Final answer:
The weight of a body varies inversely as the square of its distance from the center of the earth. To find the weight of a person at 500 miles above the earth's surface, we can use the inverse square law. Calculate the weight using the formula to get the answer.
Step-by-step explanation:
The weight of a body varies inversely as the square of its distance from the center of the earth. This means that as the distance from the center of the earth increases, the weight of the body decreases. To find the weight of a person at 500 miles above the earth's surface, we can use the inverse square law.
First, we need to find the weight of a person at the surface of the earth. We can use the equation:
Weight = k/(distance)^2
where k is the constant and distance is the distance from the center of the earth. Given that the radius of the earth is 4,000 miles and the constant k is 3.2 * 10^9 pounds/mi², we can calculate the weight of a person at the surface:
Weight = (3.2 * 10^9)/(4000)^2
Once we have the weight at the surface, we can use the same equation to find the weight at 500 miles above the surface. However, we need to remember that the distance in the formula is the distance from the center of the earth, so we need to account for the radius of the earth. The total distance from the center of the earth to 500 miles above the surface is 4000 + 500 = 4500 miles.
Plug in the values into the formula:
Weight = (3.2 * 10^9)/(4500)^2
Calculate the weight using the formula and you will get the weight of a person at 500 miles above the earth's surface.