve a proper estimate, a simulation where the population is propagated should be performed. The average angular velocities are lower and closer to median than in case S17, which is a natural result following higher visible object counts. The ⇣lim partly explains why the average is close to 6°/day. The average angular velocities of visible minimoons are not that high in observatory locations close to Earth because even though the fastest minimoons are close to Earth, not many of them are visible and thus a↵ect the average. To have similar computational load as in case TS, the velocity search range would have to be only 2°. Such decrease would enable longer single exposures and therefore ⇡± the read noise contribution would decrease which in turn would increase the limiting magnitude of the system to 22.63 mag. In that case, the highest visible fractions would be achieved from Earth-Sun L1, as Figure 6.5 illustrates, an expected result of reduced velocity search range. Nonetheless, the increased limiting magnitude does not make up for the lesser velocity search range and the visible fraction at its highest, at (4.5 LD,0,0), is only 0.007008, which is about half of the unmodified S18 at the same location and one-fourth of the highest value what was reached with unmodified S18.

43 Figure 6.5: Case S18: Visible fractions at observatory locations when ⇣lim =2°/day to have sub-hundred GFLOPS computational load.

The peaks in the Figures 5.2 and 5.3 were discussed in Section 5. The consequence of the peaks is a region with higher minimoon density which is visible in Figure 6.6. This high density region in Cartesian coordinates is situated at approximately x = -100,000 - 100,000, y = -100,000 - 100,000 and z = 100,000 - 200,000. If observed from (1 LD,0,0), the region contains approximately 7% of the visible synthetic minimoons but only 1% if observed from (2.5 LD,0,0). There are less visible synthetic minimoons if observed from (0.5 LD,0,0) than from (1 LD,0,0) because at that distance the majority of the synthetic minimoons have too high angular velocities. This high density region is another reason why in Figures 6.3 and 6.4 the highest values are little above the ecliptic plane.

44 Figure 6.6: Case S18: ecliptic x- and y-coordinates of visible synthetic minimoons from (1 LD,0,0). Dots are not in scale.

6.3 Case NS

In case NS, the bin counts are lower than with S17. The counts are not sucient to draw conclusions from the patterns in the sky-plane distributions at any observatory location. The visible fractions are very small at every location. The relatively high FOVd due to shorter exposures resulted in high vfd/vf but the low Vlim and ⇣lim cause the weak perfor- mance. The lower ⇣lim expectedly made the locations further away from Earth to perform better. The location which is 1 LD away from Earth towards East quadrature performed the best. Observed from that location, Earth does not decrease the vf significantly and the minimoons in the sky-plane travel slower.

45 Table 6.3: Results from the ten best, highest visible fraction, and the worst locations with NS. The average ⇣ considers only visible minimoons.

de e [ °] e [ °] vf vfd Minimoons Average ⇣ [ °/day] 1.0 LD -90 0 0.000042 0.000026 0.0010 1.7 1.0 LD -90 -15 0.000041 0.000025 0.0009 1.9 2.5 LD 0 0 0.000041 0.000026 0.0009 2.1 3.5 LD 0 15 0.000039 0.000025 0.0009 1.7 4.0 LD -15 0 0.000039 0.000019 0.0009 2.0 4.0 LD 15 0 0.000039 0.000021 0.0009 1.7 3.0 LD 0 15 0.000037 0.000021 0.0008 1.9 3.0 LD 0 0 0.000037 0.000025 0.0008 1.9 3.5 LD 0 0 0.000037 0.000025 0.0008 1.6 4.0 LD 0 0 0.000037 0.000032 0.0008 1.9 4.5 LD 180 -15 0 0 0 -

6.4 Case TS

The bin counts in the sky-plane distribution are high enough for analysis at the best locations. The visible fractions at the observatory locations where the visible fractions are the highest are approximately half of what they were in case S18 as it can be seen from Table 6.4. Despite a slightly larger aperture the limiting magnitude is half a magnitude smaller than in case S18 because of higher background noise contribution which is due to the larger pixel scale. In spite of the larger pixel scale the vfd is drastically smaller in case TS because of the smaller sensor size.

de e [ °] e [ °] vf vfd Minimoons Average ⇣ [ °/day] 2.0 LD 0 0 0.013875 0.001723 0.3150 5.9 2.5 LD 0 0 0.013447 0.002301 0.3053 5.6 2.0 LD 0 15 0.013249 0.001892 0.3008 5.9 1.5 LD 0 15 0.012793 0.002260 0.2905 5.9 1.5 LD 0 0 0.012603 0.001230 0.2862 5.8 2.0 LD 0 -15 0.012072 0.001265 0.2741 5.8 2.5 LD 0 15 0.012018 0.001762 0.2729 5.4 1.0 LD 0 15 0.011990 0.001760 0.2722 5.8 3.0 LD 0 0 0.011900 0.002246 0.2702 4.9 1.0 LD 0 0 0.011710 0.001022 0.2659 5.7 4.5 LD 180 -15 0.001517 0.000053 0.0344 3.7

Table 6.4: Results from the ten observatories which had the highest visible fractions and the observatory location where the lowest visible fraction was recorded with TS. The average ⇣ considers only visible minimoons.

46 The high density region is clearly visible in the sky-plane distributions, as in the one illustrated in Figure 6.7. At (1 LD,0,15°), spherical coordinates, the e↵ect of the high density region is the most pronounced, the synthetic minimoons inside the volume constitute approximately 13% of the visible fraction.

Figure 6.7: Sky-plane distribution of visible minimoons at the observatory location, (2 LD,0,0), with the highest visible fraction with TS.

6.5 General comments on the examined cases

Cases S17 and NS did not have enough visible synthetic minimoons in the sky-plane dis- tributions to be able to draw conclusions from the patterns in the sky-plane distributions. This was due to relatively low limiting magnitudes. The highest visible fractions were recorded at observatory locations at the ecliptic plane and in the space between the Moon and Earth-Sun L1. Other than the aforementioned high density region 100,000 km above Earth, the highest counts in the sky-plane distributions were around opposition and close to ecliptic plane. Whether or not the high density region is due to a rare phenomenon needs to be investigated. A total of 0.3% of the total steady-state population were gen- erated in the bin which centre semi-major axis value is 0.000625 AU, 100,000 km. At ⇡ most this constituted a total of 13% of the visible fraction, which occurred in case TS at observatory location (1 LD,0,15°). Observatory points in the anti-Sun direction from Earth do not benefit from the high density region, which might falsely benefit locations which had the region close to zero phase angle and are not too close. However, the possible errors due to the counts regis- tered from the high density region are not large enough to drastically change the results. Observatories close to Earth had decreased visible fractions because of the presence of Earth as Figure 6.8 illustrates. Naturally the survey strategy would be adapted accord-

47 ing to orbital location and thus, an adapted FOVd and comparison by vfd could improve results of observatory locations in cislunar space. However, the visible fractions even in the best bins of close Earth observatory locations do not reach the ones of more distant observatory locations.

Figure 6.8: Case S18: The sky-plane distribution at LEO. The Earth decreases the visible fraction by reducing the observable sky and therefore the number of visible objects.

6.6 Performance on speculated orbits

The maintainability of the observatory locations with the highest visible fractions was not considered in the earlier subsections. At GEO, the visible fractions do not change noticeably during the orbital period but at a speculated circular orbit with a radius of 2 LD the visible fraction would be 0.016 on average which is the same as the average at GEO for S18. Table 6.5 shows the approximated visible fractions for S18 on speculated orbits. The values of LEO, GEO and Earth-Moon L4/L5 or polar Moon orbits are averaged from four observatory locations. Earth-Sun L1 does not move in this frame. Earth-Moon L1 or L2 are not good locations because for some of the time the Moon disrupts observation radically. The results are close to each other. As expected, the average topocentric angular velocity is the lowest at Earth-Sun L1, for which reason the refresh rate would most likely be the lowest there. For S18 as described in Table 5.3, the other alternatives are more promising. To have a more general understanding of the suitability of these four alternatives, the variations in the visible fractions are presented next for S18 if its limiting magnitude or velocity search range is varied.

48 Table 6.5: Case S18: Results for speculated spacecraft orbits. LEO: Sun-synchronous orbit with 2,000 km altitude. GEO: 35,786 km altitude. Earth-Moon L1 approximated with de = 1 LD orbit. The Earth-Sun L1 and L2 orbits approximated with observatory locations (4 LD,0,0) and (-4 LD,0,0).

Orbit vf vfd Minimoons Average ⇣ [ °/day] LEO 0.015879 0.005758 0.3606 5.3 GEO 0.016954 0.005021 0.3850 4.9 Earth-Moon L4/L5 or polar Moon 0.017804 0.006004 0.4043 5.2 Earth-Sun L1 0.017345 0.009319 0.3938 3.5

The limiting magnitude is highly dependant on the aperture size. However, the TS case well demonstrated that also other parameters such as the pixel scale and the sensor parameters have significant e↵ect. The use of synthetic tracking enables the long total exposure of 800 s, which explains why the limiting magnitude can be as high as Figure 6.9 shows for relatively small apertures. The figure illustrates how much the limiting magnitude increases as aperture diameter is increased while other S18 parameters are kept as they are presented in Table 5.3. It can be seen from Figure 6.10 that larger di↵erences between the speculated orbits would be seen with systems with larger limiting magnitudes. That could be achieved with longer exposure times but that would increase the already very high computational load. Given the S18 aperture size, Figure 6.11 shows an interesting result. The visible fraction from Earth-Sun L1 does not grow much by increasing the velocity search range. Per- forming the synthetic tracking search only in 6°/day velocity range, would decrease the ± computational load by an order of magnitude, which would in turn set the power require- ment in a more sustainable sub-hundred watts class. Decreasing the velocity search range would also allow longer single exposures which would decrease the read noise contribution and therefore increase the limiting magnitude slightly. Having the same computational re- sources, the freed resources could be spent on increasing total exposure time which would further increase the limiting magnitude. In addition, a surveillance system at Earth-Sun L1 would observe the space between Earth and Earth-Sun L1 which is not observable from Earth due to Sun exclusion. Figure 6.12 shows the distribution of visible fractions in the EMS for S18 with sub-hundred GFLOPS configuration. The decrease in visible fraction would be negligible at L1. There would be a 50% probability of having a visible minimoon in the sky-plane and over 39% probability of having it inside the FOVd.

49 Figure 6.9: Limiting magnitude as a function of aperture diameter with S18. Other specifications are as they are presented in Table 5.3.

Figure 6.10: Visible fraction as a function of limiting magnitude at speculated orbits with S18, ⇣lim = 12°/day.

50 Figure 6.11: Visible fraction as a function of maximum angular velocity at speculated orbits with S18, Vlim = 22.44 mag.

Figure 6.12: Case S18: Visible fractions at observatory locations when ⇣lim =6°/day and Vlim = 22.55 mag.

51 6.7 Summary of results

The system S18 would be able to find the most minimoons. Such surveillance system would have the most minimoons in its sky-plane if it was 1 LD - 2.5 LD away from Earth towards the Sun and observe along the ecliptic and the high density region above Earth. Table 6.6 summaries the comparison between di↵erent surveillance systems. The improved limiting magnitude and velocity search range due to synthetic tracking were expectedly remarkable. The improved FOVd due to shorter exposures with NS did not make up for the decreased detection volume per exposure. The average visible fraction with S18 was over 600 times higher than that of NS. Compared to TS, S18 had twice as high visible fraction both at the best location as well as in average. The di↵erence in the vfd is an order of magnitude due to the significantly smaller FOVd with TS. However, TS had three orders of magnitude smaller computational load due to smaller sensor size. The multiple TFLOPS load required by S18 might be challenging to achieve with MicroSat platform.

Table 6.6: The highest visible fractions and average for each system.

System de e [ °] e [ °] vf vfd Average vf S18 2.0 LD 0 0 0.027150 0.012182 0.013534 TS 2.0 LD 0 0 0.013875 0.001723 0.007031 S17 2.0 LD 0 0 0.002255 0.000921 0.001173 NS 1.0 LD -90 0 0.000042 0.000026 0.000024

The performance on the speculated orbits did not vary significantly for S18. The average angular velocities were the highest if observed from the Moon orbits. Therefore it is possible that the highest sky-plane refresh rates for visible minimoons could be achieved at Moon orbits. This should be further studied as well as other orbit options to maximize time in the region in space which was shown to perform the best. However, S18 with reduced computational capabilities would have as high visible fraction as 0.017096 if placed on an orbit at Earth-Sun L1. The visible fraction would be negligibly smaller than at the speculated orbits with un-modified S18 but the ability to answer the computational load is less questionable. Such system would have approximately 21 % probability of having a minimoon in the FOVd at any given time. Considering these probabilities and the average life-time of minimoons, it can be preliminary concluded that MicroSats-based solutions have potential to discover minimoons in the EMS given that the model is correct. The results show clearly that some regions in the EMS are superior to others and give direction to more advanced simulations which could give proper estimates of detection rates. It must be emphasized that the results should be taken with great caution since the validity of the latest model is still being investigated.

52 7 Discussion

The presented results were di↵erent from the previous studies due to di↵erent distribution of minimoons in the EMS. As of late-2018, the used 6DGRTD is considered to be almost certainly wrong and it must be thoroughly investigated before further use. If the distri- bution is correct, the long lived minimoons on orbits close to Earth should be also further investigated. If there is a real high density region above Earth as the results suggest, a minimoon surveying MicroSat would benefit from having a large ba✏e to minimize stray light from Earth. Even the use of occlusion disc similar to what are used in the Sun observations could be considered. Given that the model is right, the results give a better understanding of where a MicroSat should be placed in the EMS to find minimoons. In the future, the method used in this thesis could be improved by developing an ecient method to take refresh rates into consideration. With higher computational resources and time, a simulation with propagation of the population should be performed with more accurate surveillance system performance mod- els to get a better understanding of detection rates. Such simulation could also account for the movement of the satellite. Hardware in the loop simulations should be also performed with synthetic tracking to have better understanding of the power requirements. More- over, trade-o↵studies could be performed between sky-coverage per day and exposure times. It is possible that there is no need to perform synthetic tracking in real time if the minimoons in the sky-plane do not change that often. The results could be very di↵erent in a simulation were also minimoons prior to capture would be considered. In that case, locations close to the Earth-Sun L2 could perform better. However, the space in the anti-Sun direction from Earth can be also surveyed by ground-based observatories and thus more synergy can be achieved with a space-based surveillance system which is capable of surveying the space which cannot be surveyed from the ground. A space-based surveillance system can also more likely detect minimoons close to Earth which are too fast to be detected from the ground. In the near future, more studies about the LSST’s capability to detect minimoons will be published. As of late-2018, the results have been promising. Nonetheless, there is interest in developing MicroSat-based asteroid surveillance technologies especially in the asteroid mining community.

53 8 Conclusions

This thesis provides a review of the current state of MicroSat-based asteroid surveillance technologies. There are commercial-o↵-the-shelf sensor solutions but no wide-field space telescopes for MicroSat-based minimoon surveillance. Synthetic tracking can be used to compensate for small apertures by enabling longer total exposures. The visible fractions were estimated for multiple observatory locations and speculated orbits in the Earth-Moon system for MicroSat-based surveillance systems which were mod- elled according to the findings of the literature review. From the examined systems, the one presented in Shao et al. (2018) with 800 s total exposure time had the best perfor- mance. According to the latest minimoon model, there is a high density region above Earth. If observed from 2 lunar distances away from Earth towards the opposition there could be 2.7% of the half a meter and larger minimoon population in the sky-plane. This translates to approximately 60% probability of having a visible minimoon in the sky-plane at any given time. With less capable system at Earth-Sun L1, the probability would be 40%. The first mentioned observatory location is not maintainable with known obits and thus over a longer time period the Earth-Sun L1 location would most likely perform better. Detection rates were not estimated. The used 6DGRTD is currently considered to be almost certainly wrong and therefore the results should be taken with great caution. If the distribution is later considered right, the results give direction to which type of orbits should be further studied. Simulations with propagation of the minimoon population are suggested to be able to properly account for changes in visible minimoons in sky-plane distributions. The work done during this thesis project has improved the understanding of older results. In addition, a platform for simulating sky-plane distributions at various locations with optical surveillance systems was developed. Some of the data handling must be performed manually.

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59 Appendices

A Observatory-file format

The observatory-file is given to OpenOrb with command --obs-in= in .gaia3 format, which is presented in Table A.1. Designation code, ID, refers to the target of observation. The observation time is given as days from Modified Julian Date 55197, which corresponds to 2010-01-01-0. The coordinates of the observatory are given with an accuracy of 17 digits in the geocentric equatorial frame in AU.

B Objects-file format

The objects-file is given to OpenOrb with command --orb-in= in .des format, which is presented in Table B.1. The orbital elements are given with 10 digit accuracy. Coordinate system is KEP3, which refers to Keplerian elements of the third planet from the Sun which is Earth. The orbital elements are given in the geocentric ecliptic frame in degrees and AU.

60 Table A.1 The observatory information is given in .gaia3 format.

61 ID CCD MJD 55197 + dt pos(2) pos(3) cov(2,2) cov(2,3) x y z x/day y/day z/day TCA000000001 -1 79.7305... 0 0 0 0 0 0.00868... 0.00092... -0.00213... 0 0 0 TCA000000002 -1 79.7305... 0 0 0 0 0 0.00868... 0.00092... -0.00213... 0 0 0 ...... Table B.1 The objects information is given in .des format. ID COO a e i ⌦ ! M0 H MJD INDEX NPAR MOID CC

TCA000000001 KEP3 0.013... 0.65... 171.03... 215.01... 51.34... 327.53... 32.05... 55276.73... 1 6 -1 OPENORB 62 TCA000000002 KEP3 0.00... 0.59... 176.20... 299.06... 45.873... 158.24... 33.80... 55276.73... 1 6 -1 OPENORB ...... TRITA TRITA-EECS-EX-2018:694

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