CONJUNCTION ANALYSIS AND PROBABILITY OF COLLISION USING RELATIVE ORBITAL ELEMENTS
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2018 Univelt Inc. All rights reserved. The probability of collision problem can be broken down into two main parts. The propagation stage, during which the initial conditions and distributions are propagated through the nonlinear equations of motion. And the integration stage, where the probability of collision integral is evaluated. It is well known that the equations of motion governing the time evolution of orbital elements are more linear than the Cartesian equations of motion, and therefore make an excellent choice for propagating the distributions in time. Unfortunately, all existing semi-analytical methods for computing the probability of collision require that this distribution in orbital element space be mapped into Cartesian coordinates for the evaluation of the probability of collision integral. In this paper a set of relative orbital elements are presented along with conditions for collision between two spherical bodies in the relative orbital element space. Formulating the probability of collision problem in this coordinate system is shown to make the problem more linear as well as reduce computational burden. This new method is then used to compute the probability of collision and is compared, using the CRATER collision risk assessment tool, to results from the Cartesian formulation of the probability of collision integral and Monte Carlo results on a number of test cases.
