Resonance In the Motion of a Geocentric Satellite Due To the Earth’s Oblateness

Resonance In the Motion of a Geocentric Satellite Due To the Earth’s Oblateness

Piyush Kumar1, M.R. Hassan2, T.R. Ahamad3, Md. Aminul Hassan4

1,2,3 University Department of Mathematics, T.M.B. University, Bhagalpur, India

4GTE, Bangalore, India

Abstract - This paper deals with the effects of the oblateness of the Earth on the resonant motion of a geocentric satellite. Three resonances, 1:1, 2:1, and 3:1, occur due to the perturbation of the oblateness of the Earth.

Key Words:  Inertial frame, Rotating frame, Oblateness, Geocentric Satellite and Resonance.

1. Introduction

Problems of resonance play an important role in solar dynamics while solving the equations of motion. Resonance may be manifested as the appearance of small divisors in the solution of the equation of motion of the satellite. Orbital resonance of Earth satellite concerning lunisolar gravity and direct solar radiation pressure, with particular reference to those resonances, the occurrence of which is dependent only on the satellite’s orbital inclination, was studied by Hughes in (1980).

Bhatnagar et al. (1986) examined the motion of a satellite by taking gravitational forces of the Moon, Earth and the Sun (with radiation pressure). Quarles et al. (2012) have studied the resonances for the coplanar Circular Restricted Three-body Problem for the mass ratio between 0.10 and 0.15 and used the method of maximum Lyapunov exponent to locate the resonances. They showed that for a high value of resonance, orbital stability is ensured where single resonance is present.