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?
First of all, a clarification: What astronomers look for is not the change in position of the star, but the change in velocity. Position is exceedingly difficult to measure at that precision; we aren’t anywhere close to being able to measure the position wobble of even the nearest stars. Velocity, however, (at least one component) can be measured very easily and precisely using the Doppler shift.
Now, then, Jupiter has an orbital radius 5.203 AU and a period of 11.86 years. Converting the units, this means that it has an average speed of 13.07 km/s. Since the Sun has about 1000 times the mass of Jupiter, it must have a wobble from Jupiter of 1/1000 this speed, or 12.5 m/s . I suspect that this is measureable for the Sun, but (with current technology) it would not be for other stars, since it’s harder to make measurements of fainter objects. All of the extrasolar planets we’ve thus far discovered have been gas giants (mostly larger than Jupiter) very close to their star: The closer orbits mean they orbit faster, and the high masses mean that the ratio of speeds is closer to balanced, both of which mean higher (and more easily observed) wobble speeds.
As for the effect of this wobble on the orbits of the planets, yes, it’s been measured, and conforms to predictions. It’s actually even more complicated than you imply, since not only is the Sun moving, but the planets also feel a gravitational attraction from each other. This was one of the many effects which scientists at the turn of the (last) century had to account for before concluding that Mercury’s orbit had an extra precession of 43 arcseconds per century (Einstein later explained this extra precession using General Relativity).
Isn’t this also the reason some wackos get upset and think “the end is coming”, anytime the planets get in alignment? All that pull in one direction is going to destroy the solar system :rolleyes:
For stars light years away Chronos is correct. I think from the earth we ought to be able to measure the solar wobble by position measurement.
The Sun-Jupitor system, considered by itself, orbits around a center that is just a little outside the surface of the sun. So the sun orbits a point on a radius of just over 432000 miles. The distance from earth to sun is roughly 92 million miles. This means that the position of the sun relative to the fixed stars varies by an angle of 9.4 milliradians or 32 minutes of arc. And I’m pretty sure that is within our measurement ability.
(I sure hope I haven’t made any mistakes in arithmetic.)
And by the way. You can compute the size of the wobble by imagining the sun and Jupiter on a balance beam. According to this site the sun is 1047 times the mass of Jupiter.
So if you balance the two on a beam the lever arms for balance have to be:
1047*d = (483000000 - d); d = distance of the center of the sun from the balance, 483000000 = distance of Jupiter from the sun.
This gives d = 462000 miles which is further than I thought. The radius of the sun is about 432000 miles.
That would make the wobble a little bigger than I calculated.
The wobble seen from the earth would then be 2*d/92000000 radians.