An astronaut weighs [tex]W = 180[/tex] pounds on the surface of Earth, which is about [tex]D = 4000[/tex] miles from the center of Earth. What will the astronaut weigh when [tex]D = 10,000[/tex] miles from the center of Earth?

At 10,000 miles from center of the Earth, the astronaut will approximately weigh 28.8 pounds. This is due to the inverse-square relation between weight and distance from the center of the Earth.

Explanation:

The weight of an object decreases as it gets farther away from the center of the Earth due to the reduction in gravitational force. If you double your distance from the center of the earth, the weight does not just decrease by half, but rather it decreases to a fourth of its original weight. This is because weight is inversely proportional to the square of the distance from the center of the earth.

So if the astronaut weighs 180 pounds at 4000 miles from the center of the earth (D1), then when the distance increases to 10000 miles (D2), the astronaut's weight (W2) will be:

W2 = W1 * (D1/D2)^2

Therefore, W2 = 180*(4000/10000)^2 = 28.8 pounds (approximately to the nearest tenth).

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