Explain how to calculate the position of the common centre of mass of the Earth-Moon system?

The distance from the center of mass to Earth, times the mass of the Earth, must be equal to the distance of the center of mass to the Moon, times the mass of the Moon. (For more than 2 objects, the calculation is somewhat more complicated - reading about "center of mass" can give you an idea.)

The distance from the center of mass to Earth, times the mass of the Earth, must be equal to the distance of the center of mass to the Moon, times the mass of the Moon. (For more than 2 objects, the calculation is somewhat more complicated - reading about "center of mass" can give you an idea.)

The distance from the center of mass to Earth, times the mass of the Earth, must be equal to the distance of the center of mass to the Moon, times the mass of the Moon. (For more than 2 objects, the calculation is somewhat more complicated - reading about "center of mass" can give you an idea.)

The distance from the center of mass to Earth, times the mass of the Earth, must be equal to the distance of the center of mass to the Moon, times the mass of the Moon. (For more than 2 objects, the calculation is somewhat more complicated - reading about "center of mass" can give you an idea.)