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An analytical formulation for collision avoidance maneuvers involving aspacecraft and a space debris is presented, including solutions for the maximumdeviation and minimum collision probability cases. Gauss' planetary equationsand relative motion equations are used to map maneuvers at a given time todisplacements at the predicted close approach. The model is then extended tomap changes in state between two times, allowing one to propagate covariancematrices. The analytical formulation reduces the optimization problem to aneigenproblem, both for maximum deviation and minimum collision probability. Twomaximum deviation cases, total deviation and impact parameter, are compared fora large set of spacecraft-debris conjunction geometries derived from EuropeanSpace Agency's Meteoroid and Space Debris Terrestrial Environment Reference(MASTER-2009) model. Moreover, the maximum impact parameter and minimumcollision probability maneuvers are compared assuming covariances known at themaneuver time, to evaluate the net effect of lead time in collisionprobability. In all cases, solutions are analyzed in the b-plane to leverageits natural separation of phasing and geometry change effects. Bothuncertainties and maximum deviation grow along the time axis for long leadtimes, limiting the reduction in collision probability.

Analytical framework for space debris collision avoidance maneuver design