Central configurations of four bodies with one inferior mass

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 smallm₄0; and that any 3-body equilateral triangle c.c. generates exactly 8 or 9 or 10 (depending onm₁,m₂,m₃) planar 4-body c.c. withm₄=0. Further, every one of these c.c. can be continued uniquely to sufficiently smallm₄>0 except when there are just 9; then exactly one of them is degenerate, and we conjecture that it is not continuable tom₄>0.Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.