Analysis of Resonant Curve and Phase Portrait Due to Earth’s Equatorial Ellipticity In the Earth-Moon System Using Perturbation Technique

In this paper, the resonance due to equatorial ellipticity of Earth, spin rate of Earth and angular velocity of bary-center are investigated. Using spherical coordinate system, we have determined equations of motion of the moon. By using perturbations relative to moon, equations of motion are simplified to second order ordinary differential equation containing the equatorial ellipticity parameter of the Earth. Two types of resonant curves due to the frequencies (a) (gamma)over dot, (theta)over dot (E), and (b) (alpha) over dot, (theta) over dot (E) are analyzed. It is observed that the amplitudes of the oscillation are different at different resonant points due to different size of the bandwidth. Finally, the phase portrait of the orbits of the moon and the phase spaces are analyzed by using Poincare section with periodicity pi/(gamma) over dot in time t for the unpertubed system.