Cataloguing of Objects on High and Intermediate Altitude Orbits Inauguraldissertation der Philosophisch-naturwissenschaftlichen Fakult¨at der Universit¨atBern vorgelegt von Johannes Herzog von Deutschland Leiter der Arbeit: Prof. Dr. T. Schildknecht Astronomisches Institut der Universit¨atBern Cataloguing of Objects on High and Intermediate Altitude Orbits Inauguraldissertation der Philosophisch-Naturwissenschaftlichen Fakult¨at der Universit¨atBern vorgelegt von Johannes Herzog von Deutschland Leiter der Arbeit: Prof. Dr. T. Schildknecht Astronomisches Institut der Universit¨atBern Von der Philosophisch-Naturwissenschaftlichen Fakult¨atangenommen. Der Dekan: Bern, den 18.11.2013 Prof. Dr. S. Decurtins Contents List of Figures V List of Tables VII List of Abbreviations and Acronyms IX Motivation 1 1 Introduction 5 1.1 Protected Regions and Object Classification . .5 1.1.1 Overview on Objects in geostationary and geosynchronous Orbits . .6 1.1.2 Overview on GNSS Objects . .9 1.2 The Telescope ZimSMART . 11 1.2.1 Mounts . 11 1.2.2 Optical Tube Assemblies . 12 1.2.3 Camera . 13 1.2.4 Analysis of the Performance of the third Set-up of ZimSMART . 13 1.2.5 Observations and Data Format . 14 1.2.6 Limiting Magnitude of ZimSMART and observable Object Sizes . 15 1.2.7 Observable Object Sizes . 16 1.3 Uncertainties of Orbits . 17 1.3.1 Measurement Techniques . 17 1.3.1.1 Optical Observations . 17 1.3.1.2 Satellite Laser Ranging (SLR) . 18 1.3.1.3 RADAR Measurements . 18 1.3.1.4 Position Measurements with the Global Navigation Satellite System (GNSS) 18 1.3.1.5 Microwave Position Measurements . 18 1.3.1.6 Two Line Element Set Analysis . 19 1.3.1.7 Operator Data . 19 1.3.2 Worst Case Scenarios . 19 1.3.3 Orbit Accuracies . 21 1.3.3.1 Two Line Element Catalogue Analysis . 21 1.3.3.2 GNSS Data . 22 1.3.3.3 Satellite Laser Ranging . 22 1.3.3.4 Microwave Measurements . 22 1.3.4 Pointing Accuracies . 22 I Contents 1.3.4.1 LEO . 22 1.3.4.2 MEO . 23 1.3.4.3 GEO . 23 1.4 Outline . 23 2 Survey Strategies 25 2.1 Apparent Motion of Objects . 26 2.2 Geostationary Ring . 27 2.2.1 Survey Scenarios . 28 2.2.1.1 One single Stripe . 29 2.2.1.2 One Pair of Stripes . 30 2.2.1.3 Two Pairs of Stripes . 32 2.2.1.4 Other possible Line-ups . 34 2.2.2 ZimSMART GEO Surveys . 34 2.2.3 GEO Survey Results . 35 2.2.3.1 Images taken . 36 2.2.3.2 True Coverage of the Geostationary Ring . 37 2.3 GNSS Orbit Region . 40 2.3.1 Explosion Scenario Analysis . 40 2.3.2 Observation Scenario . 40 2.3.3 Observation Mode . 43 2.3.4 Correlation between Number of observed Fields and Images taken . 43 2.3.5 Detected Catalogue Objects . 44 2.3.6 Estimated Number of populated Fields in an orbital Plane . 44 2.3.7 Results . 45 2.3.7.1 GIOVE-A orbital Plane . 45 2.3.7.2 GLONASS orbital Plane 2 . 48 2.3.7.3 GLONASS orbital Plane 1 . 50 2.3.7.4 NAVSTAR GPS orbital Plane E . 52 2.3.7.5 MOLNIYA 1-93 orbital Plane . 54 2.3.7.6 NAVSTAR GPS orbital Plane D . 56 2.4 Concluding Remarks . 58 3 Object Identification and Catalogue Built-up 59 3.1 Theoretical Background . 60 3.1.1 The Equation of Motion . 60 3.1.1.1 Gravitational Potential of the Earth . 60 3.1.1.2 Gravitational Potentials of Objects of the Solar System . 61 3.1.1.3 Non-gravitational Forces . 62 3.1.2 Orbital Elements . 64 3.1.2.1 The angular Momentum Vector per Unit Mass . 64 3.1.2.2 Keplerian Elements . 65 3.1.2.3 Synchronous Elements . 67 3.1.2.4 State Vectors . 68 3.1.3 Orbit Determination . 69 3.1.3.1 First Orbit Determination with ORBDET ................. 69 3.1.3.2 Orbit Improvements with SATORB ..................... 72 3.1.4 Orbit Propagation . 73 3.1.4.1 Analytical Propagation . 73 3.1.4.2 Numerical Propagation . 73 3.2 Processing Pipeline ZimPipe .................................. 74 3.2.1 Filter Method via Positions and Velocities { ZimOProK ............... 76 II Contents 3.2.1.1 COROBS .................................... 76 3.2.1.2 Selecting possible Connections . 77 3.2.2 Pairwise Check for possible Connection . 77 3.2.3 Filter Method via orbital Elements . 78 3.2.4 Confirmation of associated Tracklets and Storage into the Catalogue . 82 3.2.4.1 Catalogued Objects with new Tracklets . 82 3.2.4.2 Newly detected Objects . 82 3.2.5 Storage into the Catalogue . 83 3.3 Results of the Processing Cycles . 83 3.3.1 The Data Set . 83 3.3.2 First Run . 83 3.3.3 Second Run { first Part of the Data Set . 85 3.3.4 Second Run { complete Data Set . 88 3.3.4.1 Associated Tracklets . 89 3.3.4.2 Multiply and wrongly associated Tracklets . 89 3.3.4.3 The AIUB internal ZimSMART Catalogue . 90 3.4 Concluding Remarks . 93 4 Manoeuvre Detection 95 4.1 Types of Manoeuvres . 96 4.1.1 North-South Station-keeping Manoeuvre . 96 4.1.2 East-West Station-keeping Manoeuvre . 97 4.1.3 The Observer's Point of View . 98 4.2 Detection and Analysis Method . 99 4.2.1 Propagation to a selected Epoch . 99 4.2.2 Scan between osculating Epochs . 99 4.3 Analysis of identified Manoeuvres . 100 4.3.1 Known Manoeuvre Epoch tM and Thrust Vector ∆V~M ................ 100 4.3.2 Known Manoeuvre Epoch tM .............................. 101 4.4 Detecting Manoeuvres . 102 4.4.1 Distinction of Manoeuvres from close Conjunctions . 102 4.4.2 Distinction of Manoeuvres from Time Intervals without Manoeuvres . 105 4.4.3 Examples of Manoeuvre Detections . 107 4.4.3.1 Detection of East-West Station-keeping Manoeuvres . 109 4.4.3.2 Analysis of North-South Station-keeping Manoeuvres ..