Proving Kepler's Second Law

[Guest]

Use the following steps to prove Kepler's Second Law. Use polar coordinates so that r=(rcos(theta))i + (rsin(theta))j

a) Show that h = r^2 d(theta)/dt (k)

b)If A=A(t) is the area swept out by the radius vector r = r(t) in the time interval [t0,t] , show that dA/dt = .5r^2 d(theta)/dt

Kepler's Second Law: The line joining the Sun to a planet sweeps out equal areas in equal times.

I'm not really sure how to start. In proving his first law,
rxv=h (h being a constant vector)
h= r^2(uxu')
but i'm not sure if that has anything to do with proving the second law.

I would be greatful for any help.

 

[xXAceFireXx]

i am working on this problem as well...

i want to get started, but im having trouble figuring out the first step.

it says Show that h=r^2(dtheta/dt)k (where the bolded are vectors)

i really have no idea what the vector h is but i dont think it represents any kind of physical property (just a guess really, i might be wrong but it seems arbitrary)

they used in the example of this section, where they proved the first law. i can post the whole example proof if needed. i have a feeling this will be a difficult problem to solve, and it doesnt seem like most proofs on the internet prove it this way.