Find the location of the center of mass of the earth-moon system relative to the center of earth.

4765 Km

Explanation:

The center of mass for a two point system is given by the formula:

CM=  (mass  earth x distance of cm to centre of earth +  mass moon x distance of cm to moon ) / mass earth + mass moon

mass earth:  5.97 x 10^24 Kg

mass moon:  7.35 x 10^22 Kg

distance earth-moon = 384,400 Km : 3.84 x 10^6 m

The center of mass will be located between the line distance joining the earth moon but since we are told to calculate relative to the center of earth ,the distance from earth to the center of mass is cero making our calculations easier.

CM = (5.97 x 10 ^24 x 0 + 7.35 x 10 ^22 x 3.84 x 10 ^6 )/ (5.97 x 10^24 + 7.35 x 10^22)

CM=  7.35 x 10 ^22 x 3.84 x 10 ^6/ ( 6.04 x 10 ^24) m  =  4.765 x 10 ^6 m = 4765 Km

it was given as a lesson and guide for prayer.