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Answer :
Final answer:
To determine the weight of a person 8000 miles above Earth's surface, we use the inverse square law of gravitation. The individual's weight would be one-ninth of their original weight due to the increased distance from the center of the Earth, resulting in approximately 17.78 pounds.
Explanation:
The weight of an object on Earth is due to the gravitational pull between the object and Earth. Since weight varies inversely with the square of the distance from the center of Earth, we can calculate the change in weight for different distances.
If a person weighs 160 pounds on Earth's surface (4000 miles from the center), and we want to find their weight 8000 miles above the surface of Earth (which makes the total distance from the center 12000 miles), we have to consider the inverse square relation.
To find out by what factor the weight changes, we use the formula: Weight_change_factor = (Initial_distance / Final_distance)^2. This is because weight varies inversely with the second power of the distance from the center of Earth, which can also be expressed as Weight_final = Weight_initial * (Initial_distance / Final_distance)^2.
In this case, the weight change factor would be (4000 miles / 12000 miles)^2 = (1/3)^2 = 1/9. Therefore, the person's weight 8000 miles above the surface of Earth would be 160 pounds / 9, or approximately 17.78 pounds.
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