What is the condition for a circular orbit?

[vaibhavtewari]

while attempting to solve for radius of a circular orbit, I ended up getting

P(x)=0 and
dP(x)/dx=0

where P is a fourth order polynomial. I am not sure how can I solve it. Can someone shed some light on it.

Thanks

 

[Polyrhythmic]

Could you please give more detail? What kind of polynomials are you talking about? Are there any initial or boundary conditions?

 

[vaibhavtewari]

Before I try to answer that, I just want to make sure that condition for circular orbit is

dr/dt=0
and d^2r/dt^2=0