What is the distance from the Earth's center to a point in space where the gravitational acceleration due to the Earth is 1/24 of its value at the Earth's surface?

Md Ariful Islam

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Md Ariful Islam

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The radius of the Earth is approximately $4000$ miles.

Gravity obeys an inverse square law, decreasing by the square of the distance from the centre.

So the gravitational acceleration due to the Earth will be $1/24$th at a distance:

$sqrt(24)*4000 ~~ sqrt(25)*4000 = 5*4000 = 20000$ miles.

$1$ mile is approximately $1.6$ kilometers, so that's about:

$20000 * 1.6 = 32000$ kilometers.

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