The Titius-Bode law - Place for more than ten planets

Details The Titius-Bode law - Place for more than ten planets The Titius-Bode law - Place for more than ten planets

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16..209h&link_type=abstract

Celestial Mechanics, vol. 16, Oct. 1977, p. 209-213.

Physics

5

Celestial Mechanics, Four Body Problem, Terrestrial Planets, Orbit Calculation, Orbital Elements, Solar System

Scientific paper

A restricted four-body problem for two cases and a general four-body problem for three cases were solved in studies to determine the possibility that the terrestrial planets could be closer and to determine stability limits between the planets. It was found that terrestrial planets having a mass of 0.00001 solar mass are not able to render unstable the orbit of an initially circularly moving particle when its distance of closest approach is larger than a critical value. There exist rather precise stability limits between the planets, depending on planetary mass. For initial circularly moving planets, one has q (semi-major axis ratio) greater than about 1.2 and 1.4 for planetary masses of 0.00001 and 0.0001 solar mass, respectively.

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