A moon orbits a planet in 10 days from a distance of 2.0 units. A smaller moon orbits the same planet from a distance of 5.0 units. What length of time is required for this moon to orbit the planet?
Would you use the distance as the radius? How do you do it?
Would you use the distance as the radius? How do you do it?
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Distance must be considered the radius of the orbit; otherwise no solution is possible:
T is proportional to R^(3/2):
T5.0 = T2.0*[5.0/2.0]^(3/2) = 39.53 days
F = Gm1*m2/D² → m2 = F*D²/(G*m1)
m2 = 0.8 kg
T is proportional to R^(3/2):
T5.0 = T2.0*[5.0/2.0]^(3/2) = 39.53 days
F = Gm1*m2/D² → m2 = F*D²/(G*m1)
m2 = 0.8 kg