The L3 point lies on the line defined by the two large masses, beyond the larger of the two. Example: L3 in the Sun–Earth system exists on the opposite side of the Sun, a little outside the Earth's orbit but slightly closer to the Sun than the Earth is. (This apparent contradiction is because the Sun is also affected by the Earth's gravity, and so orbits around the two bodies' barycentre, which is however well inside the body of the Sun.) At the L3 point, the combined pull of the Earth and Sun again causes the object to orbit with the same period as the Earth.
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