# Celestial Mechanics: The Waltz of the Planets (Springer by Alessandra Celletti (Author), Ettore Perozzi (Author)

By Alessandra Celletti (Author), Ettore Perozzi (Author)

The purpose of this ebook is to illustrate to a much wider viewers, in addition to to a extra expert viewers, the numerous interesting facets of contemporary celestial mechanics. It units out to do that with no using arithmetic. After giving the reader the technical instruments wanted for a uncomplicated figuring out of the underlying actual phenomena (using merely ordinary mathematics), proof and figures are supplied on ancient occasions, glossy discoveries and destiny functions. Contents are divided into significant themes the place the 3 "souls" of recent celestial mechanics (dynamical platforms, sunlight approach and stellar platforms, spaceflight dynamics) play an incredible position.

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**Sample text**

The system is then back to the well-known interaction between the Earth and the Sun - a two-body problem described by Kepler's laws. A fake Jupiter having a negligible mass, like that of a cricket ball, is then introduced. Obviously it has no detectable influence on the motion of the Earth; but if we increase the mass of the pseudo-Jupiter, still keeping it small enough, the motion of the Earth will slightly change with respect to the integrable case. The trajectory is no longer a closed ellipse, still resembling it at first glance.

This is the reason why before starting to search for a solution we should try to determine whether or not the system is integrable. But again this is not an easy task; nor it is always possible. The two-body problem is an integrable system and therefore has explicit solutions to the equations of motion which correspond to three types of orbit: ellipse, parabola and hyperbola. Relying on this encouraging result it might be thought that when adding just one more celestial bodies (for example, the SunEarth-Jupiter system) the resulting motion should not be too difficult to integrate.

It soon became a powerful tool for astronomers, and the study of the dynamics of Solar System bodies governed by gravitation grew as a self-standing discipline. The French mathematician Pierre Simon de Laplace (1749-1827) named it 'celestial mechanics'. Perturbations 13 PERTURBATIONS The Sun has a mass about 1,000 times larger than the total mass of all the planets in the Solar System. Thus, according to gravitation, our star is the 'engine' driving planetary motion. Satellites are also observed to orbit the planets: large and alone like the Moon, or in good company as with Jupiter (more than sixty satellites to date) and Saturn (almost sixty satellites).