My understanding is that the Earth-Moon barycenter is about 6 kilometers from the Earth's center of mass in the direction of the moon. My question - If the Sun is on the opposite side of the moon from the Earth, would that pull the Moon slightly away from the Earth, thus moving the Earth-Moon barycenter farther from the Earth's center of mass? Would the same thing happen if the Sun was on the opposite side of the Earth from the Moon. Would the barycenter move closer and farther from the Earth's center of mass as the Sun went (relatively) "around" our Earth-Moon system? Would it be farther when the Sun is in line with the Earth and Moon, and closer when the Sun's direction is perpendicular to the Moon-Earth line?