Celestial Mechanics: Real Orbits

This chapter focusses on the perturbations that are present when the primary orbit is considered to be Keplerian. All the major perturbations that exist and that must be considered in simulating the trajectory of a spacecraft are identified, and this is followed by a discussion and presentation of the Gauss perturbation equations which may be considered to be generalization of the Lagrange planetary equations with perturbations expressed as forces rather than potentials. The primary perturbations and methods of estimating the perturbing forces including the forces due to various gravitational perturbations such as the non-spherical nature of the central body and third-body perturbations are discussed in some detail. In particular, the method of orbital averaging to identify the contributions of the perturbing forces to the secular variations in the orbital elements is introduced and applied to obtain the secular variations in the line of apsides and the line of nodes. This is followed by a discussion of the non-gravitational perturbation forces acting on the satellite in its orbit, aerodynamic forces in low Earth orbits, solar radiation and photonic pressures and the solar wind, magnetic forces, forces due to the impact of the space debris and other celestial bodies like meteorites and finally the influence of control forces and moments.