Orateur
Description
In the Jupiter system with its numerous moons there are four of them even visible without a telescope.
The three innermost ones namely Io (P=1.77d) Europa (P=3.55d) and Ganymede (P=7.15) are caught in a special 1:2:4 Mean Motion Resonance! This so called Laplace Resonance was and is a permanent topic for research in Celestial Mechanics. In our study we tackle the problem from the analytical side but also from the numerical side with extensive numerical integrations. Our interest was to find out the necessary masses of the three bodies to fulfill the requirements of stability for hundreds of thousand years.
This question is of special interest because out of the thousands of planetary systems several hundred host three and more planets where some of them are situated in these resonance chains.