The present work is concerned with evaluation the effect of gravitational waves on a planetary orbit. The components of the acceleration resulting from this effect on the orbit of the planet are derived and the perturbing forces are computed. The perturbation method adopted makes use of Lagrange's planetary equations. Numerical study is done, using the Rung-Kutta fourth order method and the Mathematica software, and carried out for different sources of gravitational waves as well as the various values of planetary orbital elements.
The first aim of the present work is to compute a more accurate and recent model for the Earth's magnetic field. The second aim is to determine the effects of the Earth's magnetic field on the motion of a charged artificial satellite to evaluate the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1 satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis.
The motion of near-earth satellite orbits with the air drag effect is developed in terms of the KS elements utilizing the Earth's zonal harmonic terms up to J 6 and an oblate atmospheric model with varying scale height dependent on altitude. The variation of the rotational velocity of the atmosphere is taken into account. Numerical studies are carried out (over a wide range of orbital parameters) with Matlab software (version7). The accuracies of the numerical computations are checked with the bilinear relations in KS elements, and are found to be satisfactory. We compared our results with those of Saad et al. (Planet Space Sci 56(3-4):537-541, 2008) and found more agreement with the observed decay of RS-1.
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