Effect of Resistive Force and Earth’s Ellipticity on Resonant Curves of Geo-centric Satellite Using Unperturbed Solution

Abstract

This research paper examines the impact of the resistive force and equatorial ellipticity of the Earth (EEE) on the
motion of a geocentric satellite. We express a satellite’s motion in a spherical coordinate system using potential
of the Earth. We apply an unperturbed solution to simplify and reduce the equations into an ODE of secondorder.
After that, we analyze the resonant curves and oscillatory amplitudes using the differential equation’s
particular solution. We observe that the resonance arises for the frequencies ϑ˙
0 (satellite’s angular velocity) and
˙γ (rate of change of EEE). Further, we analyze motion of the satellite in the three different cases: (i) ϕ = 0 and b
= 0, (ii) ϕ = 0 and b 6= 0, and (iii) ϕ = 06 and b 6= 0, with b as a coefficient of resistive force and ϕ as a latitude of
satellite. Later, we examine the effect of γ, b, and orbital elements on each case’s resonant curves and oscillatory
amplitudes.