Solar System Capture of Orphan Planets NASA recently announced that orphan planets, planets no longer orbiting a star, may be more numerous than the stars in our galaxy.
The Sun's Hill sphere, its gravitational influence within the Milky Way, is ~2.2 ly. So it's possible, however unlikely, that a Jupiter size orphan planet could attain solar system orbit, say with a semi-major axis of one light year and a ~1.6E7 year period. The barycenter of this body and the Sun would, therefore, be ~60.3 AU from the Sun. 
Could we detect the Sun's motion around the hypothetical Jupiter barycenter by its gradual anomalous displacement versus distant stars and therefore detect the existence of such a far-off massive planet?
 A: Dear Michael, yes, you could do it by observing the Sun and stars for those 16 million years or so (the exotic big planet's "year"). Then it would be as visible as the effect of the ordinary Jupiter. Alternatively, you could observe it for 8-16 years only but you would need a million times higher resolution than the resolution for which we may observe the Sun's motion because of Jupiter.
Moreover, this estimate is way too optimistic. The motion of the barycenter would look linear for periods of time much shorter than those 16 million years and to show that the motion is due to an exotic planet, you would surely have to demonstrate some acceleration of the barycenter and maybe even a few higher derivatives to show that it's moving around the curve expected from the extra planets.
In other words, I think it is impossible in practice.
A: Here is a way measurement of the Sun's anomalous movement could theoretically take place. Assuming a circular orbit (eccentricity = 0) for the distant Jupiter, the Sun's motion around its barycenter would be (2 pi (60.3) AU) / 1.6E7 years or ~3550 km/year. If a detector was placed at the barycenter, 60.3 AU from the Sun, it would find the Sun's annual displacement to be ~0.08 arcseconds. Over 10 years, the ~0.8 arsecond movement would be readily measurable. However, as Luboš pointed out, it's probably impossible to do in practice.
