Some estimates regarding a finite time stability problem of the sun-earth-Jupiter system

Details Some estimates regarding a finite time stability problem of the sun-earth-Jupiter system Some estimates regarding a finite time stability problem of the sun-earth-Jupiter system

Feb 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..55..161r&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 55, no. 2, p. 161-206.

Mathematics

Earth (Planet), Jupiter (Planet), Solar System, Sun, Systems Stability, Three Body Problem, Conservation Laws, Hamiltonian Functions, Numerical Integration, Orbital Mechanics, Torque, Transformations (Mathematics)

Scientific paper

An approach similar to that of Nekhoroshev's (1977) is used to study the spatial three-body problem of the sun, earth, and Jupiter over a finite time interval comparable with the age of the solar system. The analysis consists of three steps: (1) transformation of the Hamiltonian with the aim of shifting the planetary interaction into the third order terms; (2) estimation of both the maximal third order and resonance forces (torques) acting on the action variables of the earth; and (3) estimation of a lower bound for the time interval during which the system stays within the stability domain.

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