- #1
Davidllerenav
- 424
- 14
- Homework Statement
- A particle with angular momentum `describes the orbit
. Find the central force that produces this orbit. Find the period of the orbit. Determine the minimum energy that the particle must have to escape from this orbit.
- Relevant Equations
I've already found the potential and force that produce the given orbit. my results were:
Now, I've been trying to find the period using the equation
Using and , and multiplying by 2 to make a full orbit, I end up with the integral
The problem is that I have no idea on how to integrate this. Is there a trick or substitution to integrate it, or am I wrong somewhere?