Probability of Collision in the Geostationary Orbit*
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PROBABILITY OF COLLISION IN THE GEOSTATIONARY ORBIT* Raymond A. LeClair and Ramaswamy Sridharan MIT Lincoln Laboratory, 244 Wood Street, Lexington, Massachusetts 02420 USA, Email: [email protected] ABSTRACT/RESUME The initial Geosynchronous Encounter Analysis (GEA) CRDA spanned two years beginning in mid 1997. The advent of geostationary satellite communication During this period, Lincoln Laboratory provided timely 37 years ago, and the resulting continued launch activ- warning of encounters between Telstar 401 and partner ity, has created a population of active and inactive geo- satellites and precision orbits for these objects for use synchronous satellites which will interact, with genu- in avoidance maneuver planning [1]. In all, 32 en- ine possibility of collision, for the foreseeable future. counters between Telstar 401 and a partner satellite As a result of the failure of Telstar 401 three years ago, were supported in 24 months leading to nine avoidance MIT Lincoln Laboratory, in cooperation with commer- maneuvers incorporated into routine station keeping cial partners, began an investigation into this situation. and six dedicated avoidance maneuvers. This process Under the agreement, Lincoln worked to ensure a col- has led to a validated concept of operations for en- lision did not occur between Telstar 401 and partner counter support at Lincoln. satellites and to understand the scope and nature of the Active problem. The results of this cooperative activity and Satellites recent results to carefully characterize the actual prob- SOLIDARIDAD 02 ANIK E1 04-Oct-1999 ability of collision in the geostationary orbit are de- 114 SOLIDARIDAD 1 GOES 07 scribed. ANIK E2 112 MSAT M01 ) ANIK C1 110 GSTAR 04 deg USA 0114 1. INTRODUCTION LES 08 108 LES 09 GE 01 106 DBS 01 On 11 January 1997 Telstar 401 failed on-orbit in the SPACENET 04 104 MSAT M02 geostationary belt. It will now oscillate indefinitely DBS 03 DBS 02 near the geopotential well at 105 degrees West longi- 102 USA 0127 USA 0020 tude, next year passing within ten to thirty kilometers 100 ACTS 01 GALAXY VI WEST LONGITUDE ( of twenty-two active satellites stationed between 97 GOES 09 98 and 113 degrees West longitude. The behavior of Tel- 96 star 401, typical of inactive geosynchronous satellites, 0 200 400 600 800 1000 led six commercial satellite operators (AMSC, 11 JAN 97 (011) DirecTV, GE Americom, PanAmSat, SATMEX and RELATIVE DAY Telesat Canada) to enter into a Cooperative Research Fig. 1. Telstar 401 Encounter Situation and Development Agreement (CRDA) with MIT Lin- coln Laboratory. The resulting cooperative activities In addition, as part of the cooperative agreement, a sought to assess and respond to the threat posed by number of important research objectives were accom- Telstar 401. With over 40 years of space surveillance plished. Abbot and Thornton [2] undertook calibration technology development and sensor operations, MIT of partner satellite ranging data to establish procedures Lincoln Laboratory was recognized to be uniquely po- for routine receipt, calibration and processing of part- sitioned to properly address this geosynchronous en- ner ranging data for use in precision orbit determina- counter threat. The longitude oscillation of Telstar 401 tion. Abbot and Sharma [3] investigated the optimum and resulting encounters with active satellites are mix of sensor data needed to meet orbit accuracy re- shown in Fig. 1. quirements for encounter support, finding that a com- bination of radar and optical data synergistically pro- duces precision orbits with relatively few observations. *This work was performed under a cooperative Research and Development Agreement (CRDA 922) between MIT Lin- coln Laboratory and PanAmSat. Opinions, interpretations, conclusions, and recommendations are those of the authors and do not necessarily represent the view of the U.S. Government. Proceedings of the 3rd European Conference on Space Debris, ESOC, Darmstadt, Germany, 19 - 21 March 2001 (ESA SP-473, August 2001) Recently, in late August 00, another satellite failed in Although it was the failure of Telstar 401 and the re- orbit in the same region of the geosynchronous orbit. sulting activity at Lincoln Laboratory which led to the Solidaridad 1 is a SATMEX satellite that was located recognition of this geosynchronous encounter problem, at 109° W sublongitude in the path of Telstar 401. the situation arises as an unavoidable consequence of From being threatened, it has now turned into a threat the recent launch history of geostationary communica- itself. Its predicted longitude drift is between 101° W. tion satellites. The first successful geostationary com- and 109° W thus overlapping a part of the path of Tel- munication satellite, Syncom II, launched in 1963 in- star 401. In addition, there was significant concern augurated a flurry of geostationary launch activity raised by Galaxy 7, owned by Panamsat, when it also which gave rise to the initially rapid but continuing failed in situ at 125° W sublongitude in late November increase in the geostationary satellite population shown 00. However, Boeing and Panamsat were successful in in Fig. 3, using data from the Lincoln Space Surveil- regaining control and boosting it out of geosynchro- lance Center (LSSC) databases. Initially this launch nous orbit. These incidents illustrate that unexpected activity was dominated by military launch activity but failure of large satellites in GEO may well continue to during the mid 1980s to mid 1990s commercial launch happen. activity began to dominate. In order to determine the magnitude of the geosyn- 120 MILITARY chronous encounter threat, we determined the number CIVIL 100 of encounters between all active (approximately 270) COMMERCIAL and inactive geosynchronous objects (approximately 80 430). An encounter was defined as a difference in geo- centric radius less than 200 km and in longitude less 60 than 0.2 degrees at the locations of the orbital plane intersections. Active satellites were considered to re- SATELLITES 40 side at the center of their station-keeping box given by 19-Jan-2000 the semi-major axis and longitude of the ascending 20 node of their orbit. Inactive satellites that could ap- 0 proach the geostationary radius (42,166 km) within 200 1965 1970 1975 1980 1985 1990 1995 km were propagated from August 1998 to August 1999 using DYNAMO, a precision numerical propagator LAUNCH YEAR developed at MIT Lincoln Laboratory and discussed more fully below. The resulting distribution of en- Fig. 3. Thirty Years of Cumulative Launch Activity counters as a function of the distance of closest ap- proach is shown in Fig. 2. Considering only those en- As a result of the encounter support concept of opera- counters with a distance of closest approach not more tions developed and validated at MIT Lincoln Labora- than 50 km, the results indicate 4152 encounters, be- tory and the accompanying investigation into the scope tween an active, geostationary satellite and an inactive, and nature of the problem, the initial two year CRDA geosynchronous object, will occur annually. has been extended for an additional two years. As part of the continued CRDA activity, Lincoln Laboratory INTERSECTIONS - Aug 98 to Aug 99 will develop a system to monitor encounters between 600 all cataloged, inactive threatening resident space ob- jects and GEA CRDA partner satellites. Objectives of 500 the system include automation of encounter support to 400 produce the highest quality orbits and fewest false alarms while minimizing sensor time and analyst in- 300 volvement. A conceptual block diagram of the Geo- synchronous Monitoring and Warning System 200 (GMWS) is shown in Fig. 4. 31-Jan-2000 100 In addition to the development of the GMWS, Lincoln TOTAL ANNUAL ENCOUNTERS 0 has taken a careful look at the probability of collision 0 50 100 150 200 in the geostationary orbit, the description of which DISTANCE OF CLOSEST APPROACH (km) forms the purpose of this document. Fig. 2. Distribution of Encounter Distance of Closest Approach SSN LL Analysts LL Analysts Catalog CRDA Partner CRDA Partner Orbit Encounter Encounter Partner Orbit GMWS Encounter ALERT Encounter WARNING Determination Monitoring Warning Data Determination Catalog Monitoring (-60 days) Warning (-15 days) System System System System System System • Ranging • Uses available SSN • Uses additional Data Tracking Observations MHR observations • Maneuver Data • Uses best available • Uses DYNAMO Schedules element set element set EncounterEncounter Tasking Tasking SystemSystem MHR Fig. 4. Geosynchronous Encounter Monitoring and Warning System Concept 2. PROBABILITY OF COLLISION 1 f 2 (x, z) = ´ 2 2ps xs z 1- r xz Several authors have considered the problem of on- (1) é 2 2ùé ù orbit collisions. For geostationary satellites, Hechler æ x ö æ x öæ z ö æ z ö ê 1 ú êç ÷ ç ÷ç ÷ ç ÷ ú - ç ÷ -2r xzç ÷ç ÷+ç ÷ ê ú and Van der Ha [4] consider the probability of collision ê s x s x è s z ø è s z ø ú æ 2 ö ëêè ø è ø ûúê 2ç1-r xz ÷ ú for the population of geostationary satellites on-orbit in e ë è ø û 1981 and determine an annual collision rate of 6´10-6. r In the same year, Kessler [5] presents a straightforward where sx, sz, and xz are the separation standard devia- approach, which may be used to estimate the collision tions and correlation coefficient. For the case in which probability between orbiting objects in general. Kess- the collision radius, ra, is much less than sx and sz, ler’s approach is adapted and discussed below. Much f2(x,z) may be integrated over the collision area, to ob- more recently, a number of authors, including Alfriend tain the collision probability P = òò f 2 (x, z)dxdz , by [6] (and others) and Chan [7], have considered the A probability of an on-orbit collision using the orbital using the constant value f2(xe,0), where xe denotes the covariances.