Shape-Based Method for Non-Keplerian Orbit Design

The orbit under artificial control is termed Non-Keplerian orbit which does not follow Kepler's Laws. The transfer orbit design under the continuous limited thrust is one of the most important topics in this new field. Shape-based method for Non-Keplerian orbit design is developed. Firstly the nondimensional equations of motion are established. The general equation is derived with which common curves could be utilized in orbit design with respect to polar coordinates. In addition, Forbes' spiral is presented in two assumptions, which is restrictive. So the tangential thrust assumption is ignored and then the orbit design method is described based on the assumption that the radius r is a polynomial function of time. The requisite thrust magnitude and direction are available analytically. In the end, an example of the transfer orbit is given. The result demonstrates the feasibility of shape-based method applied to orbital transfer problem under the continuous thrust.