Question on gravitational field

  1. 1. The problem statement, all variables and given/known data
    Considering only the gravitational fields of the Earth and the Moon, find the distance from the Earth at which a space capsule travelling between the Earth and the Moon is subject to zero gravitational force.

    Mass of the Earth = 5.98 x 1024kg
    Mass of the Moon = 7.35 x 1022kg
    Radius of Moon's orbit = 3.84 x 108m
    Radius of the Earth = 6.38 x 106m
    Radius of the Moon = 1.74 x 106m


    2. Relevant equations



    3. The attempt at a solution

    Let x be the distance between the centre of earth and the point of zero gravitational field

    Gravitational field due to Earth = Gravational field due to Moon
    GME/x2 = GMM/(R - x)2
    (ME/MM)1/2=x/(R-x)
    x = (ME/MM)1/2R/((ME/MM)1/2 +1)
    = 3.79 x 108

    But the answer provided is 3.46 x 108

    Can anyone tell me where I went wrong?
     
  2. jcsd
  3. Filip Larsen

    Filip Larsen 1,007
    Gold Member

    Since the symbolic result is correct you must have made an error during the actual calculation of the number.
     
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