Some estimates regarding a finite time stability problem of the Sun- Earth-Jupiter system
type: Item
instance of: scholarly article
title: Some estimates regarding a finite time stability problem of the Sun- Earth-Jupiter system
zbMATH Open document ID: 0770.70009
DOI: 10.1007/BF00692426
author: Alexander Rauh
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1993-05-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 167663
zbMATH Keywords: Nekhoroshev's theory
zbMATH Keywords: maximal gravitational forces
zbMATH Keywords: conservation of energy and angular momentum
zbMATH Keywords: first-order resonances
zbMATH Keywords: third-order rest term
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00692426
OpenAlex ID: W1990495292
description: scientific article; zbMATH DE number 167663