Now, to calculate 8r we assume the object of interest has volume v. and the collider has independent volume and the position probability space of the initial When n is the number of subvolume spaces, V is to be divided into and integrated over. With V so divided, let 8r be the largest linear dimension of the space (e.g., if spheroid use the largest major axis; if prism use the largest side; etc). With the volume thus partitioned, then for each discrete r, we need to construct an appropriate set of r; which will satisfy both come apriori selected probability densify model and Eqns la+b. With a discrete set of r7 and q and their associate probabilities for each satellite, an appropriate collision database can now be populated and a collision probability can be calculated. The next section will recap the procedure in general terms, from process initiation to termination for the case of a single possible collision. Overall Schematic for the Collision Requirements and Satellite Trajectory Analysis (Crystal) Prototype After a decision has been made to invoke CRYSTAL (this via a 427M COMBO* run indicating a collision between two objects is possible), two accurate element sets for both objects need to be constructed just prior to the “collision”, (the closer to the collision and the more accurate, the better). With this information now available appropriate rg and rQ vectors may be constructed and, in accordance with conservation of energy and angular momentum requirements, a statistical ensemble constructed, each state having some intrinsic probability assigned to it (this to be determined, using perhaps a unit random or a gaussian distribution). This is done for the satellite pair over the time of a single, possible collision. Each case is propagated (this can be accomplished by using three points; before, at or about, and after the conjunction/collision; and then using an interpolation technique such as Sterling's Approximation for each x, y,z coordinate variable)3. After each specific case that the propagation curves are determined it may be useful to translate the absolute motion of the satellite pair in space to relative motion (i.e., hold one object to be always at the origin). A collision geometry can then be selected (box. sphere, spheroid, etc.) for the object at the origin, which would include in it the intrinsics of the now “moving” object. The moving object would be treated as a point mass traveling along a space curve. If the space curve intersects the predefined
RkJQdWJsaXNoZXIy MTU5NjU0Mg==