Fundamental Astrodynamics

Abstract

Publisher Summary This chapter reviews some notions in orbital mechanics and presents a brief treatment of the vast field of astrodynamics. The chapter explains some of the coordinate systems in practice. The Keplerian two-body problem is introduced, and the equations of motion in polar coordinates are solved. The orbital mechanics of Keplerian motion as well as perturbed motion are introduced. Main concepts discussed include Gauss variational equations, the concept of averaging, first-order secular rates in the orbital elements due to the J2 perturbation, and the estimates of impulse requirements to mitigate the absolute and differential effects of the perturbations. Equation of conic sections in polar coordinates, also referred to as the conic equation, is elaborated. Solution of the inertial equations of motion is presented. An analogy between orbital motion and rigid body attitude dynamics is drawn by using the Euler parameters. Concepts of non-Keplerian motion and orbital perturbations are explained in detail. Lagrange's planetary equations are presented as the differential equations describing the temporal change of the classical orbital elements for a conservative, position-only dependent perturbing potential. The chapter concludes with a discussion on Averaging theory.