%0 Journal Article %T Short-Period and Long-Period Effects of Weak Gravitational Waves %A M. H. A. Youssef %J International Journal of Astronomy and Astrophysics %P 230-237 %@ 2161-4725 %D 2017 %I Scientific Research Publishing %R 10.4236/ijaa.2017.73019 %X 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¡ªtwo 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 i and not changing with revolution and the short period perturbations on a, e and changing with revolution during the interval of time (t−t0 ) which is changing from 0→4π. %K Gravitational Waves %K General Relativity %K Celestial Mechanics %K Perturbation %K Orbital Mechanics %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=79392