On the homographic solutions of the three-body problem

Abstract

The object of this raper is to prove the following theorem: The only homographic solutions of the three-body problem of celestial mechanics with a law of attraction inversely proportional to any power rα of the distance rare: (i) The pure dilatations. (ii)The collinear solutions, (iii) The equilateral solutions, (iv) The Isosceles solutions of BANACHIEWITZ. (α = 3) and (v) the scalene solutions given in this note, also for α = 3, the first three kinds being the only planar solutions for any value of α.