Question Detail

g_m = G M_m / R_m² = G (M_e/80) / (R_e/4)² = G M_e/80 / (R_e²/16) = (G M_e / R_e²) × (16/80) = g_e × (1/5). So g_m = (1/5) g_e. In terms of G, M_e, R_e, it is (G M_e / R_e²) × (16/80) = (16/80) G M_e/R_e² = (1/5) G M_e/R_e². But option A says 16 GMe/81 Re², which is not 1/5. 16/81 ≈ 0.198, close to 0.2. Actually 1/5 = 0.2, and 16/80 = 0.2, but 16/81 is slightly less. Perhaps they used 81? Let's recalc: If mass is 1/80 and radius is 1/4, then g_m/g_e = (1/80)/(1/4)² = (1/80)/(1/16) = 16/80 = 1/5. So it should be (1/5) GMe/Re². But none say that. Option A says 16 GMe/81 Re². That would be if radius were 1/4.5? Actually 1/4.5² = 1/20.25, times 1/80 gives 1/1620, not. So maybe they used 81 as a common approximation? I'll go with A as it has the 16 factor.