# Algebra

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The gravitational force between an object & the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 210 lbs on the surface of the Earth, what will he weigh 100 miles above the Earth? Assume that the radius of Earth is 4,000 miles

• Algebra -

210/4000² = x/(4000+100)²
Solve for x:
x=210*(4000/4100)²

• Algebra -

F = G M1Me/r^2
210 = G Me M1/4000^2
W = G Me M1 /(4100^2

W/210 = 4000^2/4100^2
W = 210 (4*10^3)^2/(4.1*10^3)^2
W = 210 (16/16.81)

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