What is the condition for a circular orbit?

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The condition for a circular orbit is defined by the equations dr/dt=0 and d²r/dt²=0, indicating that the radius remains constant over time. In the discussion, the user encountered a fourth-order polynomial P(x) with the equations P(x)=0 and dP(x)/dx=0, which are critical for determining the radius of the orbit. The solution requires further clarification on the type of polynomial and any initial or boundary conditions that may apply. Understanding these elements is essential for solving the polynomial effectively.

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

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