In this report, we analyze general relativistic effects on celestial bodies, including gravitational strength in different metrics, gravitational radiation, and frame-dragging. We present simulation methods for classical and general relativistic motion, through the use of systems of equations that may be numerically integrated. The amount of energy leaving the system as gravitational radiation is approximated using the quadrupole formula, and by using a binary pair of planetary bodies as an approximation for orbital motion. Here we demonstrate that classical approximations may be suitable in low-mass high-distance scenarios. The eccentricity of an orbit also affects the gravitational radiation and would have to be much less than one for reliable results. It is concluded that frame-dragging effects are negligible for slowly rotating objects only, which is a well-known result.