Collision probability of composite cubesats hovering in leader-follower configuration

Analytical expressions are obtained for computing the collision probability of a large Composite CubeSats hovering in the close vicinity of another large Composite CubeSats in a Leader-Follower configuration. The composite is constructed from a large number of Unitary CubeSats arranged in a cuboid volume. The study involves the modeling of the growth of a time-dependent probability density function over a period of time and the effects of that growth on the collision probability. Studies of collision probability as a function of time are performed in terms of the parameters: separation between neighboring orbiters, covariance size (different in three directions) and the size of the two cuboid CubeSat Composites. It was found that certain combinations of parameters resulted in collision probability curves which intersected and others did not. This curve-crossing phenomenon cannot be predicted in advance but must be demonstrated quantitatively by performing detailed computations. This knowledge may be used to advantage in the design of distributed systems and in the orbital maintenance of their configuration. Moreover, the Principle of Scaling is used to obtain collision probabilities using the results obtained from a relatively small number of case studies so as to circumvent the effort to perform copious computer runs when the input parameters are changed.