When the center of Earth is 3.8 × 105 kilometers from the center of the moon, the force of gravity between Earth and the moon is
about 20.46 × 1025 newtons. Use these values, along with the mass of Earth and the gravitational constant you found in part c, to estimate the mass of the moon.
Given: r = 3.8x10⁵ km = 3.8x10⁸ m, the distance between the earth and moon, F = 20.46x10²⁵ N, the gravitational force between the earth and the moon, G = 6.674x10⁻¹¹ m³/(kg-s²), gravitational constant M = 5.972x10²⁴ kg, the mass of the earth.
Let m = mass of the moon. Then F = (G*M*m)/r^2 or m = (F*r^2)/(G*M)
In SI units, m = [20.46×10²⁵ * (3.8×10⁸)²]/[6.674×10⁻¹¹ * 5.972×10²⁴] = 7.4125×10²⁸ kg
