The geometry of the orbits of artificial satellites

A novel approach to the study of the orbits of artificial satellites is presented. Emphasis is placed upon the basic geometry and other aspects of satellite motion which are of first importance to satellite engineering. The motion of the orbital plane as a rigid body is introduced and a non-elliptical orbit motion in this plane is defined. The plane orbit so defined possesses the very desirable feature of representing a succession of satellite positions and hence reveals the true motion of the satellite. An analytical treatment yields a completely general second order theory of earth satellite motion which is suitable for engineering purposes. In the latter development, particular attention is paid to the apsidal motion of the orbit and the concomitant resonance effects at the critical orbit inclination. The basic nonlinear features of the apsidal motion, which have not been recognized in earlier theories, are incorporated in the analytical development so as to produce a theory valid at all angles of inclination of the orbit.