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Formula for gravity/circular motion in terms of V? (i think )

  1. Nov 16, 2008 #1
    If F=mg, and Fc=Fg, Fc=mv2/r (thats v squared; my apologies, i have no idea how to use the superscript button), and Fg=Gm(1)m(2)/r2 (squared), where m(2) is the mass of, say, the earth, and m(1) is the mass of the object orbiting the earth. By substituting these equations together, we get

    mv2/r=Gm(1)m(2)/r2,

    and we can cancel out the r on the left, and the m (which is mass). but I have a problem; which mass is canceled out on the right side? is it the mass of the object or mass of the earth?


    thanks
     
  2. jcsd
  3. Nov 16, 2008 #2

    Doc Al

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    Staff: Mentor

    Which do you think? Which mass is executing circular motion as it orbits the other? Which mass are you finding the centripetal force on?
     
  4. Nov 16, 2008 #3
    I think i am supposed to be finding it with respect to the earth, so I believe then the mass of the earth is what is left
     
  5. Nov 16, 2008 #4

    Doc Al

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    Staff: Mentor

    Right.

    Force on orbiting object due to gravity: [tex]F = GM_{earth}M_{object}/R^2[/tex]

    Applying Newton's 2nd law to orbiting object: [tex]F = M_{object}V_{object}^2/R[/tex]

    Combined:

    [tex]M_{object}V_{object}^2/R = GM_{earth}M_{object}/R^2[/tex]

    [tex]V_{object}^2/R = GM_{earth}/R^2[/tex]
     
  6. Nov 16, 2008 #5
    Cancel out mass of object in revolution,thats the mass acted upon by the centripetal force.
     
  7. Nov 16, 2008 #6
    thanks a lot! that really helped.
    next time ill try to not leave my physics book at school over the weekend
     
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