Abstract
We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 77-91 |
| Number of pages | 15 |
| Journal | Celestial Mechanics and Dynamical Astronomy |
| Volume | 77 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2000 |
Keywords
- Central configuration
- Inverse problem
- n-body problem