[Boogieman]

Yes, L3 is stable, but not for anything near to Earth’s mass. We could put an artificial satellite there, and it would stay opposite to Earth, but anything much larger than that would quickly drift into its own orbit.

[kosciusko51]

No, L3 is not stable. L3 is a saddle point (stable in one direction, unstable in another). Look at the image below:

The red arrows indicate the unstable directions, and the blue, stable.