Dynamics and Control Lunisolar Perturbations for Highly-Eccentric Earth-orbiting Satellites

Abstract

Satellites in highly-eccentric orbits are unique in their ability to spend the majority of their period near the apogee. When these orbits are critically-inclined and have an argument of perigee equal to 270 • , they become well-suited for Earth-observation missions for northern regions. However, their orbital characteristics result in a complex and dynamic set of perturbation forces acting on the satellite orbit due to the gravity of the Moon and the Sun, coupled with the perturbations caused by the oblateness of the Earth.The focus of this thesis is on both the dynamics and the control of the lunisolar perturbations. The study of the dynamics involves using geometric and kinematic methods to analyze the conditions at which the rates of change of the orbital elements due to lunisolar perturbation forces are zero. The resulting analysis provides insight into the mechanisms of the various oscillations caused by the gravitational attraction of the Moon and Sun. A method to predict the future occurrences when the rates of change of the orbital elements are equal to zero is also developed.Using the enhanced knowledge of the lunisolar perturbation forces acting on the highlyeccentric orbits, a control strategy is developed to decrease the amount of ∆V needed to maintain the eccentricity, inclination, and argument of perigee near their nominal values.The control strategy uses the grazing method to exploit the oscillations of the orbital elements caused by the Moon and Sun. The strategy, which uses analytical methods to compute the control requirements, is compared to an equivalent approach that uses numerical methods to exploit the lunisolar perturbations.ii

Exploiting lunisolar perturbations using the grazing method: An orbit control strategy for a satellite in a critically inclined highly eccentric orbit around the Earth

“…Since the 2M-oscillations are relatively small compared to both the 2S-oscillations and the ΔΩÀoscillations [12], the dependency of the position of the Moon for the ODEs is removed. This is accomplished by averaging the product of the direction cosines seen in Eqs.…”