Theory of Motion of the Heavenly Bodies Moving About the Sun in Conic Sections A Translation of Theoria Motus
by Gauss, Karl FriedrichFormat: Hardcover
Pub. Date: 2004-09-10
Publisher(s): Dover Publications
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Summary
In 1801, a young mathematician stunned the scientific world by using the modest mathematical tools of algebra and trigonometry to solve the complex problem of calculating planetary orbits. He explains his methods in this volume, which is suitable for upper-level undergraduates and graduate students. Karl Friedrich Gauss' great achievement lies in his determination of two sun-centered vectors approximating a planet's position at two different times, given three Earth-centered observations of the object's latitude and longitude. His solution enabled him to determine the planet's orbital plane and the shape and orientation of its elliptical orbit within this plane. This work first appeared two centuries ago, but it remains an enduring reference in modern astronomical computation and celestial mechanics.
Table of Contents
| Preface | p. ix |
| General Relations Between the Quantities by Which the Motions of Heavenly Bodies About the Sun are Defined | |
| Relations pertaining simply to position in the Orbit | p. 1 |
| Relations pertaining simply to Position in Space | p. 54 |
| Relations between Several Places in Orbit | p. 100 |
| Relations between Several Places in Space | p. 153 |
| Investigation of the Orbits of Heavenly Bodies from Geocentric Observations | |
| Determination of an Orbit from Three Complete Observations | p. 161 |
| Determination of an Orbit from Four Observations, of which Two only are Complete | p. 234 |
| Determination of an Orbit satisfying as nearly as possible any number of Observations whatever | p. 249 |
| On the Determination of Orbits, taking into account the Perturbations | p. 274 |
| Appendix | p. 279 |
| Tables | p. 329 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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