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Detecting Minimoons in the Earth- Moon System with Microsatellite Compatible Technologies

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Detecting Minimoons in the Earth- Moon System with Microsatellite Compatible Technologies DEGREE PROJECT IN COMPUTER SCIENCE AND ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2018 Detecting minimoons in the Earth- Moon system with microsatellite compatible technologies MATIAS KIDRON KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE Detecting minimoons in the Earth-Moon system with microsatellite compatible technologies November 23, 2018 Author: Matias Kidron Supervisor: Nickolay Ivchenko Examiner: Tomas Karlsson EF233X Degree Project in Space Technology Athesissubmittedinfulfillmentoftherequirementsforthedegreeof Master in Aerospace Engineering in the Department of Space and Plasma Physics School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Abstract Minimoons, Earth’s temporarily-captured orbiters, are excellent candidates for asteroid mining technology demonstrations and general asteroid studies because of their relatively long stay in the vicinity of Earth. In this thesis, microsatellite compatible surveillance technologies are discussed and the suitability of various locations in the Earth-Moon sys- tem for minimoon surveillance is examined. This is done to acquire knowledge on which type of an orbit a minimoon-surveying-microsatellite could be placed on. The instantaneous visible fraction of the minimoon steady-state population is the figure of merit when comparing surveillance systems and locations. The visible fraction is esti- mated by simulating the distribution of visible minimoons in the sky-plane. The objects in the simulated sky-plane are synthetic minimoons, which are generated in large numbers according to the geocentric 6-dimensional-residence-time-distribution of minimoons, and thus, the bin values of the sky-plane distribution can be thought of as instantaneous prob- abilities for containing a detectable minimoon within certain ecliptic latitude-longitude range. The visible fractions are estimated for various locations with given surveillance system performance. Multiple microsatellite compatible surveillance technology configurations are examined as well as the e↵ect of limiting magnitude and maximum angular velocity. Minimoons are faint and fast moving objects and thus the use of synthetic tracking algo- rithm is beneficial and considered. Only visual band surveillance systems with aperture sizes less than 0.30 m and minimoons with diameter sizes larger than 0.50 m are considered in the simulations. i Sammanfattning Minim˚anar, jordens tempor¨art f˚angade satelliter, ¨arutm¨arkta kandidater f¨ordemonstra- tioner av asteroidbrytningteknologi och f¨orallm¨anna asteroidstudier p˚agrund av deras rel- ativt l˚anga vistelse i n¨arheten av jorden. I den h¨aravhandlingen, diskuteras mikrosatellit kompatibla ¨overvakningsteknologier och d¨artill unders¨okes l¨ampligheten av olika platser i jord-m˚ane-systemet f¨or¨overvakning av minim˚anar. Det h¨arg¨ors f¨oratt ska↵a kunskap om vilken typ av omloppsbana en mikrosatellit f¨orminim˚ane¨overvakning kunde placeras p˚a. Den momentana synliga fraktionen av den j¨amviktstillst˚and minim˚anepopulationen ¨ar den merit som anv¨ands vid j¨amf¨orelse av ¨overvakningssystem och platser i rymden. Den synliga fraktionen uppskattas genom att simulera f¨ordelningen av synliga minim˚anar i skyplanet. F¨orem˚alen i det simulerade skyplanet ¨arsyntetiska minim˚anar, vilka gener- eras i stort antal enligt den geocentriska 6-dimensionella-uppeh˚allstid-distributionen av minim˚anarna, och s˚alunda kan v¨ardena i den diskretiserade skyplanf¨ordelningen betrak- tas som momentana sannolikheter f¨oratt inneh˚alla en observerbar minim˚ane inom det specifiserade ecliptiska latitudinella-longitudinella omr˚adet. De synliga fraktionerna ber¨aknas f¨orolika platser med det givna ¨overvakningssys- temets parametrar. Flera mikrosatellit-kompatibla ¨overvakningsteknologikonfigurationer unders¨oks, s˚av¨alsom e↵ekterna av begr¨ansande magnitud och maximal vinkelhastighet. Minim˚anar ¨ardunkla och snabba r¨orliga f¨orem˚al, och s˚aledes ¨aranv¨andningen av synthetic tracking f¨ordelaktig och ¨overv¨agd. Endast ¨overvakningssystem som fungerar i visuellt band med en bl¨andarstorlek mindre ¨an0,30 m och minim˚anar med en diameter st¨orre ¨an0,50 m beaktas i simuleringarna. ii Acknowledgements I have had amazing and inspiring teachers since the very first grade in the elementary school. Thank you. I would especially like to thank Mikael Granvik and Grigori Fedorets for their scientific advice and help during this thesis project. In addition, I would like to thank my family, girlfriend, LTU and KTH for their support. iii Contents Abstract i Acknowledgements iii Contents iv List of Figures vi List of Tables vii Nomenclature viii 1 Introduction 1 2 Theory 3 2.1 Brightnessofobjects............................... 3 2.2 Cameras and telescopes . 5 2.3 Detectionandtracking.............................. 9 2.4 Shift-and-addtechnique . .. 11 2.5 Advantages of space-based surveillance . 13 3 Earth’s temporarily-captured natural satellites 15 3.1 Definitions..................................... 15 3.2 The creation of the population model . 16 3.3 Steady-state population . 16 3.4 Earlier 6D-geocentric-residence-time-distribution . 17 3.5 Sky-planedistributions. 18 3.6 Rate-of-motion . 19 3.7 Rotation rates . 20 3.8 Summary of the observational challenges with TCAs . 20 4 MicroSat asteroid surveillance technologies 21 4.1 Earlier and proposed missions . 21 4.2 Other available and researched technologies . 25 4.2.1 Telescope technologies . 25 4.2.2 Sensor technologies . 27 4.2.3 Other technologies . 27 4.3 Alternatives.................................... 27 4.4 Summary of MicroSat compatible technologies . 28 iv 5 Simulation 29 5.1 6D-geocentric-residence-time-distribution . 30 5.2 Scaled-up minimoon population . 31 5.3 Observatories ................................... 34 5.4 Observations ................................... 35 5.5 Post-processing .................................. 36 5.5.1 The e↵ects of Earth and the Moon on observing . 36 5.5.2 Examined surveillance system cases and their parameters . 36 6 Results 38 6.1 CaseS17...................................... 39 6.2 CaseS18...................................... 40 6.3 CaseNS...................................... 45 6.4 CaseTS...................................... 46 6.5 General comments on the examined cases . 47 6.6 Performance on speculated orbits . 48 6.7 Summaryofresults................................ 52 7 Discussion 53 8 Conclusions 54 Bibliography 55 Appendices 60 A Observatory-fileformat ............................. 60 B Objects-fileformat ................................ 60 v List of Figures 2.1 Definition of phase- and solar elongation angle. 4 2.2 Airypattern. ................................... 7 2.3 Angular resolution as a function of aperture diameter and wavelength. 8 2.4 Decreasing minimoon orbit uncertainty with more observations. 10 2.5 Shift-and-addtechnique.. 11 2.6 Computational load of synthetic tracking. 12 2.7 The improvement in the peak signal with synthetic tracking. 13 2.8 Atmospheric electromagnetic opacity as a function of wavelength. 14 3.1 Size of the TCO and TCA steady-state populations as a function of absolute magnitude. .................................... 17 3.2 a, e, i-residence-timedistributionofminimoons. 18 3.3 Constrained sky-plane distribution of minimoons from Earth. 19 3.4 GeocentricvelocitiesofTCAs. 19 3.5 Rotation rates of small asteroids. 20 4.1 Computer rendering of NEOSSat. 22 4.2 ASTERIApriortolaunch............................. 22 4.3 A CAD model of a synthetic tracking telescope. 23 4.4 Deployableopticsdesign. ............................ 26 4.5 SpaceFab’s Waypoint MicroSat. 26 5.1 Absolute magnitude distribution of synthetic minimoon population. 31 5.2 Distribution of minimoons in (a, e, i)-orbital element phase space. 32 5.3 Distribution of minimoons in (!,M0, ⌦,a)-orbital element phase space. 33 5.4 Observatory locations. 35 6.1 Case S17: Sky-plane distribution at highest vf location. 40 6.2 Case S18: Visible fractions at observatory locations. 41 6.3 Case S18: The sky-plane distribution at highest vf location. 42 6.4 Case S18: The sky-plane distribution of angular velocity at highest vfd location....................................... 42 6.5 Case S18 with decreased velocity search range at di↵erent observatory lo- cations. ...................................... 44 6.6 Case S18: x- and y-coordinates of visible synthetic minimoons. 45 6.7 Case TS: The sky-plane distribution at highest vf location. 47 6.8 Case S18: Earth’s decreasing e↵ect on visible fraction. 48 6.9 Limiting magnitude as a function of aperture diameter. 50 6.10 Visible fraction as a function of limiting magnitude at speculated orbits. 50 6.11 Visible fraction as a function of maximum angular velocity at speculated orbits. ....................................... 51 6.12 Distribution of vf in the EMS with less capable S18. 51 vi List of Tables 2.1 Values of basis functions. 5 2.2 Geometric albedos and G1 and G2 constants for three main asteroid types. 5 4.1 The parameters used in Shao et al. (2017) to estimate system performance. 23 5.1 Bin widths and ranges used in the 6DGRTD. 30 5.2 Observatory coordinates. 34 5.3 Surveillancesystemparametersusedintestcases. 37 6.1 S17results. .................................... 39 6.2 S18results. .................................... 41 6.3 NSresults. .................................... 46 6.4 TSresults...................................... 46 6.5 Case S18: Averaged results for speculated spacecraft orbits. 49 6.6 Resultssummaryforcases.
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