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Two planets A and B revolve around a common star in circular orbits with the following parameters: Mass of planet A: M_A = 1.0 * 10²⁴ kg, orbital radius R_A = 1.0 * 10¹¹ m Mass of planet B: M_B = 2.0 * 10²⁴ kg, orbital radius R_B = 4.0 * 10¹¹ m Mass of star: M_S = 24 * 10³¹ kg, G = (20/3) * 10⁻¹¹ N*m²/kg² Both planets orbit in the same direction. Treating planets as point masses with no self-rotation, find the ratio of their angular momenta about the star: L_A / L_B.
- 1/2
- 1/4
- 2
- 4
Correct answer: 1/4
Solution
In a circular orbit, gravitational force provides centripetal force: G*M_S*M/R² = M*v²/R, so v = sqrt(G*M_S/R). Angular momentum L = M*v*R = M*R*sqrt(G*M_S/R) = M*sqrt(G*M_S*R). The ratio L_A/L_B = (M_A/M_B)*sqrt(R_A/R_B).
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