Satellite A is located at at time i0 and at at time ip A similar relation exists for satellite B at points r’and At some time t0 < < T we say satellite A will collide with satellite B (note rj (ip need not necessarily be identical to Tq (ip, this depending on the size and orientation of the satellite, and the impact geometry). If we had perfect information of ^(Tq)/’/^^),^0, as well as all other pertinent information* , we could state with certainty the probability of the two bodies colliding to be either 0 or 1. We will ignore for the moment satellite specific factors (representing them as two perfect spheres of known radii in space), and consider the motion to be classical Keplerian. We assume the measurements take at t0 and their time derivatives) are not perfectly known, but can be represented by some statistical ensemble (random variables). Further, we claim the probability of the independent variables rp and rQ,) to be the somehow related to two constants of the motion (the constants acting as state boundaries). Where 8E and 8h are acceptable variations in the quantities known as energy (scaler) and angular momentum (vector), which are quantitives not directly measured; * satellites shape, size, orientation, etc For a classical orbital case, consider Figure 10:
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