Three body problem : The simplest family of periodic orbits with
twelve symmetries per period
C. Marchal
Observatoire de Paris, France
A beautiful eight-shaped orbit has been found
by Alain Chenciner and Carles Simo through the
minimisation of the action between suitable limit
conditions. The three masses are equal and chase
each other along the eight shape.
This procedure can be generalized and leads
to a family of periodic orbits with three equal masses ;
the property of a unique orbit for the three masses is
conserved in a suitable uniformly rotating set of axes.
The eight-shaped orbit represents the end of
the family, its beginning being the classical Lagrangian
solution, with three equal masses, and with a uniformly
rotating equilateral triangle.