Stationkeeping of Geosynchronous Spacecraft Using a Hybrid Orbit Propagator and Optimization Technique

WITH advances in space technology, current-generation geostationary spacecraft are often designed to operate for at least 10 years and are driven by multiple-mission scenarios. The ideal geostationary orbit has a constant sernimajor axis, zero eccentricity, and zero inclination. These orbital elements, however, tend to deviate from the ideal values because of various perturbing forces, including the Earth's oblateness, the gravitational forces exerted by the sun and moon, the solar-wind pressure, etc. Therefore, stationkeeping (i.e., maintaining the position of a geostationary spacecraft within a designated longitude slot) becomes necessary, and the requirements for stationkeeping are becoming more stringent, not only because of the limited longitudinal resource, but also because of the real possibility of signal-frequency interference with neighboring spacecraft. The objective of stationkeeping is to maintain the satellite within certain allowed limits for a given period of time. The classical strategy for stationkeeping is to separately control its position and velocity in two directions: that is, along the longitudinal and latitudinal directions (east-west and north-south stationkeeping, respectively). For example, drift-rate compensation targeting and the perigee sun-tracking method are used for east-west stationkeeping, whereas the inclination-vector drift is controlled for north-south stationkeeping [1,2]. Precise orbit propagation based on high-fidelity orbit models and accurate numerical integrators is used to plan an orbit-maneuver schedule in both directions within the constraints of the operator's work schedule. This classical method is indirect in the sense that the values of the orbital elements are controlled based on predictions of the expected future trend of their variation rather than by directly controlling the spacecraft position. Therefore, the aim of this Note is to propose a method of directly controlling the position of a geostationary spacecraft for stationkeeping purposes. The advantages of highly precise numerical orbit propagation and the computational simplicity of an approximate closed-form analytical solution to the perturbed-geostationary-orbit problem are effectively combined to yield a so-called hybrid orbit propagator, which is used to predict spacecraft drift with respect to a reference position. We then proceed to plan stationkeeping such that a given cost function (e.g., fuel usage) is minimized while the spacecraft is