I don't really see how it's more precise than our own. Especially since the orbital period has changed since their time. (I think we have a few more leap seconds now, right?)
It's an interesting idea, K, but, whilst we couldn't see it optically, we'd be able to see the effects of it's gravitational pull, since dark matter appears to be very, very heavy.
So we'd be able to detect it still, especially in the Oort belt, as we'd see an unusual concentration of the asteroids.
There's a lot we don't know about that region of space though. Like there is a lot of space we don't know about.