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The gravitational force, \( F \), between an object and the Earth is inversely proportional to the square of the distance from the center of the Earth. If an astronaut weighs 215 pounds on the surface of the Earth, what will the astronaut weigh at a distance of 4000 miles above the Earth's surface? Assume that the radius of the Earth is 4000 miles.

Round off your answer to the nearest pound.

Answer :

Final answer:

The gravitational force between an object and the Earth is inversely proportional to the square of the distance between them.

If the radius of a planet is doubled, the gravitational force at the surface would reduce by a factor of (1/2)² = 1/4.

Explanation:

The question states that the gravitational force between an object and the Earth is inversely proportional to the square of the distance between them.

If an astronaut weighs 215 pounds on the surface of the Earth, we can calculate their weight on a different planet using the proportionality principle.

For example, if the radius of the planet is doubled, the gravitational force at the surface would reduce by a factor of (1/2)² = 1/4, so the person would weigh only one-fourth as much.

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