Short-Period and Long-Period Effects of Weak Gravitational Waves

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 n_w is much smaller than the particle’s orbital n_p. 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 i？and not changing with revolution and the short period perturbations on a, e and M？changing with revolution during the interval of time (t−t0 ) which is changing from 0→4π.