Chapter 2 - The Orbit Problem

Abstract

This chapter provides key steps in the development and the interpretation of various treatises on orbital mechanics, especially within the context of the main purpose related to the determination of the orbit. The classic problem of two bodies was solved by Newton, which is repeated in a modern form by all treatises on celestial mechanics. The classic treatment describes the motion of two point masses. However, human experience demonstrates that the Earth has physical dimensions, and a point mass Earth is a serious stretch of the imagination. Nevertheless, a spherical body with constant, uniform mass distribution can be shown to be gravitationally equivalent to a point mass. The description of orbital dynamics in the chapter is Newtonian in nature. Inclusion of relativistic corrections is important for those applications that require high accuracy, and the relevant terms are described. The description of satellite motion is developed, beginning with the two-body gravitational model of satellite motion.