Semi-Equatorial Orbits Around an Oblate Body

A study was conducted to develop an approximation scheme to the exact equations of motion in cylindrical coordinates for semi-equatorial orbits around an oblate body. These equations were solved analytically in some special case, while approximate equations were derived for the general case. The orbits described by these approximations were pared numerically to those obtained from the exact equations of motion. The special solutions given by a number of equations contained only two arbitrary constants, allowing only a subset of semi-equatorial orbits to be described by these solutions. All numerical integrations were performed using adaptive backward Runge-Kutta of order four with a relative error of 1 × 10-14 in each step.