Is the Solar System's Barycenter Inside or Outside the Sun?

[Fiery Phoenix]

I understand how barycenters work in relation to the difference of mass between two orbiting objects; for example, the Sun-Jupiter system's center of mass lies outside of the Sun because the mass difference is smaller than that of the Sun-Earth system, which is a lot larger and thus its center of mass lies inside the Sun.

But what about the Solar System overall? My understanding is that, since the Sun-Jupiter system is the only one with the a non-negligible mass difference, then the Solar System's center of mass is outside of the Sun's sphere. Do I have this right?

[profloater]

You can find this published it varies of course and goes outside the surface when large planets are on one side, notably Jupiter and Saturn.

[profloater]

image.jpegthis is an image of the path of the barycentre

[schlaugh]

This graphic and animation from NASA may help as well. Short answer is that the solar system barycenter wobbles.

https://spaceplace.nasa.gov/barycenter/en/


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[Fiery Phoenix]

This graphic and animation from NASA may help as well. Short answer is that the solar system barycenter wobbles.

https://spaceplace.nasa.gov/barycenter/en/


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So pretty much what I figured. Makes sense.

[Hornblower]

This graphic and animation from NASA may help as well. Short answer is that the solar system barycenter wobbles.

https://spaceplace.nasa.gov/barycenter/en/


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The barycenter does not wobble. In accordance with conservation of momentum, it is either stationary or moving at nearly constant velocity through interstellar space, depending on the frame of reference. It is the Sun itself that is wobbling as the gravitational action of the giant planets jerks it around.

[schlaugh]

The barycenter does not wobble. In accordance with conservation of momentum, it is either stationary or moving at nearly constant velocity through interstellar space, depending on the frame of reference. It is the Sun itself that is wobbling as the gravitational action of the giant planets jerks it around.

Ah, beg pardon. The use of the word "it" threw me off on a first reading of the NASA page.


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[Robert Tulip]

It is the Sun itself that is wobbling as the gravitational action of the giant planets jerks it around.

The spiral path of the sun with respect to the arc of the barycenter is not a function of "gravitational action". If gravity was the cause, Uranus would have a bigger effect on the position of the centre of mass than Neptune does, since Uranus exercises stronger gravity being closer. However, Neptune is further from the Sun, and about the same mass as Uranus, but has a bigger pull on the center of mass than Uranus does. As with two people of equal weight on a see-saw, the one furthest from the fulcrum pulls the bar down more.

[Hornblower]

The spiral path of the sun with respect to the arc of the barycenter is not a function of "gravitational action". If gravity was the cause, Uranus would have a bigger effect on the position of the centre of mass than Neptune does, since Uranus exercises stronger gravity being closer. However, Neptune is further from the Sun, and about the same mass as Uranus, but has a bigger pull on the center of mass than Uranus does. As with two people of equal weight on a see-saw, the one furthest from the fulcrum pulls the bar down more.

If gravity is not the cause of the spiral motion, then what is the cause?

Seriously, that opening sentence is absurd. What is correct is narrowing it down to say that the location of the barycenter with respect to the current locations of the bodies is purely a function of the mass ratio.

[Hornblower]

If gravity is not the cause of the spiral motion, then what is the cause?

Seriously, that opening sentence is absurd. What is correct is narrowing it down to say that the location of the barycenter with respect to the current locations of the bodies is purely a function of the mass ratio.

In hindsight I have decided that I was unnecessarily harsh in saying it that way. I would rewrite it as, "Seriously, that opening sentence is mistaken. The curvature of the path is very much a function of the gravitational action."

[George]

The spiral path of the sun with respect to the arc of the barycenter is not a function of "gravitational action". If gravity was the cause, Uranus would have a bigger effect on the position of the centre of mass than Neptune does, since Uranus exercises stronger gravity being closer. However, Neptune is further from the Sun, and about the same mass as Uranus, but has a bigger pull on the center of mass than Uranus does. As with two people of equal weight on a see-saw, the one furthest from the fulcrum pulls the bar down more.

The see-saw analogy is appropriate. It's fulcrum is regarded as fixed, so like shifting people from one side to the next, the biggest person would necessarily shift accordingly. It is easier to see the Sun shift than to try and fix it, though GR math works either way.

[Hornblower]

In all fairness to everyone here, I can see how this can be counterintuitive if we do not do the mathematical analysis correctly. Anyone could wonder how a more distant planet, with its weaker gravitational action because of the greater distance, can move the Sun farther from the mutual barycenter. We just need to recognize that the barycenter location for any given separation is dependent only of the mass ratio, and that the gravitational action determines the orbital velocity needed to maintain that separation. At that velocity, the radius of motion stays the same because the weaker gravity means less curvature than in the case of a closer orbit. In a nutshell, the gravity does not move the Sun away from the barycenter. It just keeps it there.

[tony873004]

You can try for yourself to see how each planet affects the barycenter.
http://orbitsimulator.com/gravitySim...arycenter.html

[Robert Tulip]

The overall orbital mechanics of the solar system is a function of gravity, but gravitational action of a planet has a narrower meaning, for example how the gravity of Neptune causes the orbit of Uranus to speed up and slow down.
Planetary effects on the solar system barycenter are different from this type of gravitational action.

[profloater]

The overall orbital mechanics of the solar system is a function of gravity, but gravitational action of a planet has a narrower meaning, for example how the gravity of Neptune causes the orbit of Uranus to speed up and slow down.
Planetary effects on the solar system barycenter are different from this type of gravitational action.

I am afraid that makes no sense to me. Newtonian gravity is enough to explain the movement of the barycentre. Near enough any way.

[Hornblower]

Once again, the gravitational action of the planets does not affect the movement of the barycenter. It affects the motions of the planets and the Sun relative to it.

The overall orbital mechanics of the solar system is a function of gravity, but gravitational action of a planet has a narrower meaning, for example how the gravity of Neptune causes the orbit of Uranus to speed up and slow down.
Planetary effects on the solar system barycenter are different from this type of gravitational action.

Please try to show us, in appropriate mathematical detail, what you mean by these remarks.

[George]

I am afraid that makes no sense to me. Newtonian gravity is enough to explain the movement of the barycentre. Near enough any way.

A dynamic model is necessary since the Sun would move toward a planet if we remove all angular momentum.

If we use Newton's equation and simply multiply mass times the inverse square of the distance to get a relative index affecting the barycenter (relative to Earth), then I get the following factors: [I am too rusty with angular momentum to know whether or not this is an accurate picture, but I am curious if this is accurate enough to be helpful. This is the see-saw analogy but using the inverse square law for gravity, unlike the linear multiplier for distance on the see-saw.]

Mercury......0.37
Venus.........1.56
Earth..........1.00
Mars...........0.05
Jupiter.......11.76
Saturn.........1.04
Uranus........0.04
Neptune.......0.02

[grapes]

A dynamic model is necessary since the Sun would move toward a planet if we remove all angular momentum.

If we use Newton's equation and simply multiply mass times the inverse square of the distance to get a relative index affecting the barycenter (relative to Earth), then I get the following factors: [I am too rusty with angular momentum to know whether or not this is an accurate picture, but I am curious if this is accurate enough to be helpful. This is the see-saw analogy but using the inverse square law for gravity, unlike the linear multiplier for distance on the see-saw.]

I haven checked your calculations, but I think the see-saw is the way to go, for barycenter:
https://en.m.wikipedia.org/wiki/Barycenter

Mercury......0.37
Venus.........1.56
Earth..........1.00
Mars...........0.05
Jupiter.......11.76
Saturn.........1.04
Uranus........0.04
Neptune.......0.02

[profloater]

A dynamic model is necessary since the Sun would move toward a planet if we remove all angular momentum.

If we use Newton's equation and simply multiply mass times the inverse square of the distance to get a relative index affecting the barycenter (relative to Earth), then I get the following factors: [I am too rusty with angular momentum to know whether or not this is an accurate picture, but I am curious if this is accurate enough to be helpful. This is the see-saw analogy but using the inverse square law for gravity, unlike the linear multiplier for distance on the see-saw.]

Mercury......0.37
Venus.........1.56
Earth..........1.00
Mars...........0.05
Jupiter.......11.76
Saturn.........1.04
Uranus........0.04
Neptune.......0.02

Yes Jupiter is the big one. If you simplify the solar system to assume it is stable at any time and the orbits are circles, which they are not of course, it's like having strings instead of gravity, but the see saw analogy shows that Jupiter alone causes the barycentre to shift. I did not check your figures, I thought Saturn from memory was more significant. And Jupiter orbit is eccentric. Some years ago I was arguing that the barycentre shift must affect the sun, which is fluid. The sun spins at different rates through its body and the barycentre as a proxy for Jupiter, must cause tidal like disturbances to the radial heat flows.

[George]

Yes Jupiter is the big one. If you simplify the solar system to assume it is stable at any time and the orbits are circles, which they are not of course, it's like having strings instead of gravity, but the see saw analogy shows that Jupiter alone causes the barycentre to shift. I did not check your figures, I thought Saturn from memory was more significant.

Yeah, I expected a little more from Saturn, too, but it is ~ 1/3 the mass and at almost 2x the distance, (4x when applying the inverse square law), thus a net of about 1/12th the effect.

[grapes]

Yeah, I expected a little more from Saturn, too, but it is ~ 1/3 the mass and at almost 2x the distance, (4x when applying the inverse square law), thus a net of about 1/12th the effect.

I think it should be 1/6 the effect.

[George]

I think it should be 1/6 the effect.

Hmmm? 1/3 x 1/4.... but you know what I'm doing, so what am I missing?

[George]

I haven checked your calculations, but I think the see-saw is the way to go, for barycenter:
https://en.m.wikipedia.org/wiki/Barycenter

Ah, I missed this earlier post (sorry, small iphone screen). Now I see why you are saying 1/6th for Saturn. The Tullip's see-saw analogy is closer than I thought. Why wouldn't the distance behave in an inverse square fashion? There must be a distance multiplier in there somewhere.

Using your link math, if I understand it and assuming it is a linear model...

Mercury......0.14
Venus.........1.13
Earth..........1.00
Mars...........0.07
Jupiter.......61.17
Saturn.........9.92
Uranus........0.76
Neptune.......0.57

[Oops, note the updated version in the post below, which seems to negate this updated version of my original table. Ug!]

[CJSF]

My head asplode!

CJSF

[George]

It gets worse....

Using the radial shift formula in Wiki (r = a x ratio of masses) and making the Earth a unit shift distance for the Sun....

Mercury......0.02
Venus.........0.59
Earth.........1.00
Mars..........0.16
Jupiter...1,652
Saturn.....911
Uranus....280
Neptune...516

I was once pretty good on a see-saw, too.

[Robert Tulip]

Please try to show us, in appropriate mathematical detail, what you mean by these remarks.

My mathematical point is a clarification of the comment from Hornblower that “It is the Sun itself that is wobbling as the gravitational action of the giant planets jerks it around.”

Hornblower’s comment is correct in the sense that “gravitational action of the giant planets” is a description of the overall orbital patterns of the solar system. However, ‘gravitational action’ also means the direct interaction or attraction between the sun and each planet, which is a potentially misleading description of the effect of planetary orbits on the barycentre.

This is shown very clearly by George’s list of the inverse square relations between the sun and the planets, which gives results that bear no relation to the calculation of the barycentre position.

At a thread from 2012, https://forum.cosmoquest.org/showthr...69#post2057269 for which unfortunately the attachment has fallen off due to the shift from BAUT to Cosmoquest, I presented detailed calculation of the drivers of the barycentre. Rather than individual planets, the position of the sun is mainly affected by planetary pairs.

Newton calculated that Jupiter and Saturn are the main drivers, with the barycentre inside the sun when Jupiter is at superior conjunction to Saturn (opposite), and outside the sun when Jupiter is inferior conjunct to Saturn. The more recent discoveries of the other gas giants and advances in computing since then have enabled much more accurate calculation, but Newton’s basic model is a good start to provide a simple mental picture of what is happening at the system level.

The overall orbital mechanics of the solar system is a function of gravity,

That is a simple statement of the use of gravitational calculation to predict planetary orbits.

but gravitational action of a planet has a narrower meaning,

The phrase “gravitational action” refers to gravity as a fundamental interaction of nature. Gravitational interaction, also termed gravitational attraction, is the cause of the formation, shape and trajectory (orbit) of astronomical bodies, quantified by the inverse square law. But the barycentre-sun relation is driven by momentum, and the inverse square calculation, while foundational, does not directly deliver the distance from the sun to the centre of mass.

for example how the gravity of Neptune causes the orbit of Uranus to speed up and slow down.

The discovery of Neptune using its gravitational action upon Uranus is a classic story in astronomy, which some have called the original dark matter. Such gravitational action should not be confused with the system dynamics used to calculate the solar system barycentre.

Planetary effects on the solar system barycenter are different from this type of gravitational action.

I attach again the Fourier Transform of the SSB which illustrates that the phrase ‘wobbling as the gravitational action of the giant planets jerks it around’, while technically correct, has potential to be misleading and produce an incorrect assumption.

[Hornblower]

It gets worse....

Using the radial shift formula in Wiki (r = a x ratio of masses) and making the Earth a unit shift distance for the Sun....

Mercury......0.02
Venus.........0.59
Earth.........1.00
Mars..........0.16
Jupiter...1,652
Saturn.....911
Uranus....280
Neptune...516

I was once pretty good on a see-saw, too.

Those numbers are in accordance with the definition of the barycenter, and have nothing to do with the mutual gravitational interactions of the bodies. The barycenter is conceptually useful because it does not move in the absence of outside forces on the bodies, regardless of how they gravitationally affect each other in free fall. This is a consequence of conservation of momentum, and it is also the point about which the bodies would balance if mounted on a hypothetical rigid but massless structure and suspended in a uniform gravitational field. That is the seesaw analogy.

I will take a shot at a technical definition: Find a point and reckon the position of each body as a vector originating at that point. Multiply the length r of each vector by the mass m of the respective body. Find the vector sum of all of these vectors of length mr. If they add to zero, the origin point is by definition the barycenter.

Let me remind everyone that the barycenter is not a physical object. It does not mechanically disturb a body such as the Sun in which it may or may not be immersed depending on the positions of the outer giant planets. Each planet contributes a gravitational gradient that tidally elongates the Sun slightly. This gradient is smoothly distributed across the Sun whether the barycenter is inside or out.

[tony873004]

If Planet 9 gets discovered the barycenter will have to be recalculated.

[profloater]

Those numbers are in accordance with the definition of the barycenter, and have nothing to do with the mutual gravitational interactions of the bodies. The barycenter is conceptually useful because it does not move in the absence of outside forces on the bodies, regardless of how they gravitationally affect each other in free fall. This is a consequence of conservation of momentum, and it is also the point about which the bodies would balance if mounted on a hypothetical rigid but massless structure and suspended in a uniform gravitational field. That is the seesaw analogy.

I will take a shot at a technical definition: Find a point and reckon the position of each body as a vector originating at that point. Multiply the length r of each vector by the mass m of the respective body. Find the vector sum of all of these vectors of length mr. If they add to zero, the origin point is by definition the barycenter.

Let me remind everyone that the barycenter is not a physical object. It does not mechanically disturb a body such as the Sun in which it may or may not be immersed depending on the positions of the outer giant planets. Each planet contributes a gravitational gradient that tidally elongates the Sun slightly. This gradient is smoothly distributed across the Sun whether the barycenter is inside or out.

In the thread about tides and the moon, the concept of equipotential gravity field was used and surely we have the same in the solar case, on a larger scale, so actually the barycentre is a representation of the current field which must be causing tides in the spinning sun. Those tides will differ as the centre moves.

[grapes]

If Planet 9 gets discovered the barycenter will have to be recalculated.

Check out the effect on the barycenter of Andromeda, or, for that matter, a tennis ball at the edge of the universe.

In the thread about tides and the moon, the concept of equipotential gravity field was used and surely we have the same in the solar case, on a larger scale, so actually the barycentre is a representation of the current field which must be causing tides in the spinning sun. Those tides will differ as the centre moves.

The barycenter calculation has zero effect on the tides. Rotate a fixed orientation body around a barycenter, you'll see that the centrifictional forces at each point of the body are equal and parallel.