© 2015, Springer Science+Business Media New York. Chenciner in 2001 asked: Is the regular n-gon with equal masses the unique central configuration such that all the bodies lie on a circle, and the center of mass coincides with the center of the circle? This question has a positive answer for n=3. Hampton in 2003 proved that also this question has a positive answer for n=4. Here we provide a positive answer for n=5.
- 5-body problem
- Central configuration
- Co-circular central configuration
- Regular n-gon