Semantics aren't silly in science, nor in education. I don't think it's so uninteresting as to be worthy of ridicule. It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun. The casual mental model (and all physical models I've ever seen) of the solar system we all share puts a metaphorical or mechanical axis through the center of the sun, around which we all the revolve.

What may be a shorthand for you is the obscuring of deeper truth for others, and discovering that deeper truth is a wonderful 'Aha!' moment for those who experience it.

"It is not, in fact, obvious to the layperson that the Jupiter-Sun System would have a barycenter that doesn't lie inside the mass of the sun."

a point doesn't lie in a mass, it lies in closed surface. ;p

someone, somewhere, might have an 'Aha!' moment from that.

You can't make a physical model of the solar system that has the axis outside the surface of the sun because if the radius of sun and planets was in the correct proportion to the distances of the planets, they would be too tiny to see. Nor would you see the microscopic offset of the axis. If the sun was grossly oversized compared to the orbits (as it usually is), then the tiny offset of the center of rotation would still be visually indistinguishable from being at the center of the sun.

Absolutely, I'm not criticising the construction of solar system models. I'm simply pointing out that if you lack a deeper understanding of the system they represent (or don't interrogate your understanding adequately), the simplifications of any model can quickly become understood as truth.

If we are going to be pedantic, it's an N-body problem and we don't know if some planet will be eventually shot out of the solar system.

And the Earth-Moon system orbits their common center, though that center happens to be inside the Earth.

That's true of all planets no? The Earth and sun orbit the center of mass of the Earth-sun system.

I wonder? If Jupiter has the power to move the Sun, then other planets should be affected to. From this and the fact planet orbits are still said elliptical, I infer that other planets actually also orbit the Jupiter-Sun barycenter. Correct?

The planet orbits are approximately elliptical. There are deviations, precisely due to the mass of Jupiter, as well as the other planets. See https://en.wikipedia.org/wiki/Discovery_of_Neptune#Irregular... for a practical example.

To the extent that the planets orbits can be considered elliptical, they orbit the barycenter of the entire solar system, including the Sun, Jupiter, and the other planets. Where that's located relative to the Sun-Jupiter barycenter changes a bit, as the Sun-Jupiter system as a whole orbits around the common barycenter.

But we can make some estimates for how big that offset is. The Sun-Jupiter barycenter is offset from the center of the sun by M_{Jupiter}/(M_{Sun} + M_{Jupiter}) * R_{Sun-Jupiter}, here M_{X} is the mass of X and R_{X-Y} is the distance from X to Y. At aphelion, Jupiter is at 8.16e11m from the sun according to https://en.wikipedia.org/wiki/Jupiter, and its mass is about 9.5e-4 that of the sun, so the offset ends up being about 7.8e8m. The radius of the sun is about 6.96e8m, for comparison (according to https://en.wikipedia.org/wiki/Sun).

OK, what about the other planets? Saturn is about 1/3 the mass of Jupiter and about 2x further from the sun. So its impact on the overall solar system barycenter is about 2/3 that of Jupiter. Neptune is about 18x lighter than Jupiter and about 6x further away, so that's another 1/3. Uranus is about 22x lighter than Jupiter and about 4x further away, so that's another 1/6-1/5. The other planets don't really matter for this calculation with the number of significant figures we're using, because they're both lighter and closer in (e.g. Earth is about 1/316 the mass of Jupiter and 5x closer to the sun, so its impact is about 1/1500 that of Jupiter).

So if Jupiter, Saturn, Uranus, and Neptune all happened to line up the barycenter of the Sun-Jupiter system would be about halfway between the center of the sun and the solar system barycenter. To the extent that they don't all line up, the separation between the Sun-Jupiter and overall barycenters will be smaller. And if Saturn and Neptune both line up on the opposite side from Jupiter, that puts the solar system barycenter pretty close to the center of the sun.

And that's one of the way we detect exo-planets.

But doesn't this show that the main players of the solar system are the sun and Jupiter?

Apologies for the source, and my clear lack of knowledge in astronomy.

All planets orbit the centre of mass of themselves and the local star, modulo interactions with other planets. The position of the centre of mass relative to the surface of the star is completely immaterial.

NB for smaller bodies, Jupiter is involved in perturbing or capturing their orbits to a great extent -- but we could conceivably have several very large planets contributing to that dynamic. Yes, Jupiter is the largest planet.

They are the two most massive, so that is tautologically true...

The contribution of Jupiter to the overall solar system barycenter is about the same as that of Saturn and Neptune combined (see numbers in https://news.ycombinator.com/item?id=14576751 ). So I guess it depends on how you define "main"....