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Question on gravitational field

by gaobo9109
Tags: field, gravitational
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gaobo9109
#1
Jul25-10, 04:38 AM
P: 66
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?
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Filip Larsen
#2
Jul25-10, 05:13 AM
PF Gold
Filip Larsen's Avatar
P: 959
Since the symbolic result is correct you must have made an error during the actual calculation of the number.


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