TABLE OF CONTENTS The potential energy due to the gravitational field of an astronomical body is a function of the mass distribution of the body itself. When a flight vehicle is near a large astronomical mass, such as the Earth, equations of motion such as Eqs. (2.35) and (2.45) must be rewritten to include the gravitational effects of the non-homogeneous distribution of mass within the gravitating body.
The total energy of a system of mass particles at some point near a large planet, such as the Earth, can be defined by Eq. (3.12). For this analysis, we locate an inertial coordinate center at the center of mass of the planet, and in this case let the planet be represented by a system of ? mass particles. Unlike the aerospace vehicle as depicted in Fig. 3.3, the vehicle here is simply represented by the point mass m i. Summations indicated in Eq. (3.12) can be divided into the energy of the space vehicle and that of the planet, i.e., E T = E + E P, and we can write
where the first term is the kinetic energy of the vehicle, and the second term is its potential energy relative to the mass of the planet. The third term is the kinetic energy of the planet due to its rotation in the inertial frame, which is given by Eq. (3.23). The kinetic energy of the planet due to...
