Orbital motion under continuous tangential thrust

Abstract

The effect of continuous tangential thrust on the orbital motion and mass loss of a vehicle initially in a circular orbit is investigated analytically. It is shown that, for a thrust-to-weight ratio of greater than 0.16175, escape speed will eventually be reached along an unwinding spiral trajectory. For lower thrust-to-weight ratios, escape speed is never attained, and the flight path oscillates around a logarithmic spiral trajectory. Formulas are obtained for the approximate orbital motion and time of flight along each type of trajectory and for mass loss due to expenditure of rocket propellant.