Resonant curve of geo-synchronous satellite including effect of earth’s equatorial ellipticity and resistive force using perturbations technique

In this paper, we have investigated the effect of earth’s equatorial ellipticity parameter and resistive force on the resonant curve of a geo-synchronous satellite using perturbations technique. Equations of motion of the satellite are determined in spherical coordinates (r,θ,ϕ) with the help of gravitational potential of the earth. Furthermore, the equations of motion of the satellite are simplified in the form of second order differential equation by using perturbations technique. It is observed from the solution that resonance occurs due to the frequencies θ˙E (angular rate of rotation of the earth) and γ˙ (where γ be the measured from minor axis of the earth’s equatorial ellipse to the projection of the satellite). Finally, we study the effect of the earth’s equatorial ellipticity parameter and the resistive force on the resonant curve with the help of different graphs. It is observed that amplitude A decreases when the magnitude of the resistive force increases.