# Motion of Artificial Satellites about the Earth (UMAP)

### Author: Yue-Kuen Kwok

This module guides the readers through the analytic methods of determining the shape of the orbit and the period of revolution of an artificial satellite about the earth. It also discusses the various cosmic velocities of launching a satellite. The description begins with the governing physical laws for the motion of a satellite and approximations made to simplify the analysis. The dynamic equations for the motion are set up, which are then integrated to derive the conservation laws of energy and angular momentum. The orbital path is associated with the general form of a conic section and it is shown that if the satellite were to remain in the orbit the shape of the orbit must be elliptic. The emphasis is on the close interaction of the physics of the motion and the corresponding mathematical analysis. Throughout the module Kepler's three laws of planetary motion are related at various stages of the analysis.** Table of Contents:PHYSICAL LAWS FOR THE MOTION OF AN ARTIFICIAL SATELLITE** History of Artificial Satellites

Kepler's Laws

Newton's Law of Universal Gravitation

Launching of an Artificial Satellite

Approximations Made in the Analysis of Satellite Motion

**DYNAMIC EQUATIONS FOR THE MOTION**

Two Bodies Problem

Units of Measurement

Conservation Laws

**THE ORBITAL PATH, PERIO OF REVOLUTION AND COSMIC VELOCITIES**

Orbital Path

Period of Revolution

The Cosmic Velocities

**SUMMARY**

FURTHER EXERCISES

ANSWERS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHOR

FURTHER EXERCISES

ANSWERS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHOR

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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