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Homework Help: Lagrange Points

  1. Sep 22, 2003 #1
    Estimate the distance of the L1 point from Earth.

    S-------------r------------L1--(a-r)--E

    The centripetal force on this object at L1 is equal to the net force on the object. At L1, (to the left of L1 is negative)
    F_net=F_sun+F_earth
    -(mv2)/r=-GMsm/r2+GMem/(a-r)2
    Solving for r gives a polynomial of 5th degree!!!
    How do I go about this in an easier fashion???
     
  2. jcsd
  3. Sep 23, 2003 #2

    krab

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    Science Advisor

    The key word is your first one: Estimate. Make use of the fact that the sun's mass is far larger than the earth's. This will mean for example that a-r<<a. Rewrite the equation in terms of say a and delta = a-r. Then you will find terms like (a-delta)^3, which can be approximated as a^3-3a^2*(delta). After that, it's easy.
     
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