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?

1 Answer
May 24, 2016

Answer:

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.