Analyzing of High Order Earth Gravity Harmonics Effect on Orbits

The study has investigated the perturbed earth orbits and changing of orbital elements due to the Earth oblateness considering the zonal harmonics, up to 10 times. At the firstreview, after analyzing the Earth potential pattern, the next purpose was the analysisof this effect on polar coordinate system inorder to generate Gauss perturbeddifferential equations. The Legendre polynomial extended up to order 10 and required simulations were performed for a typical satellite. Analysis of each of coefficient effects, j2 to j10, has been done, and produced the net effect of each Jn and combined effect of J2 to J10. These results led to the production process and the behavior of the elements changes with increasing Jn and provided the evaluation of the contribution of eachfactor on each of six orbital elements.