The design of spacecraft quasi-synchronous orbits around Phobos for landing on its surface

The design of spacecraft quasi-synchronous orbits around Phobos is considered. Quasi-synchronous orbits are retrograde quasi-satellite orbits outlying from Hill sphere in the plane elliptic restricted three-body problem. The orbit should pass through the preset point at the prescribed instant of time and at minimum distance from Phobos surface every time it passes over assumed region of landing. The dynamical equations are presented in form describing the orbit as composition of motions along two ellipses: inner and outer. The formula describing the relation between semiaxes of inner and outer ellipses is derived. This formula has been used for an evaluation of the initial approach to the numerically designed orbit. Thus computing process was greatly simplified and accelerated. The tables containing evaluated initial conditions are reported.