Dynamics of Resonant Curves of Earth-Moon system under the influence of Resistive Force using Unperturbed Solution

Abstract

This work investigates the dynamical behavior of the resonant curves in the motion of the Earth-Moon system under the influence of resistive force. In this study, the resonance arises in this motion due to the rate of change of Earth’s equatorial ellipticity (EEE) (˙ γ), the Moon’s angular velocity (˙ θmo) around the Earth, and angular velocity of barycenter (˙ α0) around the Sun, including the coefficient of resistive force (b). The configuration and equations of motion are expressed in a spherical coordinate system using the Earth’s potential. Applying the unperturbed solution reduces and simplifies the system into a second-order ODE and obtains a particular solution. It is observe that the commensurability occur between the frequencies: (i) ˙ γ and ˙ θm0, (ii) ˙ θm0 and ˙ α0 with the coefficient of resistive force. Finally, we analyze the dynamical behavior of the resonant curves for the orbital elements and the coefficient of resistive force.