Orbital mechanics and analytic modeling of meteorological satellite orbits. Applications to the satellite navigational problem

Using the invariant two body Keplerian orbit as the basis of discussion, an analytic approach used to model the orbital characteristics of near Earth satellites is presented. The basic concepts involved with satellite navigation and orbit mechanics are defined. In addition, the various measures of time and coordinate geometry were reviewed. The two body problem was then examined beginning with the inverse square force field law. The mathematical analysis of a procedure used to calculate celestial position vectors of a satellite is described. It was shown that a transformation of Kepler's time equation to an expansion in powers of eccentricity removes the need for numerical approximation.