Orbit raising with low-thrust tangential acceleration in presence of earth shadow

The problem of low-thrust tangential thrusting along small-to-moderate eccentricity orbits in the presence of Earth shadow is analyzed. Given the orbital elements and the shadow geometry at the start of each revolution, the changes in the in-plane orbit elements after one revolution of intermittent thrusting are evaluated analytically for a given level of constant acceleration. These perturbation equations are valid for small to-moderate eccentricities (0 less than or equal to e less than or equal to 0.2), except for the argument of perigee, which is valid for My eccentricity larger than 0.01 due to the well-known singularity at e = 0 associated with the use of the classical elements, When e is less than 0.01, a nonsingular set of equations is used instead so that the orbit is continuously updated with negligible computational effort. These analytic guidance equations valid for low-thrust accelerations on the order of 10(-4) g and less are developed for implementation in efficient transfer simulation programs for systems design optimization and preliminary mission analysis work. Furthermore, for the problem of continuous constant low-thrust tangential acceleration, the analytic integration of the orbit equations is shown to be accurate for several tens of revolutions in low Earth orbit and about 10 revolutions in geosynchronous Earth orbit, The analytic integration is further extended to include the effect of the Earth oblateness on the expanding orbit. This analytic long-term orbit prediction capability will minimize the computational loads of an onboard computer for autonomous orbit transfer applications and allow, among other things, the consideration of long multiorbit data arcs for analytic orbit determination updates, thereby decreasing considerably the frequency of these updates.