Trajectory of a spacecraft with constant radial thrust

The trajectory of a spacecraft under constant radial thrust was studied. Great deals of efforts were dedicated to investigate the boundedness and periodicity. The case of elliptic parking orbit was focused. First, the equations of motion were formulated in polar coordinates and simplified into quadratures by using of energy integral and angular momentum integral. Then, the orbital boundedness was analyzed by transforming the original problem into solving a cubic inequality. Basing on different initial parking true anomaly, the problem was researched separately. The bounds of motion and escaping conditions were obtained in terms of thrust. Next, the periodicity of motion was studied by utilizing elliptic integrals. The periodicity of radial motion and periodicity in polar angle changing were explained. A property of quasi-periodicity in motion was described. The quasi-periodic motion could degenerate into periodic orbits, if a condition among initial parking parameters and thrust were satisfied. Meanwhile, a Newton-Raphson algorithm was given to obtain periodic orbits numerically. Several numerical examples were given to support the conclusion.