  In this paper, a surface geometric constraint approach is used in designing
the orbits of a solar sail. We solve the solar sail equation of motion by
obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption
that the cone angle is constant throughout the mission. A family of orbit
equation solutions can then be specified by defining a constraint equation that
relates the radial and polar velocities of the spacecraft and is dependent on
the geometry of the surface where the spacecraft is expected to move. The
proposed method is successfully applied in the design of orbits constrained on
cylinders and to displaced non-Keplerian orbits.
