Question on gravitational field

AI Thread Summary
To find the distance from Earth where a space capsule experiences zero gravitational force between Earth and the Moon, the gravitational fields from both bodies must be equal. The equation derived is GME/x² = GMM/(R - x)², leading to x = (ME/MM)^(1/2)R/((ME/MM)^(1/2) + 1). The calculated distance is 3.79 x 10^8 m, but the expected answer is 3.46 x 10^8 m. The discrepancy suggests a calculation error in determining the numerical value rather than the symbolic result. Accurate calculations are essential for resolving this issue.
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?
 
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Since the symbolic result is correct you must have made an error during the actual calculation of the number.
 

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