Some estimates regarding a finite time stability problem of the Sun- Earth-Jupiter system
The spatial three-body problem of the Sun, Earth, Jupiter is studied over a finite time interval comparable with the age of the solar system. Some basic concepts of Nekhoroshev's theory are adopted; however, because of the finite time horizon considered, the canonical transformation scheme can be stopped with a third-order remainder. The overall effect of Jupiter is estimated from its maximal gravitational forces acting on the orbital elements of the Earth. This is done both analytically and numerically. The conservation of energy and angular momentum are rigorously taken into account. As part of a rather extensive programme which has not yet been completed, the effects of the first-order resonances and of a typical third-order rest term are estimated.
conservation of energy and angular momentum
scientific article; zbMATH DE number 167663
scientific article