anonymous
  • anonymous
Show that kepler's law of areas is equivalent to the conservation of angular momentum
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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IrishBoy123
  • IrishBoy123
really simple approach is to look at the area element in polar: \(dA = \frac{1}{2}r^2(\theta) d\theta\) so \(\frac{dA}{dt} = const \implies \frac{1}{2}r^2(\theta) \frac{d\theta}{dt} = const \implies r^2 \omega = const \) that's bag of a cigarette backet. but i think it would lead to something nice if you had the time.
IrishBoy123
  • IrishBoy123
and ellipses in polar are a mare. IMHO.
ganeshie8
  • ganeshie8
Hey just a naive quesiton \(r\) isn't a constant with respect to time for ellipse right ?

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Astrophysics
  • Astrophysics
Nice one @IrishBoy123 Also check this out https://www.princeton.edu/~wbialek/intsci_web/dynamics3.4.pdf
IrishBoy123
  • IrishBoy123
astro, that article really takes it places. good spot. ganesh, i agree i mention ellipses only because i recall reading [Bill Bryson's book, not a physics book!] that Newton worked out that the orbit **had to be ** elliptical, and it came to light in some curious episode involving Hooke and Wren and quite some shenanigans . my suspicion is that if you used r(theta) for an ellipse in the MIT stuff you'd get to see something magical. ellipses are mentioned only 3 times in the article, in the second to lat paragraph of the piece. maybe that is where one could start looking at it. doing it just for a laugh, which i would if i could, is sadly beyond my abilities.....

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