Digital Communications with Emphasis on Data Modems

16SATELLITE ORBITS

16.1 INTRODUCTION

The analysis and characterization of satellite orbits considered in this chapter are based entirely on Newton’s laws of motion, his law of universal gravitation, and Kepler’s laws of planetary motion. Briefly stated, Newton’s laws of motion are as follows: a body will remain in its present state until influenced by an outside force; the rate of change of angular momentum of a body is proportional to and in the direction of an applied force; and every action has an equal and opposite reaction. Newton’s law of universal gravitation states that the force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Similarly, Kepler’s laws are summarized as follows: the planetary orbit is an ellipse with the Sun at one focus; for all of the planets, the line between the planet and the Sun sweeps through equal areas in equal time intervals; and the square of the orbital period is proportional to the cube of the mean distance to the Sun.

This chapter applies these laws to the Earth’s elliptical satellite orbits with the Earth at one focus; the circular orbit being a special case. The emphasis is on characterizing communication links between the Earth and various satellites and cross‐links between satellites. In addition to elliptical satellite orbits, the results also apply to ballistic missile trajectories. Parabolic and hyperbolic orbits are involved more ...