A planet behind the Sun

A popular science fiction plot involves a planet in Earth’s orbit opposite the Earth behind the sun.  It emerges in articles in magazines like Popular Science on a semi-regular basis.

Only one problem, such a position would be gravitationally unstable.  It would be like balancing a pencil on it’s point.  The pencil will fall in one direction or the other.  If such a planet were ever so slightly ahead of the mid-position relative to the Earth in it’s orbit, it would be pulled ahead on average by the combined effect of the Earth and the Suns gravity, and if behind, behind, so it would, over a sufficiently long time, be pulled out of it’s position 180° opposite the Earth in Earth’s orbit.

If extraterrestrials are visiting from us, it’s not from a planet hiding in Earth’s orbit behind the sun.