I am doing this project on kepler's law and can't figure out something.(adsbygoogle = window.adsbygoogle || []).push({});

part a (in the process of proving kepler's second law)of this is to show that h = |r|^2(d(theta)/dt) k when r = (|r|cos(theta))i + (|r|sin(theta))j and h = r x r' = r x v. I showed it by taking derivative of r and cross producting it with the original r.

I did this part, but now i don't know how to deduce that r^2(d(theta)/dt) = |h|. I actually have no understang of what h represents and stuff. If you can explain to me how to deduce this relationship, it would be helpful.

Another question that's about proving kepler's third law is that

i have to show that h^2/(GM) = ed = b^2/a.

Its previous part was to show that T = 2(pi)ab/h (where a=major axis, b=minor axis) and h = the magnitude of vector h). I proved it using the second law of kepler and showing T is equal to the total area divided by the rate of the area swept by the planet. I don't know what e and d are though. any clues? and how might i approach this problem(showing that h^2/(GM) = ed = b^2/a)?

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# A question in Kepler's second and third laws.

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