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. Give n the orbital elements and the shadow geometry at the start of each re volution, the changes in the in-plane orbit elements after one revolut ion of intermittent thrusting are evaluated analytically for a given l evel of constant acceleration. These perturbation equations are valid for small to-moderate eccentricities (0 less than or equal to e less t han or equal to 0.2), except for the argument of perigee, which is val id for My eccentricity larger than 0.01 due to the well-known singular ity 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 e ffort. These analytic guidance equations valid for low-thrust accelera tions on the order of 10(-4) g and less are developed for implementati on in efficient transfer simulation programs for systems design optimi zation and preliminary mission analysis work. Furthermore, for the pro blem of continuous constant low-thrust tangential acceleration, the an alytic integration of the orbit equations is shown to be accurate for several tens of revolutions in low Earth orbit and about 10 revolution s in geosynchronous Earth orbit, The analytic integration is further e xtended to include the effect of the Earth oblateness on the expanding orbit. This analytic long-term orbit prediction capability will minim ize the computational loads of an onboard computer for autonomous orbi t transfer applications and allow, among other things, the considerati on of long multiorbit data arcs for analytic orbit determination updat es, thereby decreasing considerably the frequency of these updates.