(adsbygoogle = window.adsbygoogle || []).push({}); 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/(R-x)

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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# Question on gravitational field

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