  An analytical formulation for collision avoidance maneuvers involving a
spacecraft and a space debris is presented, including solutions for the maximum
deviation and minimum collision probability cases. Gauss' planetary equations
and relative motion equations are used to map maneuvers at a given time to
displacements at the predicted close approach. The model is then extended to
map changes in state between two times, allowing one to propagate covariance
matrices. The analytical formulation reduces the optimization problem to an
eigenproblem, both for maximum deviation and minimum collision probability. Two
maximum deviation cases, total deviation and impact parameter, are compared for
a large set of spacecraft-debris conjunction geometries derived from European
Space Agency's Meteoroid and Space Debris Terrestrial Environment Reference
(MASTER-2009) model. Moreover, the maximum impact parameter and minimum
collision probability maneuvers are compared assuming covariances known at the
maneuver time, to evaluate the net effect of lead time in collision
probability. In all cases, solutions are analyzed in the b-plane to leverage
its natural separation of phasing and geometry change effects. Both
uncertainties and maximum deviation grow along the time axis for long lead
times, limiting the reduction in collision probability.
