# Periodic Planar Collisionless Three-Body Orbits with Unequal Masses

Periodic Planar Collisionless Three-Body Orbits with Unequal Masses

The three-body problem considers the orbits of three masses under their mutual gravitation interactions. Periodic solutions are very hard to find and only a small set of solutions is known. A set of 1349 families of periodic planar collisionless three-body orbits with unequal mass [1] is shown, labeled by . These orbits are divided into five classes according to their geometric and algebraic symmetries. The solutions are represented in two dimensions and on a "shape sphere" based on Jacobi three-body coordinates. The red dots on the shape sphere are related to the three two-body collision points.

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