That's true... My suggestion is a little different than what theronrr was suggesting.
Something else worth noting is that the 2nd Earth (since it's as large as the 1st) will have a detectable pull on the 1st and change its orbit. The L1, L2, L3 points are all inherently unstable too and won't last too long even under perfect conditions. L4 & L5 are stable and will last indefinitely.