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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