In the present paper, we have determined the equations of motion of the Moon in spherical coordinate system using the gravitational potential of Earth. Using perturbation, equations of motion are reduced to a second order differential equation. From the solution, two types of resonance are observed: (i) due to the frequencies–rate of change of Earth’s equatorial ellipticity parameter and Earth’s rotation rate, and (ii) due to the frequencies–angular velocity of the bary-center around the sun and Earth’s rotation rate. Resonant curves are drawn where oscillatory amplitude becomes infinitely large at the resonant points. The effect of Earth’s equatorial ellipticity parameter and resistive force on the resonant curve is analyzed. From the graphs it is observed that the effect of Earth’s equatorial ellipticity on the resonant curve is very small while the effect of resistive force is significant. It is also observed that oscillatory amplitude decreases when the magnitude of resistive force increases. Finally, the phase portrait is analyzed when the system is free from forces. Orbits in the phase space are also studied by applying the method of Poincare section. A necessary condition for the bifurcation is derived at the end.
Yadav, Sushil; Kumar, Mukesh; and Aggarwal, Rajiv
(R1889) Analysis of Resonant Curve in the Earth-Moon System under the Effect of Resistive Force and Earth’s Equatorial Ellipticity,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
1, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss1/13