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gaobo9109
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Homework Statement
Considering only the gravitational fields of the Earth and the Moon, find the distance from the Earth at which a space capsule traveling 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
Homework Equations
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?