ENERGY CONSERVED PLANAR SPACECRAFT MOTION WITH CONSTANT THRUST ACCELERATION

Spacecraft motion with constant thrust acceleration in the direction perpendicular to the velocity is studied. A spacecraft in an initial circular orbit obtains a minimum (perigee) radius along an inbound trajectory or a maximum (apogee) radius along an outbound trajectory, after which the vehicle returns to the initial circular orbit. The energy of the system is the only integral of motion. A full analytical solution does not exist; however, a solution to the flight direction angle, that is, the angle between the position and velocity vectors, is found in terms of the position magnitude. This solution leads to the range of acceleration magnitudes for prograde motion, proving periodicity of the position magnitude, and finding periodic orbits.