# Introductory Orbit Dynamics

His discussion of the concepts of "respectable errors" round-off and truncation errors and "blunders" shows how to lead the reader along the beautiful but hard path of numerical celestial mechanics. The book contains many well-selected examples and problems, offers a solid astronomical background, gives details of physical and orbital elements of planets and of comets, and lists basic references. Since the first artificial satellite was placed in orbit, initiating the space age, many introductory textbooks have appeared in the literature.

This excellent introductory textbook is strongly recommended for undergraduate courses in celestial mechanics, orbit dynamics and astrodynamics. A new edition of Fundamentals of Celestial Mechanics is a welcome sight to those of us who teach this subject to advanced undergraduates or beginning graduate students.

One of the best features of the original was its large variety of problems and exercises, and the new edition has even more The expanded sections and new material have broadened the text's applications.

## Spacecraft Dynamics and Control Specialization

This second edition has been substantially revised and enlarged and demonstrates in a dramatic manner how the use of computers of all sizes has allowed teachers and students alike to gain a much deeper understanding of a subject requiring substantial numerical computation It is also cheap enough for students, who are interested in the finer details of numerical computation of orbits, to purchase their own copy.

The Observatory. The Measurement of Time 11 2. Spherical Trigonometry 37 3. Problems 53 4. Ellipsoidal Figures of Rotating Fluid Masses 6. Projects 7. Using a Previous Estimate: Recursive Methods 8.

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Problems 9. Problems The Perturbations of?

## Astrodynamics | Aeronautics and Astronautics | MIT OpenCourseWare

Problems Appendix A. Pole and Polar Appendix B. The Rotation of Axes Appendix C. Miscellaneous Data Appendix D. Elliptic Motion Appendix E. The Greek Alphabet Appendix I.

Perturbed Motion References and Bibliography Index The programs fall into three categories. The second category is closely related to the text, Fundamentals of Celestial Mechanics , second edition. All of these programs appear here, in Pascal, and several additional programs have been added.

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As I just got started on my classes for my master's degree, I thought I'd start posting about the most interesting thing I'm learning so far. That would be orbital mechanics. Orbits come in different shapes and sizes. In the early s, Kepler first described orbits as elliptical and, in fact, they all are.

We typically think of them as circular, but this is only a special case. In reality, every orbit is slightly elliptical. The point at which the satellite is closest to the Earth is call the perigee and the point at which it is farthest is called the apogee. Kepler also observed that the area per time swept out by the arc of the satellite's orbit is equal across the entire orbit. Translated into the English: the satellite moves faster during the parts of its orbit when it is closer to Earth, and moves more slowly the further it is away.

An orbit that moves from west to east counter clockwise when looking down from the north pole is said to be a "posigrade orbit" and one moving from east to west is said to be a "retrograde orbit. So in order to give it a new orbit, you have to change its momentum. This generally utilizes thrusters of some kind. By firing thrusters and changing the direction of motion, you can bump the satellite from one orbit to another.

Of note, the initial orbit and the final orbit will always overlap at the burn point.

### Bibliographic Information

If you start with a roughly circular posigrade orbit and you initiate a posigrade burn, you'll increase the satellite's velocity and fling it farther out into space. The resulting orbit will be elliptical, with the perigee at the burn point. And because orbits further out are slower, the resulting elliptical orbit will also be slower which is counter intuitive since you increased its velocity with the burn.

Conversely, if you initiate a retrograde burn, you slow the satellite down and allow it to fall closer to the Earth, which actually makes it orbit faster. You can also do the opposite to make an elliptical orbit more circular. Namely if you start with an elliptical orbit and initiate a posigrade burn at apogee i.

Or you can initiate a retrograde burn at perigee i. Typically, you're not trying to get a satellite from a circular orbit onto an elliptical one. You're trying to get it from one circular orbit to another, but you cannot do this directly. The simplest but not the fastest way to do this is by utilizing an intermediary elliptical orbit.

To go from a lower altitude circular orbit to a higher one, initiate a posigrade burn such that the apogee of the new elliptical orbit will be at the altitude of the desired circular orbit. Once the satellite gets to apogee, initiate another posigrade burn to circularize the orbit. To go from a higher altitude circular orbit to a lower one, do two retrograde burns only this time the first burn will then mark the apogee of the new elliptical orbit, causing the satellite to fall inward toward the new perigee.