Resonance in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity

Abstract

Resonances in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity have been investigated. The resonance at two points resulting from the commensurability between the mean motion of the satellite and Γ (angle measured from the minor axis of the Earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. We have observed that the amplitude and the time period of the oscillation decrease as Γ increases in the first quadrant. The radial deviation (Δr) and the tangential deviation (rcΔθ) have been determined. Here rc represents the synchronous altitude. The effects of the arithmetic sum of amplitudes λi involved in the perturbation equations on orbital inclination 0∘≤α0≤90∘ are shown. It is observed that \(\sum_{i = 1}^{46} \lambda_{i}\) increases as α0 increases. We have also determined the displacement ΔD (called drift) due to the oscillatory terms under the summation sign involved in the equations of motion of the satellite. We have observed that the value of ΔD is less than 0.5∘.