Forbidden tangential orbit transfers between intersecting Keplerian orbits

Abstract

The classical problem of tangential impulse transfer between coplanar Keplerian orbits is addressed. A completely analytic solution which does not rely on sequential calculation is obtained and this solution is used to demonstrate that certain choices of initial true anomaly can produce singularities in the parameters of the transfer orbit. A necessary and sufficient condition for the existence of such singularities is that the initial and final orbits intersect.