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Gravity Ratios using pronumerals

  1. May 20, 2008 #1
    1. The problem statement, all variables and given/known data
    There are two planets called Alpha and Beta.
    mass of alpha=M
    mass of beta=0.01M
    They are distance R apart.

    At what distance, expressed in terms of R, from the planet Alpha, along a straight line joining the centres of Alpha and Beta, will the ratio of [force alpha : force beta] on an asteroid be equal to 8100?


    2. Relevant equations
    I avoided the use of newtons universal theory of gravity since there are no actual numbers. i used ratios instead.


    3. The attempt at a solution
    here goes...

    [mass (alpha)/distance (alpha)] / [mass (beta)/distance (beta)]=8100

    let x be the distance between alpha and the asteroid.
    [M/xR] / [0.01M/(R-xR)]=8100

    Simplify:
    [1-x/0.01x]=8100

    Solve for x:
    x=0.012R

    but the answer is 0.909R!!!

    Thanks for your help.
     
  2. jcsd
  3. May 20, 2008 #2
    sorry, quick correction to the answer to the above question.

    the book says the answer is 0.1R.
     
  4. May 20, 2008 #3
    dont worry, did it
     
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