In this tread on talk.origins, one of those useless little bits of trivia cropped up recently which caught my attention: The barycenter (or ‘center of mass’) of the Sun-Jupiter system is actually just outside the surface of the Sun. I’ve heard it said that one can consider that a planet has a moon only if the barycenter of the planet-moon system is inside the planet (as is the Earth-Moon system), but what if a planet has a barycenter outside the surface of the central star? It it still “in orbit“?
Well, in cases like this, common sense prevails, and of course, the Sun’s mass (1.981*10^30 kg) dominates the mass of Jupiter (1.899*10^27 kg), by a factor of a thousand to one. So, while technically, the Sun and Jupiter are orbiting a common barycenter outside the sun, the relative masses dictate that the planet is gravitationally bound to the Sun, and therefore ‘in orbit’ around it.
Another wikibit: if all of the planets are lined up on one side of the Sun, the common barycenter would be 500,000 kilometers above the surface.
AstroGeek 
An outstanding share! I have just forwarded this
onto a coworker who had been doing a little homework on this.
And he actually ordered me breakfast because I stumbled upon it for him…
lol. So let me reword this…. Thank YOU for the meal!! But yeah, thanx for spending time to discuss this issue here on your website.
Is the barycentre between the Earth abd the Moon outside the Earth surfac?
Hi;
The barycentre of the Earth-Moon system is about 1700 km under the surface of the Earth.
See https://en.wikipedia.org/wiki/Barycenter#Inside_or_outside_the_Sun.3F The barycenter of the Earth-Moon system is at about 73% of the Earth’s radius.
Does this sun-Jupiter “wobble” cause the sun to change solar positions in such a way or cycle to influence Earth climate change(s)..? Global watming or ice ages, or both..?
No, not unless contributes to the Milankovich cycle (which is a very long term trend, not the short term human-activity caused climate change we’re seeing today)
I am going back to school. I always took this Sun orbiting nonsense with religious zeal. Now i must get wiser. What else have they told me that is not established for real?
To be clear, this is just a technicality. Jupiter clearly orbits the sun because the Sun’s gravity dominates the Sun-Jupiter system, and the barycenter is just barely above the Sun’s surface.