Question

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?

Answer 1

Approximately `20,000` miles or `32,000` kilometers.

Explanation:

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.