An orbital environment debris evolutionary model for low Earth orbit has been developed at Kyushu University. A fast orbit propagator is essentially needed in such an evolutionary model because the number of space debris larger than 1 cm in low earth orbit is very large and it takes much time to compute long-term orbital changes of space debris. The effects of orbital perturbations are investigated for hundreds of years, and the rate of change in orbital elements were invented by earlier publications. New expressions of the rate of change in orbital elements are presented to account for gravitational forces of the Sun and Moon. This paper analyzes the long-term effects of orbital perturbations based on the new analytic models of third body forces and conventional analytical models of atmospheric drag, solar radiation pressure, and zonal harmonics. Some results are shown that can predict the changes of the orbit. The models shown in this paper will be useful for long-term calculation of the satellite orbits.