I learned about Lagrange points today and the physics behind L1, L2, L4 and L5 make intuitive sense to me. But I'm stumped by L3.
Wikipedia says "L3 in the Sun–Earth system exists on the opposite side of the Sun, a little outside Earth's orbit but slightly closer to the Sun than Earth is. (This apparent contradiction is because the Sun is also affected by Earth's gravity, and so orbits around the two bodies' barycenter, which is, however, well inside the body of the Sun.) At the L3 point, the combined pull of Earth and Sun again causes the object to orbit with the same period as Earth."
Why doesn't an object at L3 start to drift closer towards the sun? An object at L1 avoids that drift because Earth's gravity counteracts the Sun's pull. But it would seem to me that not only is an object at L3 missing a counteracting force pulling away from the Sun, but perhaps the gravity of the Earth is also pulling it towards the Sun.