If the earth had a pair of identical moons on opposite sides of the same orbit, then the center of the gravity of the double-moon-earth system would be at the center of the earth
The gravitational pull of the moon pulls on the earth, especially in the parts closest to the moon. As a result of this force, the earth's crust rises slightly (a few centimeters). Even ponds and lakes like the Great Lakes experience neap tides. But this gravitational pull can lift the Earth's oceans (and atmosphere) many meters. The moon orbits the earth, creating a "bulge" in the ocean.
On the other side of the Earth's Moon, the gravitational pull is weaker than on any other part of the Earth, and the ocean is "left behind" in another bulge. As there will be identical moons on exact opposite sides, there will be equal gravitational pull, thus we could have gravity at the center of the art.
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