Astronomers believe the Moon used to be much closer to the Earth (mass = 5.98 x 1024 kg). When it was at 1.92 x 108 m (half its current distance), what was its orbital period (in days)?

Answer 1

GMm/r² = mv²/r, where G is gravitational constant, M is mass of Earth, m is mass of Moon, v is velocity of Moon. From here v = (GM/r)^1/2 = ( 6.67 × 10⁻¹¹ N m²/kg²·5.98·10²⁴kg/(1.92·10⁸m))^1/2 = 1441.33 m/s

Then period T = 2πr/v = 2π·1.92·10⁸m/1441.33m/s = 836985 s = 9.7 days