Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

160 days

Explanation:

Using the equation

rA^3/TA^2 = rB^3/TB^2

Where rA is radius of Moon A = R

TA is Time for moon A complete one orbit = 20 days

rB is radius of Moon B =4R

TB is Time for moon B complete one orbit = ?

Therefore

rA^3/TA^2 = rB^3/TB^2

R^3/20^2 = (4R)^3/TB^2

Cross multiply to solve for TB, then we have

TB^2 × R^3 = (4R)^3 × 20^2

TB^2 × R^3 = 64 × R^3 × 400

TB^2 × R^3 = 25600 × R^3

Divide both sides by R^3

TB^2 = 25600

Square root both sides

TB = sqrt 25600

TB = 160days

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