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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

Emma Arguello

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

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

Gravity decreases by the square of the distance from the center according to the inverse square law.

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.

One mile is roughly one and a half kilometers, so that's about:

#20000 * 1.6 = 32000# kilometers.

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Answer 2

Harper Clark

Three times the radius of the Earth is the approximate distance between the Earth's center and the designated point in space.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.