Question

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.

Answer 1

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

Answer:  7.4125x10²⁸ kg