Author(s)

M. H. A. Youssef

Astronomy Department, Faculty of Science, Cairo University, Cairo, Egypt.

This work deals with the numerical solution of the gravitational waves effects on the orbital elements of the planets in case of commensurability between the wave’s frequency n_g and the planet’s mean motion n_p. Taking Mercury and Pluto as practical examples for low frequency and high frequency, the variations of the orbital elements of Mercury due to resonance of gravitational wave are different and small than the perturbation on Pluto. The amount of changing in the orbital elements under the effects of gravitational waves is different from planet to planet according to the planet’s mean motion n_p. For low frequency n_g, the secular variation in orbital elements will be negative (i.e. decreasing) in the inclination, semi-major axis and the eccentricity (i, a, e) like as Pluto. For high frequency n_g like Mercury, the secular variation in all the orbital elements will be positive (i.e. increasing). The perturbation on all the orbital elements of two planets is changing during each revolution except the eccentricity e of Mercury and the mean anomaly M of Mercury and Pluto during the time.

Gravitational Waves, Celestial Mechanics, Perturbation, Orbital Mechanics, Numerical Techniques

H. A. Youssef, M. (2018) Numerical Studies of Resonance and Secular Effects of Gravitational Waves. World Journal of Mechanics, 8, 182-191. doi: 10.4236/wjm.2018.85013.