A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body

This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and, in addition, a complete polynomial system when considering the perturbation produced by the zonal harmonics from the gravitational force of an oblate celestial body. These orbital elements present no singularities and are able to represent any kind of orbit, including elliptic, parabolic and hyperbolic orbits. In addition, an application to this formulation of the Poincaré-Lindstedt perturbation method is included to obtain an approximate first order solution of the problem for the case of the J2 perturbation.

Design of Artificial Sun-Synchronous Orbits with Main Zonal Harmonics and Solar Radiation Pressure Using Continuous Low-Thrust Control Strategies

Artificial sun-synchronous orbits are suitable for remote sensing satellites and useful in giving accurate surface mapping. To design such orbits accurately with arbitrary orbital elements, three control strategies are provided with the consideration of main zonal harmonics up to J4 and solar radiation pressure (SRP). In this paper, the continuous variable low-thrust control is used as a way to achieve these artificial orbits and given by electric propulsions rather than chemical engines to enlarge lifespan of the spacecraft. The normal continuous low-thrust control is used to illustrate the control strategies. Furthermore, formulas for refinement of normal control thrusts are applied to overcome errors due to approximations. The results of the simulation show that the control strategies explained in this paper can realize sun-synchronous orbits with arbitrary orbital parameters without side effects and the effect of solar radiation pressure is very small relative to main zonal harmonics. A new technique is suggested, ASSOT-3, to minimize fuel consumption within one orbital period more than others. This technique is based on computing the root mean square of the rate of ascending node longitude instead of the average.