Stability Study of the Orbits of Satellites around the Earth

In this research, we have studied of the motion of satellite orbits and rotation around the earth and that are subject to the laws of kepler and relationships associated with this motion, such as changing angular and circular time league and the gravitational constant, etc. In the case of circular orbits of Earth satellites. As compounds are calculated position vector and vector velocity compounds any time satellite orbiting the earth geocentric spherical coordinates . It was a study tracks and various forms taken by this motion in both cases using the language (Matlab). Were also study the stability of the motion of satellites using chetayev method assisted integrals were finding the conditions stabiliting motion.