Find the force function for a particle subject to a central

[Futurestar33]

Homework Statement

The problem is stated as Find the force function for a particle subject to a central field for each of the orbits as follows
a.) r=roCosθ
b.) r=roe^kθ[/B]

Homework Equations

We know the F(x)= dv/dx

here I am assuming F(x)=dv/dθ

The Attempt at a Solution

Do I just take the derivative of the orbit. I believe so but it must be in a different way.
Should I make r=√(x^2+y^2) or simply just take the derivative?

 

[haruspex]

I don't think that either F(x)=dv/dx or dv/d theta. You could have mdv/dt or mv dv/dx.

 

[ehild]

Homework Statement

The problem is stated as Find the force function for a particle subject to a central field for each of the orbits as follows
a.) r=roCosθ
b.) r=roe^kθ[/B]Do I just take the derivative of the orbit. I believe so but it must be in a different way.
Should I make r=√(x^2+y^2) or simply just take the derivative?

Work in polar coordinates. What are the radial and azimuthal components of the acceleration? What do you know about the angular momentum in a central field?