Abstract
The number of equivalence classes of central configurations (abbr. c.c.) in the planar 4-body problem with three arbitrary and a fourth small mass is investigated. These c.c. are derived according to their generic origin in the 3-body problem. It is shown that each 3-body collinear c.c. generates exactly 2 non-collinear c.c. (besides 4 collinear ones) of 4 bodies with smallm 4≥0; and that any 3-body equilateral triangle c.c. generates exactly 8 or 9 or 10 (depending onm 1,m 2,m 3) planar 4-body c.c. withm 4=0. Further, every one of these c.c. can be continued uniquely to sufficiently smallm 4>0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable tom 4>0.
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References
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Arenstorf, R.F. Central configurations of four bodies with one inferior mass. Celestial Mechanics 28, 9–15 (1982). https://doi.org/10.1007/BF01230655
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DOI: https://doi.org/10.1007/BF01230655