Orbital motion of spacecraft under the action of constant radial thrust acceleration admits closed-form solutions. If the orbit is circular before thrusting begins, some analytical results of practical interest are known to exist. In particular, it is now well understood that when the radial thrust acceleration is sufficiently small, the spacecraft starting from an initial circular orbit cannot reach escape conditions. Under such conditions, it will attain a maximum radius (“apogee”) along an outbound trajectory. If the radial thrust acceleration is maintained even beyond this point, the vehicle returns to the initial radius along an inbound trajectory. An interesting property of this problem is that whereas the time intervals for these outbound and inbound trajectories are identical, the trajectories themselves are very different from one another. The primary contribution of this paper is to investigate this feature, which we accomplish by constructing a Poincaré map associated with the governing dynamics. Such a construction is shown to be canonical in the sense that the phase space of this dynamical system is approximately periodic. All the analysis for this problem is developed using analytically determined relations governed by an incomplete elliptic integral of the third kind. These equations may be viewed as generalizations to Kepler’s equation for the low radial thrust acceleration problem.
On Low Radial Thrust Spacecraft Motion
J of Astronaut Sci
The Journal of the Astronautical Sciences ; 48 , 2-3 ; 149-161
2000-06-01
13 pages
Article (Journal)
Electronic Resource
English
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