The Sitnikov Problem

There are good reasons to include a description of the Sitnikov problem in this introductionary course on Celestial Mechanics We argue that it provides a very clear example for introducing students to non-integrability and chaos (see Hevia 30 ) In fact this dynamical system it is quite often cited as a perfect example for the chaoticity of a dynamical system. The Sitnikov problem can be regarded as a special case of the restricted three body problem the configuration consists of two equally...

Planetary Motion and Classical Perturbation Theory 71 Historical Remarks

A remarkable confirmation of Newton's law of gravitation was the prediction of the appearance of the comet Halley for 1758, which was done by Edmund Halley (1656-1742) who used several observations and assumed an elliptic orbit with a very large eccentricity for this comet. It was much more difficult for the next generation of astronomers to solve the n-body problem41 -although the only force acting between them is the gravitation Leonhard Euler (1707-1783) was the one who found the ten...