Method for Calculating Collision Probability Between a Satellite and a Space Tether

Abstract

A method for calculating the collision probability between an orbiting object and a space tether, given the respective state vectors and error covariance matrices, has been developed. The methodology employs an efficient computational scheme that was used successfully in predicting the collision hazard for asymmetrical satellites. The tether is modeled as a very long, slender body having a predefined serpentine shape with a circular cross section. The colliding space object is assumed to be spherical in shape. Analytical techniques are used to reduce the collision prediction problem to that of integrating a two-dimensional symmetric probability density over a region representing the collision cross section of the tether and space object. The symmetric form of the probability density enables the two-dimensional integral to be reduced to a one-dimensional path integral that permits easy numerical implementation. Test case results indicate collision probabilities significantly higher than satellite-satellite collision probabilities.