Alisbet said:
Science and everything we know about physics and gravitation say no, OP, but my Lovecraft-obsessed self wants to go with "OH, GOD, YES. OH, DEAR LORD, YES! WE'RE DOOMED! SQUID PEOPLE ON EARTH TWO! WE'RE ALL DOOMED!"
*ahem*
Sorry for adding to the pile of trolls, but this was just too good to pass up. With all due respect, of course.
As others have said before:
a) we'd have found it by now, if it existed;
b) another planet mirroring our orbit around the Sun could have catastrophic consequences which we'd have noticed by now.
I'll add the Ferni Paradox, which more or less can be vulgarized as saying that the odds of little green men making contact with us are astronomically low because we're either too far away, too technologically advanced, too much *behind* these hypothetical aliens, or simply of no worth to them whatsoever.
Think about it. Assuming there is a spaceship defeating the Sun's gravitational pull and staying safely out of sight at all times, then why in God's name would it even stay cloaked? It's a lot easier and a lot more probable to just go with the fact that there's a whole lot of nothing behind the Sun, except the other planets of our solar system as they pass on the other side.