One of the “oldest” problems in mechanics and dynamics is the investigation of the motion of celestial bodies in the sky. One of the measures in judging ancient civilizations is how detailed their observations were of the heavenly bodies and how well they applied such knowledge in setting calendars and in making farming systematic. A new branch of celestial mechanics called astrodynamics resulted. It deals mainly with the orbit and motion of artificial bodies, like spacecraft and satellites, in space. This chapter considers the motion of a rigid body under gravitational pull such as a projectile of a mass near the surface of the Earth. The motion of a mass under gravitational pull must be within a three-dimensional plane. By neglecting the gravitational effects from other planets, the motion of the satellite is solely controlled by the gravitational pull of the Earth. Newton’s universal law of gravitation works fine most of the time in predicting the motions of celestial bodies.