It's come to my attention that I asked my original question all kinds of wrong. I gave a bad example and I didn't give enough important story details. I've also realized I didn't even ask the question I'm really looking for the answer to anyway. I apologize for all of the above.
What I'm really looking for is how possible/plausible it is that any space agency could spot some truly massive object that doesn't reflect light heading towards us in time to give us somewhere around 50 years or so to come up with a solution while in no way alerting civilians to our impending doom. I'd also like to know how close this "thing" could get to Earth before amateur astronomers would notice it.
Another important detail: Gravity has no effect on this thing. Its path isn't affected by the gravitational pull of other objects and it doesn't pull anything towards it.
I hope this edit makes it fit this site better. And thanks to everyone who answered my original question.