Resonant curves of geo-centric satellite under the gravitational effect of the Earth-Moon-Sun system including Earth's equatorial ellipticity and resistive force using unperturbed solutions

Abstract

This research article presents the effect of the Earth's equatorial ellipticity and the resistive force on a geocentric satellite's resonant curves. The resonance occurs in the motion of the satellite due to the frequencies, the angular velocity of the satellite, the rate of change of Earth's equatorial ellipticity parameter (γ̇), the steady-state angular velocity of the Moon around the Earth (ϑ0̇), and the steady-state angular velocity of barycenter (Θ̇) around the Sun. We express the equations of motion of the satellite in a spherical coordinate system by using the Earth's potential. By applying the unperturbed solution, we reduced the system of equations into a second-order differential equation and obtained its solution. From the solution it is observed that the resonance appears between the frequencies δs0̇,γ̇,Θ0̇ and ϑ0̇ at ten resonant points. We analyze the resonant curves corresponding to the resonant points and show the effect of resistive force and latitude of a satellite. Also, We show the effect of eccentricity (e) and semi-major axis (a) on the oscillatory amplitudes (Ai), for i=1,2,3…21.