The force of gravity, F, exerted between two objects is equal to the product of the gravitational constant, G, the mass of the first object, m1, and the mass of the second object, m2, divided by the square of the distance between their centers, d. This is often used to determine the gravitational attraction between two massive bodies, such as planets, in space.
The formula for F described in the situation above is F=G m1m2/d2
1) Rewrite the original formula to solve for one of the mass values.
2) 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.
F = [G * M * m] / d^2, solve for M
M = (d^2 F)/(G m)
M = (3.8E8^2 * 2.046E20) / (6.67428E-11 * 5.974E24)
M =~ 7.4 x 10^22 Kg - The mass of the Moon.
Note: You have the gravitational force between the Earth and the Moon listed as 20.46 x 10^25 N, which is wrong. The actual force is about: 2 x 10^20 N.