From the basics of gravitation and basic laws of physics it is clear that in a system of N bodies the velocity of the barycenter is constant .So if we say that our solar system moves through space ( fi. relative to te MWay) this means that all planets move trough space , especially the barycenter of our system . Although our sun has an enormeous mass it moves "around" the solar systems barycenter . This barycenter also moves relative to the MWay .

Here is my take on the basics, starting with simple hypothetical cases.

Suppose we had only the Sun and Jupiter. They will be on opposite sides of their barycenter, at radii inversely proportional to their masses. Their mutual gravity will cause them to orbit the barycenter instead of flying off on tangents, with a period of about 12 years. In accordance with conservation of momentum, we can choose an inertial frame of reference in which the barycenter is stationary. The Sun's orbital radius will be about half a million miles, and Jupiter's will be about 1,000 times that, or half a billion miles.

Suppose we have only the Sun and Saturn. In this case the planet has about 1/3 the mass of Jupiter, but has about 1.8 time the orbital radius, making the Sun's barycentric radius upwards of half of what it would have been with Jupiter. This does not in any way contradict the fact that the gravity is only about 8% of Jupiter's. The Sun's orbital motion simply is slower in this case, with the centripetal acceleration at 8% of what it would have been with Jupiter. The orbital period is about 30 years.

In each case the orbits are Keplerian ellipses, with radii inversely proportional to the respective masses.

Now let us consider Jupiter and Saturn combined, with no other planets. The barycenter of all three bodies remains stationary, but the motions of the bodies around it cease to be simple ellipses. The Sun follows a looping path that places it farthest from the barycenter when the planets are in inferior conjunction and nearest at superior conjunction. This cycle takes about 20 years. The orbits of the planets are deformed by perturbations, but are roughly approximated by ellipses whose foci are near the center of the Sun and the barycenter, but heaven only knows exactly where. I would need some input from celestial mechanics experts on this one.

A small body very close to the Sun will have its orbit closely approximated by an ellipse with its focus virtually at the Sun's center, not the overall barycenter. The Sun and the planet's orbit will move around the barycenter nearly in unison, with the orbit only slightly perturbed by the large planets.

A small body far beyond Saturn's orbit, say in the outer parts of the Kuiper belt, will be in an orbit approximated by an ellipse with its focus close to the overall barycenter. The larger the outlying orbit, the better the approximation will be.

I don't understand tusenfem's reasoning. The first line is physically impossible for a simplified model with only the Sun, Jupiter and Saturn. The second line is valid, and the Sun will gravitate toward the planets, and thus toward the barycenter. The orbital motions keep them separated, just as in simple two-body orbital motion.

That was the whole point of the first "drawing" that it does not make sense so say that the BC or CoM is created by gravity.

Nice post tho, HB.

__________________

Any comments in glorious red are to be considered in ModeratorMode.


善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Since I made the statement in question, let me clarify.

The second of your two diagrams is correct. But the first one does not illustrate what I was trying to say. Even in the second of your diagrams, the planets can still pull the sun in the direction of the barycenter.

Consider the following 4 illustrations. They contain a purple planet and a yellow star orbiting a common barycenter. The star : planet mass ratio is 10:1. The barycenter is marked by the green dot.

In frame #1, the barycenter is inbetween the star and the planet as it must be, and is 10x closer to the more massive star. The star's velocity vector is to the right of the screen, and the planet's is to the left. At this instantaneous moment, the y-component of their velocities are 0. If the star and planet didn't pull on each other, despite having mass, they would continue on these straight-line paths. There would still be a barycenter as the objects still have mass. But these objects would not orbit the barycenter. Rather, they would distance themselves from the barycenter for eternity. The barycenter would never disappear. It would always be be located between the two masses, 10x closer to the star.

But since they do pull on each other, as the planet and star distance themselves on the x-axis, their pulls slow their x-component velocities, and also introduce y-component velocity: up for the star, and down for the planet. Their mutual pulls are bending their otherwise-straight line trajectories into circular orbits around the barycenter.

In frames #2-4, the velocity vectors change, as do the directions of the pulls, but the result is the same. By pulling on each other, the masses cause each other to orbit the barycenter, rather than distance themselves from it in the directions of the instantaneous velocities.

__________________
www.gravitysimulator.com