Nelson, L.A. and Chau, W.Y. (1982) Orbital Perturbations of a Gravitationally Bound Two-Body System with the Passage of Gravitational Waves. Astrophysical Journal, 254, 735.
https://doi.org/10.1086/159785

has been cited by the following article:

• TITLE: Short-Period and Long-Period Effects of Weak Gravitational Waves

  AUTHORS: M. H. A. Youssef

  KEYWORDS: Gravitational Waves, General Relativity, Celestial Mechanics, Perturbation, Orbital Mechanics

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.7 No.3, September 28, 2017

  ABSTRACT: We compute the long-term orbital variation of a test particle orbiting a central body acted upon by normal incident of plane gravitational wave. We use the tools of celestial mechanics to give the first order solution of canonical equations of long-period and short-period terms of the perturbed Hamiltonian of gravitational waves. We consider normal incident of plane gravitational wave and characteristic size of bound—two body system (earth’s satellite or planet) is much smaller than the wavelength of the wave and the wave’s frequency nw is much smaller than the particle’s orbital np. We construct the Hamiltonian of the gravitational waves in terms of the canonical variables (l,g,h,L,G,H)and we solve the canonical equations numerically using Runge-Kutta fourth order method using language MATHEMATICA V10. Taking Jupiter as practical example we found that there are long period perturbations on ω,Ω and iand not changing with revolution and the short period perturbations on a, e and Mchanging with revolution during the interval of time (t−t0 ) which is changing from 0→4π.