# Method for finding periodic orbits in the CR3BP

1. Feb 11, 2014

### NRotunda

Is there a formula or other easy method or algorithm for finding stable, periodic orbits in the Circular Restricted Three Body Problem (CR3BP), besides trial and error?
Example: In a two-dimensional x-y plane, the two primaries lie along the x-axis and are not in motion. The third body is in periodic motion around the smaller primary. If I know the initial position of the third body, i.e. 100 km to the left of the smaller primary, and I want to apply an initial velocity in the positive y-direction; what initial velocity should I apply in order for the resulting orbits around the smaller primary to periodic, stable and close together (meaning each successive orbit is the same distance from the primary as the one before). Is there a formula or other method for determining this initial velocity? Currently, I only know to use trial and error, incrementally changing the initial velocity until I find something that works. Thank you!