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Kepplers first law

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data
    i am examining a proof of kepplers first law for my conics project and im a bit rusty on the physics, it begins withe the following line

    2. Relevant equations
    To begin with, we will start off by applying Newton's law of motion and Newton's law of universal gravitation together to find that

    m a = (-G m M/r^2) r

    i think there is an extra r in this equation? if no where does it come from??

    here is the link if it helps
    http://members.kr.inter.net/joo/physics/curriculum/kepler/proof.html [Broken]
    3. The attempt at a solution
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 14, 2009 #2


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    The r is in bold which indicates its a vector. So the force of gravity has a magnitude of (-G m M/r^2) along the unit vector r.
  4. Apr 15, 2009 #3
    thanks, altho the more im looking at this the more i dont understand it,
    can anyone explain where the negative comes from?
  5. Apr 15, 2009 #4
    or if anyone knows of a link to a clearer proof, that would be appreciated also
  6. Apr 15, 2009 #5


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    The negative is there because the force of gravity is attractive.
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