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I have, for years, been an Astronomy and physics nerd. For the first while, I was a total astronomy nerd. Then I slowly transitioned into physics and have been, for less than a year, a physics nerd. In this shirt while, I have taught my self calculus up to Calculus II (over summer and early this school year; I was 14 then). I know how to do geodesics, Schrodinger's equation, classical physics, etc and I'm teaching myself QFT and even planning to make one on quintessence. When I was an astronomy nerd, I didn't know how to do a lot of this math, and so I quit. Now, I am in an "astronomy comeback" phase. There's still one particular thing involving classical physics and astronomy that I still can't quite get-

The question- How exactly, with steps and math shown, do you derive the masses of asteroids via perturbations? please, no links, because I have searched and searched for years and can't find anything. Thank you!

P.s. An extra thank you if you read the whole thing(including the story)! 😄

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  • $\begingroup$ Cross-posted from astronomy: astronomy.stackexchange.com/q/10247 $\endgroup$ – HDE 226868 Apr 2 '15 at 0:06
  • $\begingroup$ They wouldn't answer there. Very few questions are posted on ASE- but a question was posted a split second after I cross-posted this one.... Tells you the difference, huh!๐Ÿ˜„๐Ÿ˜„๐Ÿ˜„๐Ÿ˜„ $\endgroup$ – Damon Blevins Apr 2 '15 at 0:09
  • $\begingroup$ I'm not aware that this is done. The planet Neptune was famously predicted based on its perturbations of the orbit of Uranus, but those are relatively isolated giant planets. The dominant perturbation on most of the objects in the asteroid belt is Jupiter. Do you have a source for the calculation you're trying to duplicate? $\endgroup$ – rob Apr 29 '15 at 6:52
  • $\begingroup$ Any planet with any mass. Even pluto on other pluto now $\endgroup$ – Damon Blevins Apr 29 '15 at 10:55
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    $\begingroup$ Asteroids perturbing asteroids gravitationally. $\endgroup$ – Damon Blevins Apr 29 '15 at 19:22
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This answer is originally from here. Here is a PDF file from the Astronomical Applications Department of the U.S. Naval Observatory. It explains how Asteroid masses and densities are calculated.

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    $\begingroup$ Welcome on Physics SE and thank you for the contribution :) even though this link goes to another SE website, it would be nice if you would either add a short summary or quote (the relevant parts of) your answer here $\endgroup$ – Sanya Oct 28 '16 at 16:26
  • $\begingroup$ What if I just copied my answer that is there to here? $\endgroup$ – A Child of God Oct 28 '16 at 16:33
  • $\begingroup$ as long as you leave the link, stating that this answer is originally from another SE I would be perfectly comfortable with that :) $\endgroup$ – Sanya Oct 28 '16 at 16:36
  • $\begingroup$ That is a really interesting article! It contains a lot of excellent references and an overview. While it doesn't explicitly show how to do the math, I'd expect that would be quite involved, and probably done in several related but different ways, depending on the combination of orbits. $\endgroup$ – uhoh Oct 30 '16 at 12:22
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    $\begingroup$ @uhoh: Yes, exactly this link and yes, it does time out on me, now repeatedly. Ah well, I'll have to try out a few locations on the globe then! $\endgroup$ – AtmosphericPrisonEscape Nov 1 '16 at 8:38

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