Radially accelerated trajectories for variable mass spacecraft

This paper proposes a new approach for mission design of a spacecraft with a time-variable mass and subjected to a continuous propulsive thrust in the radial direction. Two different mission scenarios are discussed according to whether the thrust remains constant along the whole mission or its modulus varies inversely proportional to the distance between the spacecraft and the primary body. In the first case a graphical solution is discussed for evaluating the spacecraft performance during an escape mission scenario. In the second case a closed-form solution, which makes use of the trigonometric integral functions, is found for describing the spacecraft trajectory in a polar reference frame. Some examples are discussed where the methodology is applied to a spacecraft with an electric thruster or a mini-magnetospheric propulsion system.