Let us compare the angular momentum of Mars (L_M)in its orbit around the Sun to that of Earth (L_E).The mean orbital speed of Mars is 24 km/s,whereas that of Earth is 30 km/s.The mean orbital radius of Mars is 228 $\times$ 10⁶ km,whereas that of Earth is 150 $\times$ 10⁶ km.If the mass of Mars is 11% that of Earth,calculate the ratio L_M / L_E. A)0.21 B)0.090 C)7.7 D)11 E)0.13

Question

Quizplus · Accepted Answer

The angular momentum of a planet in its orbit around the Sun is given by L = mvr, where m is the mass of the planet, v is its orbital speed, and r is its distance from the Sun. The ratio of the angular momentum of Mars to that of Earth is: L_M / L_E = (mMvM rM) / (mEvE rE) Since mM = 0.11mE, vM = 24 km/s, rM = 228 × 106 km, vE = 30 km/s, and rE = 150 × 106 km, we have: L_M / L_E = (0.11 × 24 × 228 × 106) / (30 × 150 × 106) = 0.13 Therefore, the answer is E, 0.13.

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