Physics Help Forum Kepler's Laws vs Energy

 Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum

 Oct 30th 2016, 03:00 PM #1 Junior Member   Join Date: Oct 2016 Posts: 3 Kepler's Laws vs Energy Screenshot by Lightshot The question is in the link above. I have already looked at unofficial markscheme for this, and it appears to have used vr=v'r' as a form of kepplers law of equal areas, which results in C being circled. I used a different method, to get B, where I equated the PE and KE to get v^2 = k/r, and then solved for k. Then I plugged it back in with the new radius to get a new velocity of about 30. I have no clue whether or not my method holds, nor why, so it'd be nice to get some clarification on this. Thanks Btw im new here, apologies if this isnt where it should be Last edited by haksaw22; Oct 30th 2016 at 04:55 PM.
 Oct 30th 2016, 04:08 PM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,347 Yes, the answer to the question as written is "about" 30 - actually 31.6Km/s. I'm wondering if there isn't a typo in tjhe question - if the radius of the orbit at maximum was 10 x 10^11Km instead of 10 x 10^10Km, there would be a nice round number for the answer. topsquark likes this. Last edited by ChipB; Oct 30th 2016 at 04:17 PM.
 Oct 30th 2016, 04:39 PM #3 Junior Member   Join Date: Oct 2016 Posts: 3 Thanks for the confirmation! I'm pretty sure there isn't a typo, which is weird given that its a non calc paper. Do you know why the law of equal areas method they've used doesn't work?
 Oct 30th 2016, 09:12 PM #4 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,347 Sorry, but I realize I made a mistake in my earlier post. Using Kepler's Law of equal area in equal time does indeed yield an answer of (c), which is 20 Km/s. My error (and I think yours too) was in mistakenly using an equation that works for circular orbits, but this problem is about an elliptical orbit. I used a formula that equates force of gravity to mass times centripetal acceleration of the comet, which is valid for a circular orbit: GMm/r^2 = m v^2/r This yields v^2r = constant, but ignores the fact that at perigee and apogee the comet in an elliptical orbit has radial as well as centripetal acceleration, so gives the wrong answer. Sorry for any confusion on this. topsquark likes this. Last edited by ChipB; Oct 31st 2016 at 06:14 AM.
 Oct 31st 2016, 03:20 AM #5 Junior Member   Join Date: Oct 2016 Posts: 3 No problem, thanks again! Makes more sense now, subtleties always catch me out.

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