Deriving Vr and V(sub-theta) from Kepler's second law and

[LordCalculus]

Deriving Vr and V(sub-theta) from Kepler's second law and...

Homework Statement

Beginning with r=[a(1-e²)]/(1+e*cos $$\theta$$) and Kepler's second law, derive general expressions for v_r and v_$$\theta$$ for a mass m₁ in an elliptical orbit about a second mass m₂. The final answers should be functions of P, e, a, and $$\theta$$ only.

P=orbital period
e=eccentricity
a=semimajor axis

That's supposed to be v(subtheta) and cosine of theta!

Homework Equations

A'(t)=L/(2*$$\mu$$)

 

[diazona]

$v_\theta$, understood. What have you done so far and where exactly did you get stuck?

 

[LordCalculus]

Not far at all. I don't even know where to begin. If you do, then please start me off. Thanks!

 

[diazona]

Well, here would be my first thought: you have some information about position, and you are asked to find velocity. What does that tell you?