Question

The mass of the earth is 5.97 ✕ 1024 kg, and the mass of the moon is 7.35 ✕ 1022 kg. the distance of separation, measured between their centers, is 3.84 ✕ 108 m. locate the center of mass of the earth-moon system as measured from the center of the earth.

Answer 1

M₁ = 5.97 * 10²⁴
m₂ = 7.35 * 10²²

r₁ = 0
r₂ = 3.84 * 10⁸

r = distance from earth center to center of mass

r*(m₁+m₂) = r₁m₁ + r₂m₂
r = (r₁m₁ + r₂m₂) / (m₁ + m₂) = (0 + 2.82 * 10³¹) / 6.0435 * 10²⁴ = 4,66 * 10⁶