As a lay astronomy geek, I’ve been fascinated by the ongoing search for extrasolar planets using the wobble method. There’s more information at the link, including a nifty animation, but the upshot is that the mutual gravitational attraction between the star and any large planet or planets makes the mutual rotation visible. In other words, it becomes clear that the planet isn’t just going around the sun; they’re going around each other. The typical metaphor has a dude swinging a weight around on a rope; he has to inscribe a slight circle in opposition to the weight in order to stay approximately in the same place.
So in thinking about it a bit, I’m wondering how pronounced this effect is with respect to our own solar system. Jupiter is friggin’ huge, containing far more mass than all the other planets put together, so its tug on the sun has to outweigh (so to speak) the rest of the system. (According to this, Jupiter accounts for about 70% of total planetary mass.) Our sun, therefore, should wobble in the same fashion as all those other stars out there.
But what I haven’t been able to find is the actual magnitude of the wobble, i.e. any figures that definitively state the sun’s back-and-forth movement as X hundred or thousand kilometers or whatever. While Jupiter is huge, its mass is about as small compared to the sun as the Earth is to Jupiter (a ratio of approximately 1:1000), so it stands to reason that its perturbation of the sun isn’t going to be that significant (in my lay imagination, probably not even approaching the sun’s own radius, though this is merely a guess).
The question: Can we detect it? Can we see the sun moving back and forth across the starry background? Presumably the effect is not visible to the unaided eye (primarily because the sun’s glare drowns out the comparatively feeble stars behind it), or the ancients who spent so much time observing the heavens would have noticed, and the old spheres-within-spheres models would have been a lot more Spirograph-y than they already were to account for it. But what about corollary effects? If the sun is being dragged back and forth, wouldn’t this cause subtle changes in the orbits of the other planets (including our own) as they try to follow the center? How pronounced are these effects? Again, apparently not enough for the ancients to have noticed, but can we with our modern instrumentation measure the variabilities?