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?
A) 20 d
B) 40 d
C) 80 d
D) 160 d
E) 320 d

Question

Quizplus · Accepted Answer

The orbital period of a moon (or any satellite) is related to its orbital radius by Kepler's third law, which states that the square of the orbital period (T) is directly proportional to the cube of the radius of its orbit (r). Mathematically, this is expressed as T² ∝ r³. If Moon A has an orbital radius r and takes 20 days to complete an orbit, and Moon B has an orbital radius 4r, then the period of Moon B can be found by setting up the ratio (T_B² / T_A²) = (r_B³ / r_A³). Substituting the given values, we get (T_B² / 20²) = (4r)³ / r³ = 64. Solving for T_B gives T_B = 20 * sqrt(64) = 20 * 8 = 160 days.

Two Moons Orbit a Planet in Nearly Circular Orbits