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Use of light curve inversion for nonresolved optical detection of satellites performing on orbit servicing in the presence of geostationary satellites Thesis Proposal

R.L. Scott

Defence R&D Canada – Ottawa

Technical Memorandum DRDC Ottawa TM 2010-257 December 2010

Use of light curve inversion for non- resolved optical detection of satellites performing on orbit servicing in the presence of geostationary satellites Thesis Proposal

R.L. Scott

Defence R&D Canada – Ottawa Technical Memorandum DRDC Ottawa TM 2010-257 December 2010

Principal Author

Original signed by Robert Scott Robert Scott Defence Scientist RAST/SSG

Approved by

Original signed by Caroline Wilcox Caroline Wilcox RAST Section Head, Radar Applications and Space Technologies

Approved for release by

Original signed by Chris McMillan Chris McMillan Chief Scientist, DRDC Ottawa

© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2010 © Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2010

Abstract ……..

This thesis research proposal presents a non-resolved optical detection research approach to infer the presence of satellites performing On Orbit Servicing (OOS) in geostationary orbit. The recent successes of autonomous robotic servicing missions such as Orbital Express and DART are showing that OOS is becoming a technically viable reality. OOS poses a new problem for space surveillance as the performance of proximity operations about client satellites is difficult to detect and differentiate at geostationary satellite ranges. The detection issue is that both the client and servicing objects are non-resolved, and cannot be differentiated by traditional optical space surveillance systems. To overcome this issue this proposal investigates the use of photometric light curve inversion to infer the presence of the secondary object. Numerical simulations will be used to estimate and parameterize appropriate kernel functions to deconvolve two optical signatures in order to provide evidence of the secondary object's presence. Applications of this work permit the detection and verification of secondary objects in close proximity to geostationary satellites in GEO orbit with low cost optical equipment. This work may potentially also be used to determine if an object has shed large breakup debris moving with slow relative motion with respect to the parent object.

Résumé ….....

La présente proposition de recherche de thèse expose une approche de recherche sur la détection optique non réglée pour déduire la présence de satellites effectuant l'entretien courant en orbite (OOS) à l'orbite des satellites géostationnaires. Le succès remporté dernièrement par les missions d'entretien courant robotisé autonome, comme l'effort Orbital Express et l'équipe d'intervention en cas de catastrophe (DART), montre que l'OOS est en voie de devenir une solution techniquement viable. L'OOS pose un nouveau problème pour la surveillance de l'espace, du fait qu'il est difficile de détecter et de distinguer le rendement d'opérations de proximité à propos de satellites clients aux distances des satellites géostationnaires. L'enjeu en matière de détection, c'est que les objets client et d'entretien courant sont tous les deux non déterminés et impossibles à distinguer à l'aide de systèmes classiques de surveillance optique de l'espace. Pour surmonter cet enjeu, dans la présente proposition on étudie l'utilisation de l'inversion de la courbe de la lumière par photométrie pour déduire la présence de l'objet secondaire. Des simulations numériques permettront d'estimer les fonctions appropriées du noyau et d'en établir les paramètres pour déconvoluer deux signatures optiques dans le but d'établir des indices de la présence de l'objet secondaire. Les applications de ces recherches permettent la détection et la vérification d'objets secondaires munis de matériel optique peu coûteux à proximité rapprochée de satellites géostationnaires sur l'orbite des satellites géostationnaires. Le présent travail pourrait également servir à déterminer si un objet a délesté de gros débris par fractionnement qui se déplacent plutôt lentement par rapport à l'objet principal.

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Executive summary

Use of light curve inversion for non-resolved optical detection of satellites performing on orbit servicing in the presence of geostationary satellites: thesis proposal Robert Scott; DRDC Ottawa TM 2010-257; Defence R&D Canada – Ottawa; December 2010.

Introduction or background: This doctoral thesis proposal proposes research aimed at the long range detection of small secondary satellites performing On Orbit Servicing (OOS) of client satellites in geostationary orbit. The recent successes of autonomous robotic servicing missions such as Orbital Express and DART are showing that OOS is becoming a technically viable reality for flight operations. As these kinds of servicing missions are feasible, OOS poses a new problem for the space surveillance community.

As the two satellites enter close formation flight with one another, it becomes very difficult for traditional space surveillance systems to differentiate the spacecraft from one another. The detection issue is that both the client and servicing objects are non-resolved (point source in appearance), and cannot be differentiated by traditional optical space surveillance systems.

This proposal, if accepted, is to investigate the use of photometric light curve inversion to infer the presence of the secondary object. Numerical simulations will be used to estimate and parameterize appropriate kernel functions to deconvolve two optical signatures in order to provide evidence of the secondary object's presence. Applications of this work permit the detection and verification of secondary objects in close proximity to geostationary satellites in GEO orbit with low cost optical equipment. This work may potentially also be used to determine if an object has shed debris moving with slow relative motion with respect to the parent object.

Results: The thesis proposal was approved by a board of four Carleton University review members (Dr. Alex Ellery, Dr. Tarik Kaya, Prof. Andrei Artemev, and Prof. Anton de Ruiter). An external reviewer Dr. Martin Levesque (DRDC-Valcartier) was also present. Minor edits to the original text of the proposal were identified and were corrected in this reproduced version. The proposal was given a passing grade and the research work is now in progress.

Significance: This research will now begin adhering to the schedule detailed in part four of this report. If successful, this research could provide a technique for small aperture systems to be used to determine the presence of secondary objects performing proximity operations. If successful, this technique could be exploitable as a means to infer the presence of objects around Canadian satellites.

Future plans: This work is planned to be completed by 2013. Conference and journal papers pertinent to this work are identified in section 4 of this report.

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While autonomous OOS space missions are not currently performed, this work could assist the space surveillance community to mitigate future problems or potential threats that this technology could bring.

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Sommaire .....

Use of light curve inversion for non resolved optical detection of satellites performing on orbit servicing in the presence of geostationary satellites: thesis proposal Robert Scott; DRDC Ottawa TM 2010-257; R & D pour la défense Canada – Ottawa; décembre 2010.

Introduction : La présente proposition de recherche de thèse de doctorat fait connaître une recherche visant la détection à grande distance de petits satellites secondaires effectuant l'entretien courant en orbite (OOS) de satellites clients sur l'orbite des satellites géostationnaires. Le succès remporté dernièrement par les missions d'entretien courant robotisé autonome, comme l'effort Orbital Express et l'équipe d'intervention en cas de catastrophe (DART), montre que l'OOS est en voie de devenir une solution techniquement viable pour les opérations aériennes. Du fait que ces types de missions d'entretien courant sont possibles, l'OOS pose un nouveau problème pour le milieu de la surveillance de l'espace.

Lorsque les deux satellites entrent en formation serrée l'un par rapport à l'autre, il devient très difficile, pour les systèmes classiques de surveillance de l'espace, de distinguer un engin spatial de l'autre. L'enjeu en matière de détection, c'est que les objets client et d'entretien courant sont tous les deux non déterminés (source ponctuelle en apparence) et impossibles à distinguer à l'aide de systèmes classiques de surveillance optique de l'espace.

La présente proposition, si elle est acceptée, vise l'examen de l'utilisation de l'inversion de la courbe de la lumière par photométrie pour déduire la présence de l'objet secondaire. Des simulations numériques permettront d'estimer les fonctions appropriées du noyau et d'en établir les paramètres pour déconvoluer deux signatures optiques dans le but d'établir des indices de la présence de l'objet secondaire. Les applications de ces recherches permettent la détection et la vérification d'objets secondaires munis de matériel optique peu coûteux à proximité rapprochée de satellites géostationnaires sur l'orbite des satellites géostationnaires. Le présent travail pourrait également servir à déterminer si un objet a délesté de gros débris par fractionnement qui se déplacent plutôt lentement par rapport à l'objet principal.

Résultats : La proposition de thèse a été approuvée par un jury composé de quatre examinateurs de la Carleton University (Alex Ellery, Tarik Kaya, Andrei Artemev [professeur] et Anton de Ruiter [professeur]). Un examinateur externe (Martin Levesque [RDDC Valcartier]) était également présent. Des modifications mineures au libellé initial de la proposition ont été identifiées et apportées, comme en fait foi la présente version reproduite. La proposition a obtenu une note de passage, et les travaux de recherche sont en cours.

Portée : Les présents travaux de recherche se dérouleront conformément au calendrier décrit en détail à la partie 4 du présent rapport. S'ils réussissent, ils pourraient se traduire par la mise au point d'une technique permettant l'utilisation de systèmes à petite ouverture en vue de l'établissement de la présence d'objets secondaires menant des opérations de proximité.

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Recherches futures : Les présents travaux devraient être exécutés d'ici 2013. Des documents pertinents à ces travaux publiés dans des revues ou présentés lors de conférences sont donnés à la section 4 du présent rapport. Bien qu'il n'y ait pas de mission spatiale OOS autonome à l'heure actuelle, les présents travaux pourraient aider le milieu de la surveillance de l'espace à atténuer les menaces possibles ou les problèmes futurs susceptibles de découler de la présente technologie.

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Table of contents

Abstract ……...... i Résumé …...... i Executive summary ...... iii Sommaire ...... v Table of contents ...... vii List of figures ...... ix List of tables ...... xi Acknowledgements ...... xii 1 Space Surveillance...... 1 1.1 Overview of Space Surveillance and On Orbit Servicing ...... 1 2 Literature Review ...... 5 2.1 On Orbit Servicing Definitions ...... 5 2.2 On Overview of Mission Profiles – Past Missions...... 6 2.3 Relative Motion in Geostationary Orbit ...... 6 2.3.1 Geostationary Orbit...... 6 2.4 Optical Detection of RSOs ...... 8 2.4.1 Optical Observations Objectives...... 8 2.4.2 Astronomical Magnitude System...... 10 2.4.3 Reflection of Light from Surface Materials ...... 11 2.4.4 RSO Magnitude Estimation From First Principles ...... 12 2.4.5 Light Curves...... 13 2.4.6 RSO Magnitude Estimation by Finite Element Approaches...... 14 2.4.7 Inversion Theory for Single Object Light Curves...... 17 2.4.8 Lambert Direct Inversion ...... 17 2.4.9 Hall’s Generic Approach...... 20 3 Extension of Light Curve Inversion As Applied to OOS Scenarios...... 21 3.1.1 Superposition of light curves ...... 21 3.1.2 Coupling relative motion and light curves ...... 22 4 Proposed Research...... 24 4.1 Thesis Research Objectives...... 24 4.2 Research Merit...... 24 4.3 Problem Complications ...... 25 4.4 Schedule and Tasks Summary...... 25 4.5 Equipment Requirements ...... 27 4.6 Conferences and Publications...... 28 5 Summary...... 30

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References ...... 31 Annex A .. Other Missions Demonstrating On Orbit Servicing ...... 35 A.1 DART (Demonstration of Autonomous Rendezvous and Docking ...... 35 A.2 XSS-10 (Experimental Small Satellite – 10)...... 36 A.3 XSS-11 (Experimental Small Satellite – 11)...... 36 A.4 Orbital Express ...... 37 A.5 Orbital Express Flight Profiles ...... 37 A.6 Engineering Test Satellite 7 (ETS-VII) Orihime & Hikoboshi...... 38 A.7 MITEX (Microsatellite Technology Experiment (DARPA) ...... 39 A.8 Geostationary Servicing Vehicle (GSV proposed 1989)...... 39 A.9 ROGER (Proposed)...... 39 A.10 Cone Express – OLEV (Proposed)...... 40 A.11 Tankersat (Proposed)...... 40 A.12 SUMO / FREND (Proposed)...... 40 Annex B .. Non Forced Relative Motion Trajectories...... 41 B.1 Clohessy Wiltshire Equations of Motion...... 41 B.2 Perch and Hold ...... 41 B.3 Linear Translation (Corridor Departure) ...... 41 B.4 CW hop...... 42 B.5 Radial Rendezvous ...... 43 B.6 CW Football ...... 43 Annex C .. Satellite Detectability Modelling with a CCD...... 45 List of symbols/abbreviations/acronyms/initialisms ...... 48

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List of figures

Figure 1: Geostationary satellites Anik F1 and Anik F1R (round objects) undergoing a visual conjunction and merging on the telescope detector plane. The objects are separated by ~12 kilometres at the time of closest approach...... 2 Figure 2: Orbital Express servicing Nextsat. The servicer (ASTRO) has the robotic arm captivated and docked with the client (Nextsat). Image credit: DARPA...... 5 Figure 3: Line of sight geometry for an optical observer on the Earth or from Earth orbit. The phase angle is the angle ĳ...... 9 Figure 4: CCD mage of two geostationary satellites undergoing a visual conjunction. As observed by the Ground Based Optical system in Ottawa, ON. Streaks are stars and the dots are the satellites. The right image is a cross section profile of the intensities of the two objects. Two point sources are visible in the profile as the objects are relatively well separated. The larger signal is from Anik F1. The secondary, smaller signal is from Anik F1R...... 10 Figure 5: BRDF values for common spacecraft surface materials. Figure reproduced with permission from [14]...... 12 Figure 6: Lambertian Sphere Model for estimating satellite brightness...... 13 Figure 7: Photometric light curves of common geostationary satellite bus classes. Satellite brightness increases asymptotically when phase angle reduces to less that 20°. The blank space between -20 and +20 degrees phase angle is due to the satellites entering Earth’s shadow...... 14 Figure 8: Vector and parameter definitions for luminance on a single facet of an RSO body as observed by the observer...... 15 Figure 9: Lambertian radiant intensity from a diffusely reflecting flat plate. When the rotation angle is -90 and +90 degrees, the cosine form of the radiant intensity become apparent. Beyond -90 and +90 the plate has no incident sunlight upon it and does not reflect towards the observer...... 16 Figure 10: The observer is indicated as o* and the sun vector by s*. The attitude of the satellite xyz body is rotated with respect to J2000 transformed such that the observer and sun vectors are described with respect to the individual surface normals of the body...... 16 Figure 11: D-shaped satellite object (left) and optical cross section, phase relationship (right)... 18 Figure 12: D-shaped satellite object amplitude phase representation (left) and Kernel cosine response, and observed light curve (from Lambert – [18])...... 19 Figure 13: Changing illumination conditions on the servicer between vectors O and S. Different facets of the secondary are illuminated during proximity flight...... 22 Figure 14: Proposed Schedule...... 29 Figure A-15: DART artistic renderings (Image credit: NASA) ...... 35

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Figure A-616: CW Football. The chaser begins its revolution above and moves in the direction indicated. Note that the football motion can be displaced in the intrack direction...... 44

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List of tables

Table 1: Equipment, Conference attendances and lead times ...... 27 Table 2: Proposed conference attendances...... 28 Table 3: Orbital Express Mission Profile Summary...... 38 Table 4: ETS-VII Relative Motion Profiles ...... 39 Table 5: CCD Noise Sources...... 46

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Acknowledgements

The author wishes to acknowledge the women and men of the Canadian Forces who watch the skies with great vigilance. The author wishes to acknowledge the support of the teams building Canada's first space based space surveillance systems (SAPPHIRE AND NEOSSat) whose efforts will pave the way to better orbital stewardship and situational awareness in space.

Funding support for this work comes from the Department of National Defence’s research organization Defence R&D Canada whose research program is directed by the Assistant Deputy Minister of Science and Technology. The 15es advanced research project titled “Space Situational Awareness, Exploitation and Future Concepts” is the activity in which this work is aligned.

From Carleton University, the author wishes to acknowledge Dr. Alex Ellery , Dr. Tarik Kaya and Bruce Burlton for their supervision instruction and direction. Space Surveillance is truly a multidisciplinary subject which uses technologies from diverse areas of engineering. The detection of satellites performing on orbit servicing was inspired and imagined from the systems described in Dr. Ellery’s Space Robotics coursework. The experiences described by Bruce Burton on geostationary satellite operations suggests that on orbit servicing technologies may pose new possibilities for geostationary repair.

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1 Space Surveillance

1.1 Overview of Space Surveillance and On Orbit Servicing

Space Surveillance is the detection, tracking and cataloguing of manmade Earth orbiting Resident Space Objects (RSOs). Both active, functioning satellites and inactive debris and remnants of satellites (space junk) are monitored in this context [1]. Objects from 10 cm to hundreds of meters in size, including the International Space Station, are regularly tracked by ground based systems. Canada’s activities in space surveillance are tied to the NORAD (North American Aerospace Defence Command) agreement where Canadian Forces personnel perform aerospace warning duties including both missile warning and space surveillance. Space Surveillance's usual aim is to maintain accurate orbital elements on RSOs in order to forecast the future positions of these objects. This orbital information is used by a variety of end users to perform mission operations such as predicting over-flights, collision possibilities and downlink opportunities. Attribution of ownership is also a critical role of the space surveillance catalogue as the United Nations mandates that the launching nation and owner of Earth orbiting objects must be identified for all objects launched into space [2]. The United States has held the primary role of maintaining the most comprehensive catalogue of ownership of launched spacecraft and maintains the SSN (Space Surveillance Network) to maintain the orbital catalog, while the Russian Space Surveillance system (RSSS) [1] also performs the same function.

The majority of Earth orbiting objects do not self-determine their positions during orbital flight thus independent sensors must measure the positions of the RSOs in order to estimate their orbits. Radar systems are generally used for monitoring low Earth orbit and for objects with altitudes less than 5000 km. Radars measure azimuth, elevation, and range and are excellent at performing all weather space surveillance. Electro-optical telescopes are employed on deep space objects (objects with altitudes > 5000 km) and generate “angles-only” [1] observations in either (azimuth, elevation) or (right ascension, declination) pairs. These observations have been economically taken from small, ground based robotic optical telescopes [3], larger custom optical systems [4] or even from space based assets [5].

During routine catalogue maintenance of orbiting objects, a daily task-track approach is used to direct both radar and optical sensors to take measurements of the orbital positions of the objects. These measurements are then sent to an orbit determination system which performs differential corrections to the orbital estimate and updates the orbit to the new orbital epoch [1]. This orbital update approach has worked well for many years to maintain object orbits within the catalogue. A weakness in this approach is that the tasking algorithms tend to consider the objects as individual entities and do not consider nearby orbiting objects as a factor when estimating times to observe the objects. This can be problematic as the light from two objects with very similar orbits can appear to merge on a CCD imaging plane when observed from long stand off distances. Figure 1 shows an example of two geostationary satellites undergoing a visual conjunction [6] where the objects appear to merge on the detector plane as observed by an electro-optic telescope using a CCD (Charged Couple Device) camera. The apparent increase in brightness is due to an illumination and observer angle effect which is described in section 2.4. The objects in Figure 1 were separated by 12 km at the time of closest approach. It can be imagined that two satellites

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performing close proximity operations within a few hundred meters of one another would merge together on the imaging plane, hence the objects would be unresolved.

A new challenge for Space Surveillance is being posed by new autonomous, robotic satellites which perform On Orbit Servicing (OOS) in Earth orbit. OOS is a broad subject area but the types of operations performed by this class of satellite mission would include:

• Orbital Inspection

• Rendezvous and/or docking

• Repair and Intervention

• Consumables replenishment (propellant, cryogenics, pressurant or battery replacement)

• Technology refresh (replacement of old devices with newer technology)

• Orbital Modification

• Robotic Orbital Construction

Some recent missions and experiments (see section 2.2) have performed demonstrations of OOS technologies using guidance systems and robotic manipulators designed for proximity operations around Earth orbiting satellites. The common factor of these operations is that the two objects involved (the servicer and client satellites) are in essentially the same orbit and are in very close proximity to one another. The servicing satellite will often begin proximity maneuvers when the objects close within 1 km of each other. Some missions have flown to within 50 meters of their client, or have even hard docked with them. While the missions described in Annex A were performed largely in Low Earth Orbit, many of them envisioned servicing applications in geostationary orbit. When observed from long stand off distances, two objects in proximity flight cannot be differentiated using typical optical techniques for space surveillance. In situations where the servicer satellite is much smaller, and less optically reflective than the client satellite, the servicer could potentially be masked by the larger optical reflectivity of the primary satellite, further worsening the problem of space surveillance.

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The most economically important orbit in deep space is Geosynchronous Equatorial Orbit (GEO) [1]. As the orbital period of an object in this orbit is the same as one sidereal day, a satellite placed in this orbit appears fixed on the sky and is convenient for regional and international radio communications. This orbit features the highest concentration of commercial and military satellites in deep space. Typically, service lifetime of a geostationary satellite is between 8-15 years [7] and is largely limited by propellant and battery life.

As technology development continues in OOS, the possibility of servicing missions flown to the GEO orbital regime could have an important impact on commercial and military satellite users. For commercial users, extension of the lifetime of a satellite has significant potential benefits for revenue generation, minimization of space debris, underwriting cost reduction and satellite maintenance. For the military community, servicing missions could reduce risk for lengthy theatre operations by provision of fuel or technology replacements. Optionally, a means to close surveillance of satellites of concern could be undertaken. The close proximity of satellites performing servicing missions, with or without a satellite owner's consent, poses a future detection challenge for space surveillance systems.

This document presents a research proposal for a doctorate thesis having an aim to investigate and develop a simulation toolset to infer the presence of objects performing OOS in GEO orbit and apply light curve inversion as the means to infer the presence of a secondary object. This toolset will model the optical behaviour of an object performing on orbit servicing and provide estimates of object detectability of the composite object pair on orbit. A kernel function approach to deconvolving the second satellite's optical signal from the combined pair will be applied as a means to infer the presence of the secondary object. Measures of this algorithm's effectiveness will also be developed to help ascertain the limits of this mechanism’s utility to infer the second object’s presence. Where possible, an estimate of the relative orbit of the secondary object will be made. An optional validation using visually conjuncting geostationary satellites is also proposed for this study using high performance CCD imagers.

The problem of detecting secondary objects at long range shares some of the technical challenges with the exo-solar planet discovery community where faint planetary companions have been detected near their parent stars using photometric and astrometric techniques. Astrometric techniques are not viable to detect satellites in relative motion as they do not cause a significant gravitational position deflection on the other object. The binary asteroid community shares a similar detection problem where light curves generated from minor planets are used to infer the presence of secondary objects. Some differences between OOS object observations and binary asteroid detection is that the asteroids have orbital periods consistent with the size of the semi major axis of the relative orbits, hence are Keplerian in their orbital motion. Artificial satellites undergoing relative motion in deep space are not gravitationally bound to one another; hence the natural periodicity observed in their relative motion is consistent with the orbital period of the objects. Artificial satellites generally have flat surfaces which have a characteristic response when reflecting sunlight sometimes glinting due specular reflection. Also, asteroids have rounded, powdery surfaces which tend to have diffuse reflectivity characteristics.

The following section provides a literature review of recent OOS missions. The literature review then expands to describe the relative motion problem for objects in nearly circular orbit geostationary orbit and describes detection theory for optical space surveillance. Light curve inversion for satellite object characterization is introduced and expanded upon for two object

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cases in section 2.5.8. Section 3 identifies how the problem of light curve inversion is expanded for the dual object case for OOS. The proposed research and methodology is identified in section 4 where a preliminary breakdown of tasks and an implementation approach are discussed. The document concludes with a schedule and resource estimate for this study.

This proposed work is sponsored by the Radar Applications and Space Technologies section of Defence Research and Development Canada (DRDC). DRDC has worked in the area of space surveillance for several years supporting the NEOSSat (Near Earth Orbit Surveillance Satellite) microsatellite and the SAPPHIRE space surveillance missions. This work is aligned with the future concepts and challenges portion of the 15es Exploitation and Future Concepts Advanced Research Project (ARP) in space surveillance. This portion of this ARP project focuses on future space surveillance mission types will cause potential problems to current space surveillance systems. OOS is one of the mission types which could become a challenge to space situational awareness.

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2 Literature Review

2.1 On Orbit Servicing Definitions

This proposal uses the following definitions for RSOs performing OOS or proximity operations.

The “client” (or “primary”) satellite is the RSO which is being serviced or is the subject of study by the secondary satellite performing the service. In robotic parlance, the client satellite could be considered the “work” on which robotic manipulation is applied. In the relative motion context this satellite is usually considered to be the center of the relative motion coordinate frame. The client satellite would be considered to be a customer in situations where the client is being assisted or aided by the servicer (defined in the next paragraph). For the missions envisaged in this thesis proposal the client satellite would be a communications or science satellite in geosynchronous orbit.

The “servicer” (also referred to as “deputy” or “secondary”) RSO is the satellite that is performing the robotic servicing and enters into relative motion with or docks with the client. The servicer would contain a set of servicing tools in order to perform inspection of the client or perform robotic intervention. This toolset could contain imaging cameras, robotic manipulators, shears, fluid interface adapters or propulsion systems in order to support the servicing operations.

Figure 2: Orbital Express servicing Nextsat. The servicer (ASTRO) has the robotic arm captivated and docked with the client (Nextsat). Image credit: DARPA

“Cooperative” and “Non-Cooperative OOS” describes the nature of the client satellite as to whether or not it is participating with the servicer during its intervention. In cooperative OOS a client would work with the servicer in order to ensure that proximity and docking operations are performed in a manner where collision risk is minimized. The client is also expecting and wanting the services of the servicer satellite.

Non cooperative OOS describes missions where the servicer is attempting to inspect or rendezvous with an uncontrolled client spacecraft. Or, the servicer could be performing proximity operations near a client satellite which is active, functional and stabilized, however the client is unaware (and possibly un-desiring) the intervention of the servicer. Military applications are also possible. OOS could be used by an adversary for covert reconnaissance or interference with

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satellite assets of friendly countries. OOS missions are not envisaged to perform this type of activity at this time as most applications emphasize on refuelling and repair of satellites, however, the technologies developed for OOS could create new military capabilities. It therefore becomes desirable for a friendly country to be able to perform long range detection of secondary objects near client satellites.

The proximity distances between the two RSOs in this proposal are largely sensor dependent as the detection system dictates the degree of resolution of two separate objects. For the purposes of this document, proximity operations are a coordinated flight profile which takes the servicer within 1 kilometre of the client satellite or less (~5 arcseconds of angular separation at geostationary satellite ranges).

2.2 On Overview of Mission Profiles – Past Missions

Several missions which have demonstrated technical aspects of OOS have been performed in the past both telerobotically, by astronauts or by autonomous flight demonstration. Astronauts have attempted servicing the Spartan satellite (where the servicing failed), but were successful with the servicing of the Westar, Solar Max, Hubble Space Telescope and International Space Station [8]. Annex A contains a listing of mission profile summaries which were examined in the preparation of this proposal. The missions primarily began proximity operations within six kilometres of one another, while more complex missions have flown within 10 meters, or had even hard docked with their clients.

2.3 Relative Motion in Geostationary Orbit

2.3.1 Geostationary Orbit

Geostationary orbit is an abstraction [9] which can only be realized if a satellite were orbiting the Earth directly above the equator and not subject to perturbations from either gravitational or other bodies. Ideally, the satellite is placed at a particular longitude with a circular orbital velocity such that the satellite completes its orbital period in one sidereal day. This corresponds to a mean motion of 7.292 x 10-5 rad/sec, hence

P n 3 AGEO |o 5.164,42 km )1( AGEO

5 3 2 Where ȝ is Earth's gravitational constant (3.986x10 km /sec ), AGEO is the semi major axis of the orbit and n is the mean motion of the satellite. Since the ideal geostationary satellite is constrained to the equatorial plane and is circular in shape, the eccentricity and inclination of the satellite is zero, hence ie )0,0(

The inertial position of the satellite is expressed as equation 2:

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ªxi º ªr cos( )cos(DG )º » r «y » «r cos( DG )sin() (2) « i » « » ¬«zi ¼» ¬« r G )sin( ¼»

Where Į is the right ascension of the satellite, į is the declination of the object. The longitude of the geostationary satellite Ȝ, known as the mean longitude of the satellite is the difference between the object’s right ascension Į and the sidereal angle to Greenwich șG (zero longitude).

O D T G (3)

Synchronous orbital elements are usually used when describing geostationary orbits. The ascending orbital node is not defined for a purely equatorial orbit however real geostationary orbits do have a defined nodal crossing. The set of synchronous elements is:

ªex º ª Z : )ecos( º «e » «esin(Z : )» « y » « » «ix » « i cos(:) » (4) « » « » «iy » « i :)(sin » « » « » ¬Ga¼ ¬ aa GEO ¼

Where ȍ is the right ascension of the ascending node and Ȧ is the argument of perigee. The eccentricity vector (ex,ey) points towards the geostationary orbit’s perigee and the inclination vector (ix,iy) is the projection of the orbital inclination vector on the equatorial plane.

2.3.2 Relative Motion of Spacecraft

The Clohessy-Wiltshire (CW) equations of relative motion are used extensively in formation flight [1] to describe motion of satellites during proximity operations. The following set of equations from Vallado [ibid] describes the relative motion of objects in circular orbits. In this convention, x is radial direction along the radius vector of the satellite's orbital position, y is the along track position of the servicer (where the curvature of the parent object’s orbit is neglected over the small distances under consideration) and z is the cross-track position which is orthogonal to the orbital plane.

2 ª f x º ª 32 ZZ xyx º « » « f » 2Zxy (5) « y » « » « » « 2 » ¬ fz ¼ ¬ Z zz ¼ P Z 3 )6( AGEO

It is evident from the above expressions that motions in the radial and along track plane are coupled while motion in the cross track direction is uncoupled from the other two directions. The motion in the cross track direction is that of a simple harmonic oscillator.

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The solution of these equations for no external forces (fn = 0) on the servicer, the CW formulation as reproduced by Vallado [1], can be solved explicitly for a set of known initial conditions for initial position and velocity (equation 7).

1 2 ª tx )( º ª 34 cos(Zt 00) Z Zt Z Zt 0))cos(1()sin( ºªx0 º « » « »« » ty )( 1(6 cos(Zt 01)) 2 Zt 4 Z tt 0)3)(sin()1)(cos( y « » « Z Z »« 0 » 1 « tz )( » « 00 cos(Zt 0) 0 Zt)sin( »«z0 » « » « Z »« » (7) « tx )( » « ZZ t 00)sin(3 cos(Zt Zt 0)sin(2) »«x0 » « » « »« » ty )( ZZ t 00)1)(cos(6 Zt 4)sin(2 cos(Zt 03) y0 « » « »« » ¬« tz )( ¼» ¬« Sin ZZ t 0)(00 0 Zt)cos( ¼»¬«z0 ¼»

>@>@>@X t)( CW X0 (8)

1 >@>X0 CW @>@X t)( (9)

These relations have been found to work well in simulated relative motion in geostationary orbit studies as Earth’s gravitational aspheric nature and luni-solar perturbations affect both satellites similarly, hence can be neglected. Kawasse [10] found in his simulations that the differences in propagation using Hills expressions and a numerical propagation using a comprehensive force model differ by approximately 10 meters. The CW relations are a good first order representation of the relative motion of two objects in close proximity flight. Examples of special motion cases are shown in Annex B.

2.4 Optical Detection of RSOs

2.4.1 Optical Observations Objectives

The objective of taking optical observations for Space Surveillance is to obtain space object characterization data (used for Space Object Identification or SOI) or metric data (orbital position measurements). The first SOI characterization of an Earth orbiting satellite was performed at the Kennedy Space center after the launch of Sputnik in 1957 [11]. Today a wide variety of electro optical sensors are deployed worldwide taking both metric and SOI data on Earth orbiting satellites.

SOI uses techniques familiar to astronomical observations of planetary or stellar objects where characteristics such as object size, rotational period, spectral content or color can be determined using the detected electromagnetic radiation from the emitting object. In cases where the satellites are sufficiently close to the observer or the observer has adaptive optics systems, resolved imaging can be performed to detail the RSO’s orientation, shape and configuration.

Metric observations are used in the orbit determination update process. Optical metric observations of the RSO are often referred to as "angles only" relative to the observing sensor and are expressed as bearing angles in either topocentric azimuth elevation, or topocentric right

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ascension and declination pairs. These observations normally use background star fields or mount gimbal angles for recording angular position. It should be noted that range is not normally determined for single sensor observations. If the sensor was equipped with an illuminating source, such as a laser ranging system, an object's range could also be added to the observations.

rsun

rRSO

Topocentric position of x observer

Figure 3: Line of sight geometry for an optical observer on the Earth or from Earth orbit. The phase angle is the angle ĳ

As deep space RSOs are generally observed at ranges from 5000 to 40,000 kilometres, the objects are non-resolved and appear as a point source of light as seen by the observer. The observed angular extent of the physical structure of the satellite is less than the minimum resolvable angle which can be produced by the optical system, often estimated by the Rayleigh and Sparrow criterions [12]. O O T 22.1 (10) T (11) Rayleigh D Sparrow D

Where Ȝ is the wavelength of light and D is the aperture diameter of the optical system. The Rayleigh limit expresses the location where diffraction limited optics produce a 50% depression in the peak intensities of two closely spaced Point Spread functions (PSF). The Sparrow limit is a tighter definition and expresses where no depression in the peaks is observed. Diffraction limited observations with a 35 cm telescope and CCD camera with a peak sensitivity at 600nm, the PSF size has an angular extent of 2.1 microradians (~0.43 arcseconds). An object orbiting in the geostationary belt with a maximum extent of 50 meters subtends an angular size of 0.26 arcseconds when viewed from the Earth. Hence the object appears non-resolved. The natural

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turbulence of Earth's atmosphere increases the dispersive effect which further degrades the point spread function of an optical imager.

Figure 4: CCD mage of two geostationary satellites undergoing a visual conjunction. As observed by the Ground Based Optical system in Ottawa, ON. Streaks are stars and the dots are the satellites. The right image is a cross section profile of the intensities of the two objects. Two point sources are visible in the profile as the objects are relatively well separated. The larger signal is from Anik F1. The secondary, smaller signal is from Anik F1R.

2.4.2 Astronomical Magnitude System

Electro-optic space surveillance is usually performed by the detection of sunlight reflected by an Earth orbiting object or the detection of the radiated heat from the object surfaces at IR wavelengths. In the optical electromagnetic waveband between 300 and 1100 nanometres, reflected sunlight from large RSOs is often bright enough to be detected by small aperture optical telescope systems. This is advantageous for Space Surveillance operators as RSOs orbiting in deep space need not be illuminated by the sensor as in radar applications. Radars suffer 1/R4 range loss in reflected power as detected by the sensor. As the illumination source is the sun, economic detection of objects can be achieved [3].

The unit of brightness used for telescope observations to describe the detected photometric flux is the astronomical magnitude system, first used by Hipparchus [13]. This system describes the “faintness” of a source where positive numbers indicate fainter objects, A 100-fold ratio of flux corresponds to a difference of five magnitudes (equation 12).

§ f · ¨ 2 ¸ MM 21 5.2 log10 ¨ ¸ (12) © f1 ¹

To estimate satellite brightness, the definition of the optical cross section of the satellite [14] is useful when referencing the sun as the illuminating source. The optical cross section is the linearized detected intensity of the reflected object as measured by the observer. The observed

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radiant intensity of an RSO as seen by an observer is estimated with respect to the object’s range and the optical cross section (ı0) which is the effective cross sectional area per steradian: I V I sun 0 (13) RSO R2

2 Where R is the range to the satellite (in meters) ı0 is the optical cross section (m /sr) and Isun is the reference intensity of the sun. Converting this expression to magnitudes [14] yields

§ V 0 · RSO MMv sun 5.2 log10 ¨ ¸ (14) © R 2 ¹

The optical cross section is a product of a surface’s reflection properties, object shape, illumination and observer geometry and surface area. The following section defines the optical cross section for an elemental plate surface.

2.4.3 Reflection of Light from Surface Materials

The degree to which materials appear shiny, or matte (diffuse) is described by a material's Bi- directional Reflectance Distribution Function (BRDF) [14]. A material with a high BRDF tends to reflect light into tight cones with little divergence and is often described as specular (mirror- like), while matte materials are described as diffuse as the reflected light intensity is unchanged at any viewing angle (such as paper). Most materials have a BRDF between diffuse and specular reflective properties. The hemispheric reflectivity of a diffuse surface [14] is determined by equation 15.

2S S U 2 BRDF ),( cos sin dd ITTTIT (15) ³³00

In practice, many materials used in space systems have BRDFs that mimic diffuse reflectors for large off-normal viewing conditions but become highly reflective and exhibit asymptotic reflectance behaviour when the observer looks into the plate normal direction. This behaviour is observed on the solar panels of large satellites when their phase angles approach zero (see figure 5). The detected magnitude of the satellites become extremely bright, consistent with the behaviour of the largest reflecting optical surfaces on the satellites of solar panel material seen in figure 4 when the viewing direction approaches the normal of the plate.

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Figure 5: BRDF values for common spacecraft surface materials. Figure reproduced with permission from [14].

The optical cross section of the satellite can be determined by summing the optical cross section of a summation of plates of which it is composed. The optical cross section of a plate is estimated by equation 16.

V 0 ³ BRDF , coscos TTTT oioi dS (16) S

Where și, șo are the incident and observer angles relative to the object surface. For diffusely scattering objects, the expression simplifies to

coscos TTUV dS (17) 0 ³ i o S

2.4.4 RSO Magnitude Estimation From First Principles

Estimation of an object’s brightness from first principles usually begins by using Lambertian diffuse scattering laws for simple shapes such as spheres (figure 6) and plates (figure 8) and ignores BRDF nonlinearities. The major factors affecting satellite brightness are the variables of solar intensity, albedo, size, shape aspect and phase angle viewing geometries.

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RSO

rSUN

rRSO

Observer “o”

Figure 6: Lambertian Sphere Model for estimating satellite brightness

The magnitude of the spherical object as seen by the observer can be estimated by equations 20 and 21 [13].

Mv 5.274.26 log10 DFA M 0.5 log10 R (20) 2 F M cos sin MMMS (21) 3S 2 where AĮ is the area-albedo product [m2], F(ĳ) is the phase function of the object under consideration, the visual magnitude of the sun is the constant (-26.74), R is the range to the object in meters and ĳ is the object centric phase angle. The phase angle is a convenient viewing geometry which provides an indication of the degree of which an object is illuminated and is visible to the observer. Smaller phase angles, similar to full moon conditions, feature a brighter object. Larger phase angles, such as new or quarter moons, are fainter and not as fully illuminated.

2.4.5 Light Curves

Measurements of magnitude versus time or phase angle can produce useful data which can be used to infer characteristics of non resolved objects. These types of measurements usually use normalized astronomical magnitude measurements. An example of light curve measurements taken on a variety of satellite geostationary buses is shown in figure 7. Depending on the viewing geometry (phase angle conditions), geostationary satellites can produce significant brightness variations depending on their physical configuration or reflectance. The Boeing 702C satellites exhibit a curled visual magnitude effect which is due to the dihedral mirror concentrators adjacent to their solar panels, while other geostationary satellites have a more linear behaviour, indicating solar panels which track the sun.

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All Observed Satellite Bus Classes

7 BSS-702C BSS-702S Eurostar 3000S HS-601 8 LM A2100AX LS-1300

10 GBO Mv,

14 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 Phase Angle (deg) Figure 7: Photometric light curves of common geostationary satellite bus classes. Satellite brightness increases asymptotically when phase angle reduces to less that 20°. The blank space between -20 and +20 degrees phase angle is due to the satellites entering Earth’s shadow.

2.4.6 RSO Magnitude Estimation by Finite Element Approaches

A flat plate which is observed under various illumination (s) and observation directions (o) as in figure 8 can be used as an elemental building block to model the total reflected sunlight from an aggregation of plates representing a competed satellite assembly.

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FSun Oobs

ok șo sk șs

akAk

Figure 8: Vector and parameter definitions for luminance on a single facet of an RSO body as observed by the observer.

ª toF pn ts pn ),(),( º tL ,, pp Aa kSun attitude k attitude (22) attitude body ¦ k k « » k ¬ S ¼

th Where nk is the normal of the k plate, ak is the reflectivity of the plate and Ak is the total surface area of the plate [15]. The dot products are the cosine terms of the incidence and observation angles relative to the plate normal and the angular brackets denote the non-negative operator which captures the effect that only the outward facing surfaces of the satellite object reflect sunlight to an observer. The non negative operator is defined in equation 23 and the cosine response nature of equation 22 is shown in figure 9.

x½ t 0x x { ® ¾ (23) ¯0¿ x 0

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Radiant Intensity For Diffusely Reflecting Flat Plate 1200

1000

800

600

400 Radiant Intensity (W/st) Intensity Radiant

200

0 -150 -100 -50 0 50 100 150 Phase / Rotation angle (degrees)

Figure 9: Lambertian radiant intensity from a diffusely reflecting flat plate. When the rotation angle is -90 and +90 degrees, the cosine form of the radiant intensity become apparent. Beyond - 90 and +90 the plate has no incident sunlight upon it and does not reflect towards the observer.

z J2000

zb s*

x J2000 yJ2000 xb yb

Figure 10: The observer is indicated as o* and the sun vector by s*. The attitude of the satellite xyz body is rotated with respect to J2000 transformed such that the observer and sun vectors are described with respect to the individual surface normals of the body.

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Inherent to this relationship is that the normal vectors for each facet, the shape and the attitude of the RSO under study must be known. The observer vector o, in the body frame of the satellite, is expressed as:

t po attitude >@>@tR ,(),( attitude op t)(* (24)

Where the * subscript denotes the inertial frame and pattitude indicates the specification of the satellite's attitude as a function of time and the R(t, pattitude) is the Euler rotation sequence. The satellite to sun (s) inertial unit direction vector can be similarly written.

t attitude >@>@t attitude ),(),( spRps t)(* (25)

When combined with the body parameters which capture the shape of the object and the reflective properties of the individual surfaces, an estimate for the Lambertian reflectance from a particular facet can be made. Inclusion of specular behaviour in the estimation of the object magnitude provides improved fidelity of the model. Assuming the range differences between the sun and the satellite are small such that the solar flux is assumed constant equation 26 can be used.

tL attitude ,, pp body

ª BRDF a cos( k to pn attitude k to attitude k ts pnpn attitude ),(),(),( º ¦ AF kSun « » (26) k ¬ S ¼

2.4.7 Inversion Theory for Single Object Light Curves

The following sections describe the application of Inversion theory to non resolved object satellite detection. Inversion theory has been used by the asteroid astronomy community (Ostro [16] and Kaasalainen [17]) to determine the shape and spin orientation of asteroids by examination of light curve and radar reflectance properties. These approaches were modified by Lambert [18] to accommodate the artificial nature of manmade satellites. In contrast to asteroids, satellites generally have flat faces and sharp edges instead of smooth, rounded and powdery diffuse surfaces of asteroids[18]. The following sections are an overview of Inversion theory as applied by Lambert. Hall [15] identifies the mathematical basis by which satellite inversion is identified as a special case of the Fredholm integral equations in section 2.4.9.

2.4.8 Lambert Direct Inversion

Lambert [18] implemented a direct inversion approach of object light curves by using the scattering law (equation 22) as the basis function for determining object shape. The light curve detected by a sensor can be modeled as the convolution of a flat plate reflection response kernel function, (the bracketed part of equation 22) distribution such as that seen in figure 9. Ignoring

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conditions where the illumination and viewing vectors cannot observe light from the plate and BRDF conditions are suppressed, equation 22 simplifies to equation 27.

aAF T coscos T L Sun i o (27) SR 2

Where the terms și and șo are the incident and observer angles relative to the plate normal and always less than ʌ/2, otherwise the terms evaluate to zero. R is the range to the object (meters) and albedo (a), area (A) and Fsun are similar to the relationships used previously. The convolution approach works by representing an object by and amplitude ( Optical Cross Section - OCS) and phase (angular) representation of an object. In the following example from [18], a "D" shaped satellite (figure 11) has a constant optical cross section between 0 and 180 degrees, and has one larger optical cross section at 270 degrees. The convolution of the kernel and optical cross section (figure 12) shows the output light curve. This amplitude (optical cross section) and phase plot can estimate the object shape when the light curve is deconvolved.

Object Shape Optical Cross Section - Phase

0° X 90° 180° 270° 360°

Figure 11: D-shaped satellite object (left) and optical cross section, phase relationship (right)

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Amplitude (OCS) - Phase Kernel (K) response of plate

0° 90° 180° 270° 360° 0° 90° 180° 270° 360° X

Observed light curve

Y =

0° 90° 180° 270° 360°

Figure 12: D-shaped satellite object amplitude phase representation (left) and Kernel cosine response, and observed light curve (from Lambert – [18]).

For a finite number of surfaces, such as the composition of satellite structures, the convolution with the kernel function is simplified to:

f 3 )( ¦ 1 2 mfmkfkf (28) m f

Where f3 is the observed light curve, f1 is a function of the phase and mean optical cross section of the object. The function f2 is the kernel function which is, for this case, the Lambertian cosine response of the flat plate.

Lambert's approach has worked reasonably well for objects with prismatic shapes in simulations. It should be noted that flat sided objects produce amplitude-phase representations which have spikes in their signatures which are surrounded by nulls. This physical effect forms the basis for detection of the secondary object where the secondary would produce additional, anomalous light curve behaviour due to the secondary's relative motion near the first object.

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Lambert’s approach is suited to conditions where the phase angle changes are small in comparison to the object's rotational motion. In situations where large swaths of phase angles are observed, the width of the Kernel function changes [18] due to the changing illumination conditions on the surfaces of the objects.

2.4.9 Hall’s Generic Approach

Hall [15] expressed the problem of satellite light curve inversion by noting that the kernel function depends on both time and the attitude of satellite object. This is expressed generically as the integral of the differential surface area, albedo-Area product (aA) and the Kernel function of response K(t,Ȧ). This is expressed as equation 22. The kernel K(t,Ȧ) is expressed as the part in square brackets in equation 22. Suppressing the attitude parameters from equation 22, the radiant intensity of an object can be expressed as:

³ tKaAdtL ȦȦȦ ),()()( (29)

This expression is a Fredholm Integral equation [15] of the first kind which is common in signal processing where observed data is a product of two or more factors. Converting this expression to accommodate the discrete nature of the assembled materials and surfaces of a satellite assembly, satellite attitude, and the finite measurements taken by a sensor, the above equation can be expressed as:

i attitude ppL body ¦ m ZZ kimk ptKaA attitude ),,()(),( (30) ,mk

This is further simplified to

i attitude ppL body ),( ¦ j , ji pKaA attitude )( (31) ,mk

Where the objects under study now have composite material and albedo area products (aAj) and a composite kernel function. Gradient descent techniques have been applied to solve these relationships in the satellite tracking field [15].

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3 Extension of Light Curve Inversion As Applied to OOS Scenarios

3.1.1 Superposition of light curves

Two Earth orbiting objects, in close proximity or performing relative motion about each other, will produce a light curve which is the superposition of each individual object's reflectance properties, shape and attitudes profiles. The total detected radiant intensity as detected by the observer would be:

F § ª º ª º · Sun ¨ ¸ Lt | « 1 j 1 , ji pKaA 1attitude )( » « 2 j 2 , ji pKaA 2 attitude )( » (32) S ¨ ¦ ¦ ¸ © ¬ ,mk ¼ Client ¬ ,mk ¼ Servicer ¹

Two simultaneously observed Kernel functions (Kni,j), two optical cross section profiles aAni,j, and two attitude profiles pn,attitude are now present in this problem. This proposal aims to numerically invert a composite light curve to seek the presence of the secondary object and to infer the relative position between them. To achieve this, relative motion properties of the objects will be applied along with the luminance information which is provided.

In contrast to asteroid light curve inversion, RSOs generally have flat sides and sharp edges which produce spikes profiles in amplitude and phase plots. These discontinuities in the amplitude and phase provide a basis in which to detect the presence of edges while monitoring the objects. Coupled with the knowledge that the secondary object is also likely to be performing visible observations on the client (while free flying about the client), the attitude of the secondary is likely to change aspect angle with the client, hence with the observer as well (Figure 3-1). The changing attitude geometry of the combined system is the hypothesized key to determining the presence of the secondary object for non-resolved cases.

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O V

O r

Figure 13: Changing illumination conditions on the servicer between vectors O and S. Different facets of the secondary are illuminated during proximity flight

3.1.2 Coupling relative motion and light curves

The relative motion of the servicer with respect to the client is difficult to estimate using photometric techniques. This thesis proposal will attempt to infer the unforced relative motion by examination of the light curve. By making some assumptions about the interceptor and its flight some information about the motion of the secondary may be possible.

In the mission profiles detailed in Annex A, the missions primarily used visible and infrared imagers which were pointed to the client satellite. If these imagers are fixed, body mounted systems, they would force a condition where one face of the servicer would stare at the client. This forces various flat panels toward the observer direction. (See figure 13). If one makes a simplifying assumption that the objects are performing operations in the same plane (Z § 0), the attitude of the secondary, if it is actively tracking the client would be constrained:

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The CW frame expression of the relative position vector is

'& * - rrr & servicer client (32)

Where rservicer is the position vector of the servicing satellite and rclient is the position of the client spacecraft. & * rCW >@ROTz D)( 'r (33)

Where ROTz is a right handed 3x3 rotation matrix to force the x axis to be collinear with the client geostationary satellite and Į is the right ascension of the client satellite.

If the servicer is forced to continuously track the client, the +Xbody face of the servicer would be constrained to point at the client along -ǻrCW. Depending on the servicer’s flight profile, this would force the panels to project a different optical cross section of the servicer toward the observer (figure 13). This would form the basis to attempt estimation of the relative motion of the objects.

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4 Proposed Research

4.1 Thesis Research Objectives

The success of the Orbital Express mission (Annex A) plus various investments being made in on-orbit autonomy and robotic rendezvous are laying the groundwork for viable autonomous on- orbit servicing. Geostationary satellite service life extension via OOS offers possibilities to reduce both cost and orbital debris. While OOS is appealing to the commercial and military space arenas, it poses a problem for optical space surveillance systems. The servicing satellites’ relative motion, close proximity, size and optical cross section pose a discrimination difficulty during routine catalogue maintenance and are a future challenge for search approaches in deep space.

If a servicing satellite manages to remain undetected while advancing towards its client spacecraft during orbital phasing, an approach to the detection of the secondary will be needed as its close proximity to the client could potentially mask its presence. If the optical cross section of the secondary is relatively small in comparison to that of the client, its presence may not be noticed from traditional, individual magnitude measurements. Light curve characterization over phase angle would be required in order to detect anomalous light curve behaviour, suggesting the presence of the secondary. If the secondary is detected, characterization should be performed in order to infer its relative orbit about the primary.

In this thesis proposal, light curve inversion is used as the basis to detect two objects undergoing unforced relative motion about each other. This work would extend the capabilities of low cost optical systems to infer the presence of secondary objects which cannot separate closely spaced, objects. OOS is not currently practiced in geostationary orbit; however the likelihood of this kind of activity occurring in the future is becoming a reasonable prospect.

The objectives of this thesis are to provide a simulation toolset to determine the effectiveness of light curve inversion as applied to objects undergoing OOS. A satellite object modeled parameters set consisting of plate area, albedo and attitude configurations of both the client and servicer allows a user to estimate the optical response of the object. Optionally, if funding is available, the validation of this approach to determine the servicer’s presence will be field tested on actual geostationary satellites performing collocated flight.

4.2 Research Merit

The field of non-resolved optical characterization (NROC) normally studies single objects at long range by examination of their reflected (or emitted) electromagnetic radiation. Traditionally, this characterization emphasized deduction of observables such as physical configuration of the object (convex shape estimation), spin axis configuration, physical size or orientation of the object in space. Other studies have identified cases where glint behaviour from structures such as wire antennae can be inferred [15], offering capabilities to infer physical structure of distant objects without need of imaging.

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This work is first to study the case where two, non-resolved RSOs in close proximity to one another is examined with an aim to determining the presence of the secondary satellite. While the binary asteroid community has performed considerable work in this area, the use of light curve inversion as applied to deep space, Earth orbiting satellites has not been noted in the literature. Potential applications of this work are:

• Expanding the capabilities of CCD based space surveillance systems to infer the presence of secondary objects near geostationary satellites.

• Detect and infer the presence of space debris which has slowly shed from the parent object during a satellite fragmentation.

• Act as a verification mechanism such that a servicing satellite has begun operations around a client satellite or to ensure that an object is not performing OOS on the parent object.

4.3 Problem Complications

There are several challenges with regard to the use of light curve inversion to determine the presence of the secondary object. If the servicer has a much smaller optical cross section compared to the client, it could become difficult to infer the presence of the secondary object and would become hidden in the noise. If both objects are comparable in size, their total luminance would form a total, stronger overall signature of the object with indications of the second object's presence superimposed in the light curve. The optical cross section of the secondary would impose limits on detection as it could be potentially masked by the secondary.

The mission examples in annex A indicate that several proximity manoeuvres were performed during search and acquisition of the target satellite. This breaks the notion that unforced motion could be used as the single model of the motion. However, it should also be noted that the satellites in annex A all used visible, infrared and laser systems for detecting the relative position of the client spacecraft when performing their operations and continually tracked the client during proximity operations. A body-mounted optical sensor would require an attitude profile to track the client object during proximity operations if the field of view is relatively modest. This could be advantageous for the detection of the secondary as this enforces a condition where the attitude of the secondary would be constrained. Perch and stare operations where the secondary follows the client would be a problematic condition as the objects would appear as non-changing in optical cross section.

4.4 Schedule and Tasks Summary

The research objectives will be achieved by completing several tasks in a sequential manner and they are listed in the following. The planned schedule of work is shown in figure 14.

1. Modelling Phase

a. Create faceted 3D optical model of one or more satellite object (aA and shape assembly for characteristic satellite bus types)

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b. Create Sensor Model (System sensitivity, optical system transmission) consistent with modern CCD imaging systems.

c. Create relative motion model for GEO proximity operations adjusted for gravitational and luni-solar perturbations.

d. Image Formation model: Transition detection to add background stars into the field of view and add viewer aspect to model.

e. Optical model of Proximity operations (add shadowing effects)

2. Establish Kernel Function Parameterization

a. Create synthetic light curves for objects undergoing OOS. Parameterize for various RSO types and relative motion profiles. In particular, CW football, CW hop and linear departure motion.

b. Parameterize the Kernel functions for the resulting light curves. Accommodate the effects of changing phase angle behaviour in the production of amplitude and phase plots.

3. Identify deconvolution approach best suited to infer the presence of the secondary satellite.

a. Test deconvolution approach on simulated data to determine suitability for space surveillance observations.

4. Establish Probability of Detection Metrics for Objects Performing OOS.

a. Determine confidence levels for the Probability of detection

b. Determine metrics which test the limits of the Probability of detection of the secondary object.

5. Infer Unforced Motion Relative Orbit

a. Determine relative position offset or relative motion parameters using non- resolved light curve

b. Determine coupling between CW motion and light curve effects via relative motion and attitude coupling.

6. Validations (Milestones)

a. Validate approach to infer presence of secondary object

b. Individual function module testing for models (software integrity milestones)

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c. Lambertian sphere case to ensure model correctness for modeling of relative orbits.

d. Test using EMCCD / or suitable alternative sensor to determine presence of secondary objects using collocated satellites which perform visual conjunctions as test cases.

e. Infer relative orbit of collocated satellites undergoing visual conjunctions

7. Write Thesis

8. Defend Thesis

4.5 Equipment Requirements

The following preliminary list of materials is identified for the performance of this research. Procurement of most materials will proceed on as-needed basis with exception of an EMCCD camera which would likely require a one year lead time to procure. Funding is allocated by 15es Space Situational Awareness Advanced Research Project managed by Defence R&D Canada - Ottawa. The 15es project duration spans fiscal years 2010 to 2014 and annual base funding at $10,000 funding has been allocated for material procurement. Supplementary funding for the optional EMCCD system will be provided separately if funding opportunities arise.

Table 1: Equipment, Conference attendances and lead times Item Notes Lead Time Quantity Cost Prototyping software Matlab Licenses -Signal Analysis Toolbox 2 months 1 seat $2500 -Image Processing Toolbox -Curve fitting toolbox Prototyping software (dll C# License 2 months 1 seat $1000 development) 3 GHz Quad core HP Zeon Z400 No cost Workstation Delivered 1 Workstation, 6GB Ram (provided) -STK Pro / integration No cost STK License N/A 1 seat -Astrogator module (provided) Low read noise EMCCD system. EMCCD Camera (option) 12 months 1 $45,000 (Pending equipment release) Spaceflight Mechanics Meeting N/A 2 $3500 (2 attendances) Astrodynamics Specialist N/A 2 $3500 Conference (2 attendances) Conference Attendance ASTRO 2010 N/A 2 $3000 ASTRO 2012 AMOS 2011 N/A 2 $7000 AMOS 2013 Validation observations on geostationary satellites 10 nights No cost EO Observatory Lease N/A 0.35m visible optical system on observation (provided) polar mount Total $68,500

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4.6 Conferences and Publications

As this work has not been published in the past, the journals and conferences in table 2 are identified as useful external forums for academic criticism of this work. Publication charges, conference travel and fees are handled by DND.

Table 2: Proposed conference attendances

Journal Type Planned Initial Submission AMOS 2011 Conference Proceedings Sept 2011 ASTRO 2012 Conference Proceedings Spring 2012 AMOS 2013 Conference Proceedings Sept 2013 American Astronomical Society Space Refereed Journal Summer 2014 Surveillance Technical Submission Journal of Guidance Refereed Journal (Option) Summer 2014 Control and Dynamics

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ug-13 Elapsed TimeElapsed (Months) Observation Campaign (Optical) NEOSSat Pause NEOSSat X X X 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 Feb-10 Apr-10 Jun-10 Aug-10 Oct-10 Dec-10 Feb-11 Apr-11 Jun-11 Aug-11 Oct-11 Dec-11 Feb-12 Apr-12 Jun-12 Aug-12 Oct-12 Dec-12 Feb-13 Apr-13 Jun-13 A y Infer Relative orbit of colocated satellites undergoing undergoing orbit of colocated satellites Infer Relative Write Thesis Defend Thesis EMCCD/Video observations of Collocated satellites to satellites of Collocated observations EMCCD/Video Test case Lambertian Sphere to ensure model Test Individual Functions forTest software models Individual Validation Milestones NEOSSat Launch and Commisioning Pause Thesis Schedule Proposal and TimelineThesis Proposal and ofSchedule Tasks Modeling Phase Create Faceted Optical model of RSO Object Model Create Optical Sensor of Model GEO Motion Create Relative Image Formation Model Operations of Proximity Optical Model Differentiated Object Cases Create of Partially Kernel Parameterization Phase Curves for Light objectsundergoing Create Synthetic Functions fordeconvolution Kernel lightcurves Determine Deconvolution Approach forspaceTest approaches suitable Deconvolution Detgermine for confidence levels POD Determine tests Metrics which limits of POD Determine Relative Orbit Using Non-Resolved non resolved appraoch using Determine orbit relative Estimate performance Covariance orbit for the relative Procurement ProcureLong-Lead Items (EMCCD / Video) identified as software Procure Camera Deliver Establish Probability of Detection (POD) Metrics (POD) Detection of Probability Establish Figure 14: Proposed Schedule

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5 Summary

This thesis research proposal presents an investigative approach to infer the presence of satellites performing on orbit servicing about geostationary satellites at long range. The recent successes of autonomous robotic servicing missions are demonstrating that OOS is becoming a technically viable reality. The close proximity of both the client and servicing satellites is a difficult problem for traditional space surveillance sensors as the objects appear to coalesce together into one non- resolved object. A technique to infer the presence of the secondary object is desirable using small aperture telescope systems by analysis of the sunlight detected by a ground (or possibly space based) observer.

The plan is to create simulated models of the reflected light profiles from satellites flying in a simulated environment (MatlabTM). Using this model, light curve inversion approaches will be inspected with an aim to 1) determine the number of objects present in the single detected source and 2) infer characteristics about the two objects such as relative formation and shape characteristics.

This work is sponsored by Defence R&D Canada. The PhD candidate is a defence scientist at DRDC - Ottawa and carries out research and development on behalf of the Department of National Defence. The work will contribute to the 15es advanced research project. 15es' main objective is the exploitation of current and upcoming space surveillance systems and future challenges and systems for space surveillance. Under future challenges, new space mission types, such as on orbit servicing, non-Keplerian orbital motion or fragmented space systems architectures provide new, future problems for space surveillance.

This research's significance would permit a single channel sensor (such as a telescope detecting reflected sunlight from a distant satellite) to infer the presence of two sources (two satellites) within one signal train. This work would identify an inversion approach and the limitations of which this approach could be successfully applied. As satellites engaged in proximity flight coalesce into one object, this would enable small telescope systems to infer the presence of two objects within the merged target pair. If successful, this approach will enable small telescope systems to determine whether or not a second object is performing proximity operations around a given satellite.

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References .....

[1] Vallado, D. Fundamentals of Astrodynamics and Applications, 3rd Edition, Kluwer Academic Publishers , El Segundo California, 2001.

[2] Outer Space Treaty. http://www.unoosa.org/oosa/SpaceLaw/outerspt.html, accessed Apr 7 2009.

[3] Kervin, P., “RAVEN Automated Small Telescope Systems,” AFRL Directed Energy Directorate, Optical and Imaging Division, Space Surveillance Systems Branch

[4] Faccenda, W. et al. “Deep Stare Technical Advancements and Status” Mitre Corporation 2003, www.mitre.org/work/tech...deepstare/faccenda_deepstare.pdf.

[5] Stokes, D., et al., “The Space Based Visible Program”, Lincoln Lab Journal vol 11, no. 2, 1998.

[6] Scott, R.L. “Small aperture Observations of Collocated Canadian Geostationary satellites”, AMOS Technical Conference 2009, Maui, Hi.

[7] Tafazoli, M., “A Study of on orbit spacecraft failures” vol. 64 issue 2-3., Elsevier, July 2008.

[8] Madison, R.W., “Microsatellite Based On Orbit Servicing Work at the Air Force Research Laboratory”, Aerospace Conference Proceedings 2000, p. 215-226 vol.4. Big Sky, MT 2000.

[9] Soop, E.M. "Handbook of Geostationary Orbits", Microcosm Inc., European Space Agency 1994.

[10] Kawase, S., Inter-satellite Tracking Methods for Clustered Geostationary Satellites. IEEE Transactions on Aerospace and Electronic Systems vol. 26, No 3. May 1990.

[11] Lambert, J.V. and Kissel, K., “The Early Development of Satellite Characterization Capabilities at the Air Force Laboratories”, AMOS Technical Conference 2004, Maui HI.

[12] Bely, Pierre., "The Design and Construction of Large Optical Telescopes", Springer, New York 2002. p120.

[13] Hejduk, M.D., Snow, D.E., “Deterministic/Stochastic Satellite Brightness Modelling”, Center for Astrophysics, Space Physics and Engineering Research Colloquium Series, Baylor University 2008.

[14] Ackermann, M., "Blind Search for Microsatellites in LEO: Optical Signatures and Search Strategies", AMOS Technical Conference 2005, Maui, HI.

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[15] Hall, D. et al. "Separating Attitude and Shape Effects for Non-resolved Objects", AMOS Technical Conference 2007, Maui HI.

[16] Ostro, Steven., “Convex Profile Inversion of Asteroid Lightcurves: Theory and Applications”, Icarus 75-30-63, (1988).

[17] Kaasalaimen, M. And Torpa, J. “Optimization Methods for Asteroid Lightcurve Inversion I, Shape Determination”, Icarus 153, 24-36 (2001).

[18] Lambert, J., "Direct Inversion of Visible and Infrared Signatures", AMOS Technical Conference 2002, Maui HI.

[19] NASA "Summary of Dart Accident Report", http://www.nasa.gov/pdf/148072main_DART_mishap_overview.pdf, Accessed 3 Jan 2010.

[20] DART - Demonstration of Autonomous Rendezvous Technologies. Orbital Sciences Factsheet FS011.01e. http://www.orbital.com/NewsInfo/Publications/DART.pdf, accessed 3 Jan 2010.

[21] Tatsch., A. et al., "On Orbit Servicing: A Brief Survey", http://www.isd.mel.nist.gov/PerMIS_2006/proceedings/PerMIS_papers/PerMIS06.Final_Tatsch.p df. Accessed Sept. 2009.

[22] XSS-11 Mission Fact Sheet, Secure World Foundation, http://www.secureworldfoundation.org/siteadmin/images/files/file_356.pdf accessed 3 Jan 2009.

[23] Space.com "Military Microsatellites to test technologies in Wednesday Launch" 20 June 2006 http://www.space.com/missionlaunches/sfn_060620_mitex_prelaunch.html. Accessed 17 Nov 2009

[24] XSS-11. Wikipedia Commons, http://en.wikipedia.org/wiki/XSS_11 accessed October 2009.

[25] Experimental Satellite System - 11, http://www.popsci.com/military-aviation- space/article/2005-10/experimental-satellite-system-11-xss-11. Accessed 3 Jan 2010.

[26] Mulder. T, “Orbital Express Autonomous Rendezvous and Capture Flight Operations – Part 1 or 2: Mission Description, AR&C Exercises 1,2 and 3”, AAS Spaceflight Mechanics Meeting 2008., Galveston TX. 2008.

[27] Mulder. T, “Orbital Express Autonomous Rendezvous and Capture Flight Operations – Part 2 or 2: AR&C Exercises 4,5, and End of Life”, AIAA/AAS Astrodynamics Specialist Conference, Honolulu, HI, Aug 2008.

[28] Ellery, A., "An Introduction to Space Robotics", Springer, New York, 2000.

[29] Engineering Test Satellite VII (ETS-VII), http://robotics.jaxa.jp/project/ets7- HP/ets7_e/rvd/rvd_index_e.html#FP-1, accessed June 2009.

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[30] Yoshida, Kazuya., ETS-VII Flight Experiments for Space Robot Dynamics and Control. http://www.ri.cmu.edu/events/iser00/papers/yoshida_flight.pdf accessed April 2009.

[31] Caron, Ryan. "Mysterious microsatellites in GEO: is MiTEx a possible anti-satellite capability demonstration?"., http://www.thespacereview.com/article/670/1 accessed Mar 2009.

[32] Yasaka, T., and Ashford, E.W., "GSV: An Approach Toward Space System Servicing", Earth Space Review, Vol. 5, No. 2, 1996.

[33] Robotic Geostationary Orbit Restorer, http://www.esa.int/TEC/Robotics/SEMTWLKKKSE_0.html, accessed 5 May 2009.

[34] Tarabini, L. et al. "Ground guided CX-OLEV rendezvous with uncooperative geostationary satellite" Acta Astronautica 61 (2007) 312-325.

[35] ConeXPress Orbital Life Extension Vehicle, "http://telecom.esa.int/telecom/www/object/index.cfm?fobjectid=17870" accessed Sept 2009.

[36] Vandenkerckhove, Jean., "Tankersat - Refueling satellites in Geosynchronous Orbit", AIAA Aeronautics and Astronautics 1982.

[37] Bosse, A., et al.,"SUMO: Spacecraft for the Universal Modification of Orbits", Proc. SPIE Vol. 5419-7.

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Annex A Other Missions Demonstrating On Orbit Servicing

A.1 DART (Demonstration of Autonomous Rendezvous and Docking

DART was launched into an 800 km, 39.6° inclined circular orbit on Apr 15 2005. [19] DART was a NASA sponsored microsatellite mission designed to perform autonomous proximity operations about another satellite, in this case, the MUBLCOM satellite. DART was to perform a variety of approaches to MUBLCOM such in r-bar (radial approach) v-bar (along the velocity vector) and forced motion towards the MUBLCOM satellite. DART utilized both GPS and visible/near infrared visible cameras to estimate its position relative to MUBLCOM. DART successfully performed several approaches to MUBLCOM however, later in the mission, DART missed a waypoint ellipse due to a navigation logic failure. DART collided with MUBLCOM 11 hours into its mission where DART’s navigation system believed it was receding away from MUBLCOM [19]. A few minutes after the collision, DART performed a retirement manoeuvre which terminated the flight.

Figure A-15: DART artistic renderings (Image credit: NASA)

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Figure A-2: DART proximity operations planned for flight. Image Credit: NASA

A.2 XSS-10 (Experimental Small Satellite – 10)

XSS-10 was a US Air Force Research Lab (AFRL) microsatellite experiment which was a part of a larger series of experiments designed to test technologies needed for OOS. XSS-10 was launched into an 800 km, 39.6° inclined circular orbit on January 29 2003 [21]. XSS-10 was launched as a secondary payload aboard a Delta II upper stage and was designed to perform semi- autonomous rendezvous and proximity operations on the Delta II. The microsatellite was battery- life limited and did not have a solar panel power subsystem to sustain operations beyond 24 hours. XSS-10 carried 2.58 kg of monomethyl hydrazine and nitrogen tetroxide propellant and 0.7kg of nitrogen pressurant. XSS-10 performed real time data transfer to the ground as no on orbit recording capability was built into the system. Critical real time control was demonstrated while performing the proximity approaches to the Delta II. XSS-10 performed 100 meter perch and stare station keeping, a move and stare maneuver, and a v-bar maneuver to close separation with the RSO to within 50 meters [21].

A.3 XSS-11 (Experimental Small Satellite – 11)

XSS-11 was managed by the US Air Force Research Lab (AFRL) and was launched 11 April 2005 into an 850x800 km orbit [24]. The mission objective was to test autonomous technologies needed for inspection and repair of non-operational US satellites and to demonstrate space

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surveillance [ibid]. The mission was to last between 12 and 18 months and demonstrate autonomous approach and rendezvous between six to eight US owned satellites [24] and debris. Mission duration was cited to be 1 year [ibid]. Little literature is available publically about XSS- 11 operation however [25] reported maneuvers by the microsatellite to within 500m of its Minotaur upper stage. XSS-11 was built by Lockheed Martin and weighed 125 kg with an excess of 600 m/s delta-v for manoeuvring [24].

A.4 Orbital Express

The Orbital Express mission flew two spacecraft (ASTRO and NextSat) to demonstrate autonomous robotic OOS and was launched into a 492x492 km 46° inclination LEO orbit on 8 March 2007 [26]. DARPA managed the mission while Boeing constructed ASTRO (Autonomous Space Transport Robotic Operations) and Ball Aerospace built the Next Generation Serviceable Satellite (NextSat) client. A robotic arm supplied by MacDonald Dettwiler and Associates [26] was installed onto ASTRO. The project aimed to demonstrate autonomous rendezvous, proximity operations, station keeping, capture, docking, hydrazine fluid transfer, battery replacement and electronics swap out. The robotic arm provided ASTRO with a capability to intervene and manipulate NextSat and was a first for autonomous US robotic operations. The mission was a success despite occasional ACS control errors where the navigation system failed, requiring manual intervention by ground control [ibid]. The docking and robotic arm manipulation experiments functioned well and several flight profiles were attempted in an effort to characterize the types of flight profiles to be undertaken by such a servicing mission. Orbital express was unique in that the mission demonstrated the first exchange of hydrazine fuel and battery replacement by autonomous robotic servicing. A computer module was also replaced, demonstrating viability of technology refresh on orbit.

A.5 Orbital Express Flight Profiles

Five flight experimental profiles for Orbital Express were identified in [26],[27]. ASTRO and NextSat were originally mated together during the initial tests and began increasingly sophisticated manoeuvres to separate, captivate and dock. Table 3 shows the types of operations performed and the maximum ranges incurred during the flight exercises.

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Table 3: Orbital Express Mission Profile Summary Orbital Profile Plan Max Range Exercise Result Express Exercise Separate and perform 12 m 12 m Succeeded 1 radial, controlled circular motion around NextSat 6 km Computer failure caused ASTRO to back 120m Back 30m below NextSat, behind NextSat. Range 2 then perform 10m circular opened until Astro was station keep 6km behind when it was finally arrested by ground control 60 x 120m CW football fly 120m Succeeded around NextSat 3 Finish with 120m station keep on +Vbar Spiral departure to 100m then 4 km Succeeded, minor issues 4 perform corridor departure to with visible image tracker -4km in track. Spiral departure to +90m 7km Succeeded radially then corridor departure to -7km intrack. 5 Approach, perform 100m circular station keep, then aproach and grapple.

A.6 Engineering Test Satellite 7 (ETS-VII) Orihime & Hikoboshi

The Engineering Test Satellite 7 (KIKU-7) was developed by NASDA (Japan) to test the viability on on-orbit servicing using a robotic manipulator and was launched 28 Nov 1997. This mission consisted of a chaser (Hikoboshi) and target satellite (Orihime) in a 550 km, 35 degree inclination orbit [28] in which robotic manipulator tests were performed. The satellite was tele-robotically controlled via the TDRSS network, however robotic subtasks were executed autonomously [28]. The attitude control system of the primary satellite was deactivated for most operations and was unstabilized during flight. Autonomous rendezvous and docking within 2 meters was achieved and station keeping relative motion out to six kilometres was also performed [29].

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Table 4: ETS-VII Relative Motion Profiles ETS-VII Profile Plan Max Range Exercise Result Experiment Separate to 2 m, approach and 2m Succeeded 1 capture 0.5 km Computer failure. Separate to 500m along Vbar, Experiment succeeded 2 approach and recapture after 3 weeks of failed attempts.

A.7 MITEX (Microsatellite Technology Experiment (DARPA)

MITEX is an experimental US Air Force project (with NRL participation) to test miniature satellites for space surveillance purposes along with upper stage servicing capability to support microsatellites in GEO [31] There is little written about the MITEX satellites in the public literature. A pair of microsatellites, plus a specially designed Delta 2 upper stage was lofted into GEO to test space surveillance technologies. Each microsatellite weighed 225 kg and was manufactured by Lockheed Martin and Orbital Sciences corporations. The locations of the two microsatellites on orbit have not been revealed [31] however it is suspected that the satellites have been deactivated on orbit. Flight profiles have not been detailed.

A.8 Geostationary Servicing Vehicle (GSV proposed 1989)

The Geostationary Servicing Vehicle (GSV) [32] was a conceptual design teaming Estec (ESA), Japan (NASDA), and Canada (Spar Aerospace) to build a geostationary satellite robotic servicing spacecraft. The concept envisioned use of telerobotic operation to perform Geostationary Satellite inspection and repair by using two remotely operated robotic arms to assist in the deployment of solar panels or antennas. Fuel transfer was not envisioned for this system nor demonstration of autonomous rendezvous, as the technologies to perform these functions were not mature at the time of this system’s proposal. Mechanical intervention was envisioned by this system with an orbital reboost capability to remove derelict spacecraft from geostationary Earth orbit.

A.9 ROGER (Proposed)

ROGER (Robotic Geostationary Explorer) was a mission proposal by ESA to remove orbital debris from the geostationary ring [33]. Two ESA contracts were awarded for the study. One was awarded to Astrium, the other to QinetiQ. It was envisioned that a Robotic ROGER satellite would approach failed geostationary satellites and reorbit them to the graveyard disposal orbit. Astrium proposed a mission architecture with 20 throw nets to captivate the errant satellites and tow them to GYO [ibid]. The QinetiQ team proposed a tentacled telescopic boom system to clasp and capture the geostationary satellite bus. Neither system was flown.

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A.10 Cone Express – OLEV (Proposed)

The Cone Express Orbital Life Extension Vehicle (CX-OLEV) [34][35] project was to develop a servicing mission for GEO built to dock with a failing geo and provide attitude and orbital control for the satellite. This would allow the geostationary satellite to continue its communications services if the amplifier system is still in operation Phase B1 of the system baseline design was completed.

A.11 Tankersat (Proposed)

Tankersat [36] was an ESA evaluation of geostationary servicing and focused on the economic viability and profitability of on-orbit refuelling. This analysis identified that orbital repair was impractical, due to the complex and uncertain nature of the types of failures and specialized mission equipment needed. Refuelling however, was considered to be a viable, standard practice [ibid] if satellites were constructed with common fluid interchange modules.

A.12 SUMO / FREND (Proposed)

Currently the DARPA/NRL SUMO (FREND) [37] mission is in the planning stages to perform an on orbit demonstration of on orbit rendezvous and docking. This mission would attempt to rendezvous with a geostationary satellite and perform orbital adjustment. The mission baseline utilizes a small-sat class bus with adequate fuel capacity to boost the client satellite above geostationary orbit. Two robotic manipulators are used to captivate the client satellite by clasping the Marmon clamp ring, launcher interface (unique to the Boeing 702 series of satellites bus) or clasping of the apogee kick motor of the satellite. 3D Laser lidar systems would be utilized to determine the pose of the client satellite relative to the servicer.

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Annex B Non Forced Relative Motion Trajectories

B.1 Clohessy Wiltshire Equations of Motion

The Clohessy Wiltshire (CW) relative motion equations for circular orbits [1] can be used to create several non-forced relative motion trajectories which are useful for proximity operations. Various combinations of relative speed and relative initial position can create simple and complex shaped trajectories. It should be noted that the motions of the objects can sometimes appear elliptical; however this elliptical motion is not driven by gravitational interaction between the satellites. The motion is largely due to the object's independent orbits about the central body. For circular orbits, the mean motion of the objects is:

B.2 Perch and Hold

This trajectory is a trivial case where a satellite is in the same orbit as the target satellite, but is simply displaced in the along-track direction either ahead or behind the client satellite.

B.3 Linear Translation (Corridor Departure)

For a given, initial radial (x) offset relative to the primary satellite, If the initial in-track velocity is set to

3 0 2 xy 0Z the chaser satellite will move in a straight line relative to the primary satellite. This linear motion is not physically possible for extended periods of time [1] as small radial motions are usually observed. If the initial radial displacement is above the client, the servicer will appear to drift behind the client, as the secondary has a higher apogee, hence a slower inertial velocity. If the object is displaced below, the servicer will drift ahead as it would have a slightly higher velocity than the client.

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Relative Motion Plot

-2 X Radial(km) -

-4

-6

-8

-8 -6 -4 -2 0 2 4 6 8 Y - Intrack (km)

Figure A-3: Linear translation motion (blue segment to the left)

B.4 CW hop

Setting the initial velocities to zero, and setting a nonzero value for the radial position produces a hoping motion relative to the primary satellite. This hopping motion is sometimes used for phasing orbits during drift approach a satellite during docking. DART and Orbital Express used this hopping motion for the approach stages of their missions.

Relative Motion Plot

X Radial(km) - -1

-2

-3

-3 -2 -1 0 1 2 3 Y - Intrack (km)

Figure A-4: CW Hop for a satellite with =-0.5km X (radial) position.

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B.5 Radial Rendezvous

Setting the radial velocity of the servicer to a nonzero value results in semi elliptical motion of the servicer about the client. The semi major axis in the intrack direction is twice the radial direction. The size of the ellipse is controlled by the magnitude of the radial velocity.

Relative Motion Plot

5000

4000

3000

2000

1000

-1000 X - Radial (km) Radial X - -2000

-3000

-4000

-5000

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 Y - Intrack (km)

Figure A-5: Motion of the chaser satellite with respect to the primary for x0 dot variations.

B.6 CW Football

For the case of combined displacements in x direction and intrack velocity variation, a special case emerges where the chaser can appear to orbit the primary. If the intrack velocity is set to

0 2Zxy 0 a CW football motion about the client can be achieved. In geostationary orbit, perturbations will result in that the motion cannot be maintained perpetually.

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Relative Motion Plot 2

1.5

0.5

X Radial - (km) -0.5

-1

-1.5

-2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Y - Intrack (km)

Figure A-616: CW Football. The chaser begins its revolution above and moves in the direction indicated. Note that the football motion can be displaced in the intrack direction.

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Annex C Satellite Detectability Modelling with a CCD

Satellite Detectability Modelling with a CCD

For the detection of a moving satellite object using an optical CCD camera, Hejduk [40] identifies the following relationship to estimate the signal

(in photoelectrons) as detected by a CCD imager.

4.0 Tvm AS eff QE F010 W atm (2) where Aeff is the effective light gathering area of the optical telescope, is the solar weighted quantum efficiency of the optical detector, F0 is the flux of a zero magnitude star in photons per 10 2 meter second (~4x10 photons/sec/m ) and Tatm is the atmospheric transmittance, which is normally set to unity as the Tvm value can be corrected for atmospheric attenuation.

For an object that is tracked with a CCD sensor (‘Track rate Mode”, TRM), the integrated signal intensity falling on the best pixel is:

T exp kTSS f (3) where Texp is the integration time of the CCD camera and kf is the ensquared energy, or the percentage of energy from the point source illuminating the best pixel on the CCD array.

For objects which are tracked in sidereal detection mode (‘Star Stare Mode”, SSM) it is difficult to estimate the signal in each pixel as it is spread all over pixels of the streak. In this case,

exp kTS f D kS f D ST ZTexp Z

Where Į is the angular size of a pixel in arcseconds, and Ȧ is the angular rate that the object moves across the detector plane (arcseconds/second).

2 2 2 V N sys BTexp DC exp STN T K QE BTexp K DCDC TN exp

The noise sources from a CCD are the following typical sources

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Table 5: CCD Noise Sources Noise Description Units Source Nsys RMS system noise e- Background sky photoelectron B e-/pixel/sec generation rate RMS variation of dark current Ș Percentage DC production rate (percent) RMS variation of detector Ș Percentage QE responsivity variation (percent) Dark current generation rate N e-/pixel/sec DC (temperature dependent) ¥ST Shot noise of signal e-

The sky background generation rate is estimated by:

4.0 BVM 2 B 10 Aeff QE F0D

Where the magnitude B is in magnitudes per square arcsecond, Į is the pixel scale of the detector.

The signal to noise ratio (SNR) is formed by simply taking the ratio of the signal and the noise terms. It should be noted that for track rate mode, the SNR is proportional to the ¥T, whereas sidereal stare mode SNR is proportional to 1/¥T. In general, longer exposures in sidereal stare mode result in lower SNR[41].

This expression is an actual underestimate of the true noise on the CCD sensor. It does not account for the accumulated noise while the charge is waiting to be read out on a frame transfer CCD area. It also ignores the impact of stellar streaks, or stray light from celestial sources on the imaging plane.

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Bibliography .....

Ashikhmin, M., Shirley, P.,"An Anisotrpoic Phong BRDF Model", Journal of Graphical Tools, Vol. 5. No.2, 2000., pp25-32.

Astro Captures NextSat, http://www.boeing.com/companyoffices/gallery/images/advanced_syst/oe_057.html, accessed Sept 2009

Burlton, B., et al, “MECH 5803 Orbital Mechanics and Space Control” Course Notes., Carleton University 2007

Eckstein, M.C. et al., "Collocation Strategy and Collision Avoidance for the Geostationary Satellites at 19 Degrees West", CNES Symposium on Space Dynamics, November 1989.

Hall, D. et al. "Photometry of small satellites", AMOS Technical Conference 2008, Maui HI.

Hedjuk., M., et al., “Modeling of Optical Sensor Performance”, AMOS Technical Conference 2004., Maui, HI.

Hibbard, Rustie., "Satellite On-Orbit Refuelling: A Cost Effectiveness Analysis", Thesis, Naval Postgraduate School, Monterrey, CA., Sept 1996.

Jah, M., "Satellite Characterization: Angles and Light Curve Data Fusion for Spacecraft State and Parameter Estimation", AMOS Technical Conference 2007, Maui, HI.

Lamour, R., “SBV Photometry Initial Results”, Journal of Guidance Control and Dynamics, 2000.

Payne, T., “SSA Analysis of GEOS Photometric Signature Classifications and Solar Panel Offsets”, AMOS Technical Conference 2006, Maui HI.

Richmond, C., "The Growth of Orbital Sciences and the Market for Small GEO Satellites", SJR, No. 55 April/May 2008.

Sydney, P. et al., “High Precision Satellite Astrometry and Photometry”, AMOS Technical Conference 2004., Maui, HI.

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List of symbols/abbreviations/acronyms/initialisms

AĮ Albedo Area product BDRF Bi directional reflectance distribution function CCD Charged Couple Device CW Clohessy Wiltshire DARPA Defence Advanced Research Projects Agency DND Department of National Defence DRDC Defence Research & Development Canada EMCCD Electron Multiplying Charged Couple Device GEO Geostationary Equatorial Orbit IR Infrared (thermal or near infrared generic) NORAD North American Aerospace Defence Command NROC Non resolved Object Characterization OCS Optical Cross Section ODR Orbital Debris Removal OOS On Orbit Servicing PSF Point Spread Function RSO Resident Space Object RSSS Russian Space Surveillance System SOI Space Object Identification SSN Space Surveillance Network STK Satellite Tool Kit

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DOCUMENT CONTROL DATA (Security classification of title, body of abstract and indexing annotation must be entered when the overall document is classified) 1. ORIGINATOR (The name and address of the organization preparing the document. 2. SECURITY CLASSIFICATION Organizations for whom the document was prepared, e.g. Centre sponsoring a (Overall security classification of the document contractor's report, or tasking agency, are entered in section 8.) including special warning terms if applicable.)

Defence R&D Canada – Ottawa UNCLASSIFIED 3701 Carling Avenue Ottawa, Ontario K1A 0Z4

3. TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C or U) in parentheses after the title.)

Use of light curve inversion for non resolved optical detection of satellites performing on orbit servicing in the presence of geostationary satellites: Thesis Proposal

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Scott, R.L.

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Technical Memorandum

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Defence R&D Canada – Ottawa 3701 Carling Avenue Ottawa, Ontario K1A 0Z4

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Space surveillance, light curve inversion, On Orbit Servicing, Orbital Debris Removal