The analytic basis for debris avoidance operations for the International Space Station

A debris avoidance process based upon collision probability has been developed for the International Space Station (ISS) using covariance information supplied by the United States Space Command (USSPACECOM). Given the debris flux and the distribution of debris covariances for conjuncting debris, it is possible to estimate risk reduction, fractional residual risk and maneuver rate for the ISS as a function of chosen maneuver threshold collision probability. 1. BACKGROUND Orbiting objects larger than about 10 cm in size are tracked both by radar and optically by a number of agencies, which maintain the orbital elements for these objects. The flux of tracked objects is small compared with the flux of objects large enough that space vehicle shielding is ineffective, but too small to be tracked. However the monetary value of the collision risk, about 10 annually, between tracked debris and the International Space Station is sufficiently large that the development and maintenance of debris avoidance process is more than economically justified. Further the flux of tracked debris is expected to increase significantly in coming years. With a debris avoidance system in place, debris avoidance is economically justified for other vehicles. 2. PROBLEM DEFINITION The simplest debris avoidance method is that of an exclusion volume in which a maneuver is considered or performed if a conjunction is expected to occur within some predefined volume about a space vehicle. Such a procedure has been adopted by the space Shuttle Program. If a conjunction is predicted to occur within a 4x10x4 km box aligned along the Shuttle velocity vector, an avoidance maneuver is performed if it is allowable within all other Shuttle operational constraints. The box size was determined by performing Monte Carlo calculations which indicated that the collision probability for any object projected to pass outside the box was 10 or less [1]. However, based on the known tracked flux, this procedure would result in from 10 to 15 maneuvers per year for the International Space Station (ISS), too many for a micro gravity laboratory. Further, the risk reduction is not quantified without knowledge of the uncertainty distribution of the tracked conjuncting objects. In this work, we show the consequences of a debris avoidance process based on collision probability. This process minimizes the number of maneuvers and allows assessment of risk reduction, but requires a state vector for both ISS and the conjuncting object and an accurate estimate of the state vector uncertainties of the two objects. 3. PROCESS USSPACECOM maintains Cartesian state vectors for all objects with perigees below 600 km, on a special Astrodynamics Workstation (ASW). These objects are tracked with a slightly elevated level of tasking. At the same time the sensors are routinely calibrated using satellite laser ranging data. If a conjunction is predicted within a 40x80x80 km pizza box about ISS, conjunctor tasking is increased and the object is watched. The Johnson Space Center (JSC) flight controllers are notified 72 hours prior to a conjunction if the object is predicted to come within a 4x50x50 km box. If the collision probability is greater than 10 and the conjunctin geometry has been stable for three of the last four state vector updates, an avoidance maneuver is performed if it is possible. 4. COLLISION PROBABILITY For conjunctions with non-zero relative velocity [2], the seemingly difficult task of calculating a collision probability reduces, in general, to a simple twodimensional problem. At some time t near conjunction, let the vector separation between the objects and the relative velocity be 0 r v and r v v . The vector separation as a function of time is given by t v r r r r v v v + = 0 . Time of conjunction is determined by use of . 2 2 0 t v v v r r r t d d r r r r r r v v v v v v ⋅ + ⋅ + = = ⋅ (1) Proceedings of the 3rd European Conference on Space Debris, ESOC, Darmstadt, Germany, 19 21 March 2001 (ESA SP-473, August 2001) The time to conjunction is given by . 2 r r r v v r t v v ⋅ − = (2) When t = 0, 0 r v is perpendicular to r v v , if r v v or r r v are not zero. Thus the conjunction will take place in a plane perpendicular to the relative velocity vector, called the collision plane. The three dimensional position covariances of the conjuncting objects can be rotated into a common coordinate frame and added. If the contributions of the velocity uncertainties over the time of the conjunction do not contribute materially to the combined position uncertainty, the position of the conjunction on the collision plane will not change over the time of the conjunction. The problem is reduced to two dimensions with the effective covariance being the projection of the three-dimensional combined covariance on to the collision plane. The spatial density of the uncertainty in the debris position relative to the space vehicle is . e C 2 1 ) r ( f ) r r ( C ) r r ( 2 1 d 1 T d v v v v v − − − −