At what distance from the earth is the center of mass for the earth-moon system? Assume that the earth has a mass of 5.97x10^24 kg, the moon has a mass of 7.35x10^22 kg, and they are 3.84x108 m apart.

Answer 1

5.97 * 10^24 * x = 7.35 * 10^22 *(3.84* 10^8 - x)
5.97* 10^2 * x = 7.35 * 3.84 *10^8 - 7.35 * x
597 x + 7.35 x = 28.2 * 10^8
604 x = 2820 * 10^6
x = 4.67 * 10^6 meters = 4670 kilometers
not even an earth radius (about 6380 km)