Celestial Mechanics: Keplerian Orbits

This chapter summarizes the concepts underpinning celestial mechanics, the space environment, the environment around the Sun, the intervening environment between the Sun and the Earth, the environment closer to the planet Earth as well as the environment around the launch site. It also covers the Keplerian orbit resulting from the solution of the two-body problem and its features, energy-based characterization of the orbits leading to the formulation of the vis-viva equation for the conservation of energy, the special features of elliptic, circular, parabolic and hyperbolic Keplerian orbits, Lambert’s problem based on the two-body problem, relative motion of a satellite in a rotating frame and the Hill-Clohessy-Wiltshire equations, real orbits arising from the solutions to the three-body problem and their equilibrium and stability features and finally some applications of the orbits arising from the solutions to the three-body problem.