Central configurations of four bodies with one inferior mass

Details Central configurations of four bodies with one inferior mass Central configurations of four bodies with one inferior mass

Oct 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28....9a&link_type=abstract

(Conference on Mathematical Methods in Celestial Mechanics, 7th, Oberwolfach, West Germany, Aug. 24-28, 1981.) Celestial Mechani

Mathematics

7

Celestial Mechanics, Four Body Problem, Mass, Equivalence

Scientific paper

The number of equivalence classes of central configurations (CC) in the planar 4-body problem with three arbitrary and a fourth small mass is investigated. These CCs are derived according to their generic origin in the 3-body problem. It is shown that each 3-body collinear CC generates exactly 2 non-collinear CCs (besides 4 collinear ones) of 4 bodies with small m4 greater than or equal to 0; and that any 3-body equilateral triangle CC generates exactly 8 or 9 or 10 (depending on m1, m2, m3) planar 4-body CCs with m4 = 0. Further, every one of these CCs can be continued uniquely to sufficiently small m4 greater than 0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable to m4 greater than 0.

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