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Question on gravitational field 
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#1
Jul2510, 04:38 AM

P: 69

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 10^{24}kg Mass of the Moon = 7.35 x 10^{22}kg Radius of Moon's orbit = 3.84 x 10^{8}m Radius of the Earth = 6.38 x 10^{6}m Radius of the Moon = 1.74 x 10^{6}m 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 GM_{E}/x^{2} = GM_{M}/(R  x)^{2} (M_{E}/M_{M})^{1/2}=x/(Rx) x = (M_{E}/M_{M})^{1/2}R/((M_{E}/M_{M})^{1/2} +1) = 3.79 x 10^{8} But the answer provided is 3.46 x 10^{8} Can anyone tell me where I went wrong? 


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