Question #17166

By what factor would your weight change if Earth's diameter were tripled and its mass were quintupled?

Expert's answer

W = your weight

G = gravitational constant

M = mass of Earth

m = mass of you

r = radius of Earth

W = GmM/r²

if the diameter of Earth were halved, so would be its radius

so your weight with radius halved and mass quintupled would be

W_new = Gm(5M)/(½r)² = 5GmM/(¼r²) = 20W_old

G = gravitational constant

M = mass of Earth

m = mass of you

r = radius of Earth

W = GmM/r²

if the diameter of Earth were halved, so would be its radius

so your weight with radius halved and mass quintupled would be

W_new = Gm(5M)/(½r)² = 5GmM/(¼r²) = 20W_old

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