# 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?

May 24, 2016

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 $\frac{1}{24}$th at a distance:

$\sqrt{24} \cdot 4000 \approx \sqrt{25} \cdot 4000 = 5 \cdot 4000 = 20000$ miles.

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

$20000 \cdot 1.6 = 32000$ kilometers.