Finding the Polar Equation of a Circular Orbit in a Central Force Field

[mark9696]

A particle moves on a circular orbit in a central force field. The origin of the force lies on the circle.

Find the polar equation of the orbit.


I am confused as to how to set up this question.

 

[Dr Transport]

Start with the equation for the invers radius of the orbit with respect to angle

$${d^2u}\over {d/ \theta^2} + u =$$

 

[Dr Transport]

Can't work it right now, back later... anyway it is r^-5.

 

[mark9696]

I need a few more steps to be explained. I am sure that if you could please explain them to me that I will get it.

 

[mark9696]

Also, I ahve never sen that queation before. IS it derived somewhere on the net?

Are you saying that the polar equation is r^(-5)? I need some help here desparately.

 

[Dr Transport]

My typing is bad, and it was late.

Start with Goldstein 3-34a,

$$\frac{d^2 u}{d\theta^2} + u = -\frac{m}{l^2u^2}f(1/u)$$

 

[Dr Transport]

My typing is bad, and it was late.

Start with Goldstein 3-34a,

$$\frac{d^2 u}{d\theta^2} + u = -\frac{m}{l^2u^2}f(1/u)$$

set $$1/u = 2acos\theta$$ and crank away. The answer should pop out when you eliminate the $$\theta$$.

For some reason, the \frac is not working...

 

[Dr Transport]

I guess it did work in the final compile...