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

[Hornblower]

Right, and I think it must be the need to consider relative angular motion in determining a useful barycenter. This is the part I seem to be missing.

I would say that a barycenter is useful for calculating orbital elements if a reference ellipse focused on it is a close fit for the actual local motion, with only small perturbation terms needed. Consider a triple star system with a close binary pair and a third star off at many times their spacing. That is necessary for stability. The motions of the two close ones can be approximated very closely by ellipses with a common focus at or very close to their local barycenter. That makes it a useful point for reckoning this component of their motion. The motion of that barycenter around the main one between the pair and the third star can be closely approximated by an ellipse focused on the overall barycenter, with the third star following a similar ellipse with the same focus, and with very little jiggling from perturbations.

[Hornblower]

Following is a sketch which may be of value to George and others who might be having trouble with the barycenter concept.

docu0163.JPG

Figure 1 shows masses M and m on a short seesaw that is rigid and massless in this thought exercise. M = 2m, and because of how leverage works the system is balanced at this point. The downward force vectors are the result of Earth's gravity, which is closely approximated by a perfectly uniform field in this exercise. I gave the definition of the barycenter earlier in this thread, and it follows from the definition that the fulcrum is at the barycenter. Clearly it is a useful concept.

Figure 2 shows what would happen if we lengthen the seesaw to the right and move m out to 2.5 times the original distance from the fulcrum, while leaving M in place. The force from m is unchanged but the longer lever greatly increases the resulting torque, throwing the seesaw out of balance.

In Figure 3 we move the fulcrum so the original ratio of the distances from the masses is restored. Now it is back in balance.

Now for the kicker: This is irrelevant to analysis of the gravitational interaction between the masses, that is, how they move in response to the gravitation they exert on each other.

Figure 4 has the same positions as Figure 1, but we have eliminated the seesaw and allowed the masses to be in free fall. As long as the external gravitational field is perfectly uniform, we can get away with ignoring it. It accelerates the masses downward in unison, not affecting their positions relative to each other. We just transform the frame of reference to make them appear stationary in the absence of interacting with each other. Then we give them velocity vectors VM and Vm to create orbital motion. The barycenter remains stationary if those velocity vectors have magnitudes proportional to the distances from the barycenter to the respective masses and have opposite direction.

(Now you may see why pictures are helpful. I like to think my technical writing is clear, but it does not always come out as well as I wished.)

The force vectors are equal and opposite in accordance with Newton's formula as shown in the sketch. The masses are separated by 30 units of length, thus the 900 in the denominator. The forces deflect the bodies into curved paths, and change their direction accordingly as the line connecting the bodies rotates. With just the right velocities they will follow circular orbits. The dynamics are such that the barycenter remains stationary.

In figure 5 the separation has been doubled, so the forces are weakened by a factor of 4. The velocities are slower to keep the orbits circular.

I will admit that the math is imcomplete here. My main point is to illustrate the fact that the barycenter location relative to the bodies at any given separation is an artifact of their mass ratio and is not a function of the strength of the gravitational interaction.

[Robert Tulip]

Spectrum Solar System Barycentre.jpg

Here is the Fourier Transform I made of the wave function of NASA JPL data for the distance of the sun to the solar system barycenter over 4096 years. It shows that the overall wave is composed of a number of component waves as follows, as previously posted at https://forum.cosmoquest.org/showthr...69#post2057269


We see here the following primary barycentric frequencies of the solar system in peak order, with their apparent planetary drivers.

1. 19.85 years: Jupiter Saturn Cycle
2. 12.8 years: Jupiter Neptune Cycle
3. 13.8 years: Jupiter Uranus Cycle
4. 35.9 years: Saturn Neptune Cycle
5. 11.9 years: Jupiter Cycle
6. 7.8 years: unknown
7. 45.5 years: Saturn Uranus Cycle
8. 9.9 years: 1/2 Jupiter Saturn?
9. 8.2 years: unknown
10. 29.5 years: Saturn cycle
11. 171 years: Uranus Neptune cycle

[George]

If we make the loads on the trailer analogous to the Sun and planets, the forces they exert on the trailer are irrelevant to how they interact among themselves.

Yes, that is helpful.

For interaction among themselves we are concerned with the horizontal gravitational forces they exert on one another. Those forces get weaker as they are moved farther apart, while the leverage the bodies exert on the trailer gets stronger.

I am having trouble with ignoring any leverage from distant bodies. You understand how the distant bodies have no affect on the barycenter in spite of their leverage, apparently, but I see increasing leverage with distance a powerful factor since that's what leverage means.

I think it boils down to combining two separate things in a grand picture to get to where you are, perhaps:

1)A static model has no barycenter, which we define as a c.g. for orbital motions, or at least I think that is an accurate simplified definition; no angular motions, no orbits, no barycenter.

2) The leverage effect from very distant objects (e.g. quasars) does not alter the barycenter since the summation of all the distant objects must be taken into account, and they apply to all masses evenly in the solar system, as well as, the entire galaxy for that matter (pun intended ).

In the first case, there is no barycenter if nothing has angular velocity with anything else. In a static scenario (initial condition), gravity alone will determine how they begin to move toward one another (unless we add a weird cosmological constant else we quickly have a dynamic model and a dynamic barycenter). [This is where I was going in #33 regarding angular motion (Lim--> 0 for omega).]

So if we had a phenomenal quantum event involving a SMBH from a distant quasar 8 Glyrs away suddenly jumping to 8 Glyrs away but 90 deg. from where we saw it (this occurring 8 billion years ago and only now affecting us simultaneously), then the apparent huge leverage it would have on the barycenter would be ineffective for two reasons (both in #2): its affect would only be a percent change of the total masses in both directions, and whatever tiny effect it might actually have would shift all the objects in the galaxy, so it would not be noticeable relative to our neighboring stars; every barycenter would get a tiny vector change. A CMBR wavenlength shift might reveal the quirk if the mass was significant enough. [Of course, this is pure hyperbole and I'm not suggesting such an absurdity of this quantum event.]

But I don't want to miss the quasi-absurdity of the leverage affect from distant objects. It's simply one of those really odd things that greatly tickles the mind that one can find in astronomy, like the impossibility of increasing surface brightness of an extended object regardless of aperture increase. I should say, "potential leverage" (regarding a barycenter), because a distant object must have enough angular velocity (rule 1) to actually have leverage on the barycenter's vector.

[George]

George,
...The Sun is part of the Milky Way.
So if you want to find a balance point between the Sun and the
Andromeda galaxy, you have to include the rest of the Milky Way
on the side of the teeter-totter that has the Sun on it.

Yes, I'm starting to get that the summation of all the masses must be considered to attempt any net leverage effect. [See my above post.]

[George]

I would say that a barycenter is useful for calculating orbital elements if a reference ellipse focused on it is a close fit for the actual local motion, with only small perturbation terms needed. Consider a triple star system with a close binary pair and a third star off at many times their spacing. That is necessary for stability. The motions of the two close ones can be approximated very closely by ellipses with a common focus at or very close to their local barycenter. That makes it a useful point for reckoning this component of their motion. The motion of that barycenter around the main one between the pair and the third star can be closely approximated by an ellipse focused on the overall barycenter, with the third star following a similar ellipse with the same focus, and with very little jiggling from perturbations.

Yep, this is like a mobile we hang from ceilings, and articulates what you mentioned earlier.

[George]

The force vectors are equal and opposite in accordance with Newton's formula as shown in the sketch. The masses are separated by 30 units of length, thus the 900 in the denominator. The forces deflect the bodies into curved paths, and change their direction accordingly as the line connecting the bodies rotates. With just the right velocities they will follow circular orbits. The dynamics are such that the barycenter remains stationary.

In figure 5 the separation has been doubled, so the forces are weakened by a factor of 4. The velocities are slower to keep the orbits circular.

The angular velocities relative to one another seems to be the key to understanding the barycenter. Let's look at hypothesized Planet 9 (to scale AND color coordinated! )....



Solar barycenters.jpg

The heavy "leverage" from Planet 9 will not have much of an effect on how we observe, say, the Sun as it goes around the "net" barycenter for the system. If we could plot the Sun's motion relative to an imaginary absolute space (aether), or from super fine CMBR dipole measurements, then we would see a broader orbit about its path around the galaxy over many millennium. If Planet 9 could greatly speed-up, it would be different, but assuming a 15k year P9 orbital period, the Sun would take similar time to complete all the hundreds of other orbits around the barycenter we already know. [Perhaps the difference could be tickled-out with the data we already have given astronomer's keen abilities, but it would be yet another Wow to see it.] Am I getting it??

[Hornblower]

Yes, that is helpful.

I am having trouble with ignoring any leverage from distant bodies. You understand how the distant bodies have no affect on the barycenter in spite of their leverage, apparently, but I see increasing leverage with distance a powerful factor since that's what leverage means.

No, I do not understand it that way. As I showed on my sketches, a distant body has a large effect on the location of the barycenter of a set of bodies that includes the distant one, which follows from the mathematical definition thereof.

I think it boils down to combining two separate things in a grand picture to get to where you are, perhaps:

1)A static model has no barycenter, which we define as a c.g. for orbital motions, or at least I think that is an accurate simplified definition; no angular motions, no orbits, no barycenter.

You appear to have invented a modified definition for which I see no justification. "Barycenter" is just a synonym for "center of mass", which has a valid definition whether the bodies are moving or not. My best guess is that orbital mechanics scientists use it because it is a single word from which a convenient adjective can be derived, as in "barycentric coordinates", which are scientifically useful under some conditions.

2) The leverage effect from very distant objects (e.g. quasars) does not alter the barycenter since the summation of all the distant objects must be taken into account, and they apply to all masses evenly in the solar system, as well as, the entire galaxy for that matter (pun intended ).

In the first case, there is no barycenter if nothing has angular velocity with anything else. In a static scenario (initial condition), gravity alone will determine how they begin to move toward one another (unless we add a weird cosmological constant else we quickly have a dynamic model and a dynamic barycenter). [This is where I was going in #33 regarding angular motion (Lim--> 0 for omega).]

So if we had a phenomenal quantum event involving a SMBH from a distant quasar 8 Glyrs away suddenly jumping to 8 Glyrs away but 90 deg. from where we saw it (this occurring 8 billion years ago and only now affecting us simultaneously), then the apparent huge leverage it would have on the barycenter would be ineffective for two reasons (both in #2): its affect would only be a percent change of the total masses in both directions, and whatever tiny effect it might actually have would shift all the objects in the galaxy, so it would not be noticeable relative to our neighboring stars; every barycenter would get a tiny vector change. A CMBR wavenlength shift might reveal the quirk if the mass was significant enough. [Of course, this is pure hyperbole and I'm not suggesting such an absurdity of this quantum event.]

But I don't want to miss the quasi-absurdity of the leverage affect from distant objects. It's simply one of those really odd things that greatly tickles the mind that one can find in astronomy, like the impossibility of increasing surface brightness of an extended object regardless of aperture increase. I should say, "potential leverage" (regarding a barycenter), because a distant object must have enough angular velocity (rule 1) to actually have leverage on the barycenter's vector.

You appear to be seeing conceptual conflicts where in my opinion there are none. Sure, the barycenter of the entire universe is indeterminate under our modern mainstream model. That does not invalidate the concept of a local barycenter for any given set of bodies, nor does it hurt the usefulness of such a local barycenter as a reference point if the net gravitational action, if any, of the outlying stuff does not deform the local set.

Consider the set consisting of the Sun, the eight major planets, and the reputed Planet 9, with the Sun and major planets being a subset of the whole. The subset has a valid barycenter, and the entire set has an equally valid barycenter a couple of million miles away in the direction of Planet 9. Because Planet 9's distance from the subset is large compared to the radius of the subset, its gravitational gradient is too weak to cause the orbital motions within the subset to differ measurably from what is predicted when ignoring Planet 9. Thus the subset barycenter remains a scientifically useful reference point for describing the orbital motions within the subset. Nevertheless, given a very long time, the feeble gravitational attraction toward Planet 9 will cause the subset to move in a lazy circle or ellipse around a point at or very near the overall barycenter, which then becomes a scientifically useful reference point for describing the dynamics of the entire set.

[grapes]

Yes, that is helpful.

I am having trouble with ignoring any leverage from distant bodies. You understand how the distant bodies have no affect on the barycenter in spite of their leverage, apparently, but I see increasing leverage with distance a powerful factor since that's what leverage means.

I think it boils down to combining two separate things in a grand picture to get to where you are, perhaps:

1)A static model has no barycenter, which we define as a c.g. for orbital motions, or at least I think that is an accurate simplified definition; no angular motions, no orbits, no barycenter.

Hmmm. Surely that's wrong. The barycenter is just the center of mass of that isolated system. OK, maybe it's not called a barycenter, but in any case, the barycenter is the center of mass. No?

2) The leverage effect from very distant objects (e.g. quasars) does not alter the barycenter since the summation of all the distant objects must be taken into account, and they apply to all masses evenly in the solar system, as well as, the entire galaxy for that matter (pun intended ).

In the first case, there is no barycenter if nothing has angular velocity with anything else. In a static scenario (initial condition), gravity alone will determine how they begin to move toward one another

O, maybe that's it. There is no trailer. Their initial speed and gravity alone (in this classical analysis) will determine how they move toward one another. The center of mass has the same role, whether it's dynamic or static (once the scenario has started, its dynamic).

(unless we add a weird cosmological constant else we quickly have a dynamic model and a dynamic barycenter). [This is where I was going in #33 regarding angular motion (Lim--> 0 for omega).]

So if we had a phenomenal quantum event involving a SMBH from a distant quasar 8 Glyrs away suddenly jumping to 8 Glyrs away but 90 deg. from where we saw it (this occurring 8 billion years ago and only now affecting us simultaneously), then the apparent huge leverage it would have on the barycenter would be ineffective for two reasons (both in #2): its affect would only be a percent change of the total masses in both directions, and whatever tiny effect it might actually have would shift all the objects in the galaxy, so it would not be noticeable relative to our neighboring stars; every barycenter would get a tiny vector change. A CMBR wavenlength shift might reveal the quirk if the mass was significant enough. [Of course, this is pure hyperbole and I'm not suggesting such an absurdity of this quantum event.]

But I don't want to miss the quasi-absurdity of the leverage affect from distant objects. It's simply one of those really odd things that greatly tickles the mind that one can find in astronomy, like the impossibility of increasing surface brightness of an extended object regardless of aperture increase. I should say, "potential leverage" (regarding a barycenter), because a distant object must have enough angular velocity (rule 1) to actually have leverage on the barycenter's vector.

[George]

No, I do not understand it that way. As I showed on my sketches, a distant body has a large effect on the location of the barycenter of a set of bodies that includes the distant one, which follows from the mathematical definition thereof.

Yes, I do understand you see and demonstrate the leverage ability of distant masses, but if we look at the solar system's barycenter we see it is close to the Sun, not light years away when one considers distant objects and their powerful leveraging. Yet this doesn't take all the other distant masses into account as well, no doubt.

You appear to have invented a modified definition for which I see no justification. "Barycenter" is just a synonym for "center of mass", which has a valid definition whether the bodies are moving or not.

Is there a textbook or legitimate site that defines it without the aspect of orbital motion? I think I understand your point, regardless, because of the leveraging effect, but given that the barycenter is found near the Sun and not lightyears away from it requires understanding the importance of orbital motions, right?

Sure, the barycenter of the entire universe is indeterminate under our modern mainstream model. That does not invalidate the concept of a local barycenter for any given set of bodies, nor does it hurt the usefulness of such a local barycenter as a reference point if the net gravitational action, if any, of the outlying stuff does not deform the local set.

Yes, and my last post might reveal better what I am trying to say. To say outlying stuff has huge leverage and that it doesn't deform the local set is interesting irony (or paradox), though you are correct, of course. I'm trying to remove the paradox by discovering why you're correct. I still think the two items (rules) work.

Consider the set consisting of the Sun, the eight major planets, and the reputed Planet 9, with the Sun and major planets being a subset of the whole. The subset has a valid barycenter, and the entire set has an equally valid barycenter a couple of million miles away in the direction of Planet 9. Because Planet 9's distance from the subset is large compared to the radius of the subset, its gravitational gradient is too weak to cause the orbital motions within the subset to differ measurably from what is predicted when ignoring Planet 9. Thus the subset barycenter remains a scientifically useful reference point for describing the orbital motions within the subset. Nevertheless, given a very long time, the feeble gravitational attraction toward Planet 9 will cause the subset to move in a lazy circle or ellipse around a point at or very near the overall barycenter, which then becomes a scientifically useful reference point for describing the dynamics of the entire set.

Voila! You say it better than I.

Let me tweak the two rules...

1)A purely static model has a c.g., but since it has no orbital motions, the barycenter is not an effective tool; no angular motions, no orbits, no barycenter.

2) An effective barycenter is the net c.g. for all the orbital bodies we deem important enough to have an effect on the motions we wish to observe in their orbit about this barycenter.

3) The leverage effect from very distant objects (e.g. quasars) does not alter the effective barycenter used since the summation of all the distant objects must be taken into account, and they apply to all masses evenly in the solar system, as well as, the entire galaxy for that matter.

Is that better?

[George]

Hmmm. Surely that's wrong. The barycenter is just the center of mass of that isolated system. OK, maybe it's not called a barycenter, but in any case, the barycenter is the center of mass. No?

Yes. But the fact that it is the c.g. point is not the complete story; no motions, no barycenter, right? I think this is very important, which is why I haven't bailed. Its' very interesting to admit to so much leverage and yet it has no effect (in the applied sense). We have a super oxymoron at work here, and I hate to miss the fun. [Ok, that's why I haven't bailed. ]

O, maybe that's it. There is no trailer. Their initial speed and gravity alone (in this classical analysis) will determine how they move toward one another. The center of mass has the same role, whether it's dynamic or static (once the scenario has started, its dynamic).

Or all of space is the trailer because the leverage effect is real, as Hornblower correctly argues. The point I give is that when all those levers are applied, it really has little effect, which is why the barycenter commonly used works so well. The Planet 9 illustration in the other post might also help see this because it considers the time variable (ie angular velocities), which must be taken into account when calculating a barycenter from our choice of orbiting objects.

[Grey]

Yes, I do understand you see and demonstrate the leverage ability of distant masses, but if we look at the solar system's barycenter we see it is close to the Sun, not light years away when one considers distant objects and their powerful leveraging. Yet this doesn't take all the other distant masses into account as well, no doubt.

Right, because if you take into account the effect of a distant quasar, you're no longer talking about the barycenter of the solar system. You're instead talking about the barycenter of a system consisting of the solar system plus some distant quasar. No matter how big the lever arm, a distant quasar has precisely zero effect on the position of the barycenter of some group of objects that does not include that quasar. The center of mass of my car is not affected in the slightest by the nearby presence of the huge mass of the Earth. This is true even though the center of mass of a system consisting of the Earth and my car together is nowhere near my car (and in fact almost exactly coincides with the center of the mass of the Earth by itself). The mass of the Earth doesn't move the center of mass of my car in exactly the same way that the mass of a distant quasar does not move the center of mass of the solar system.

The barycenter of a system of objects is determined only by the positions and masses of the objects that are part of that system. Now, you're perfectly free to choose which objects you want to include or exclude from the system when you do this calculation, and you'll get different results depending on that choice. Just like in relativity, this may give you different coordinate systems which are technically all equally valid. But some of those coordinate choices will be very useful, while others will not.

[George]

Right, because if you take into account the effect of a distant quasar, you're no longer talking about the barycenter of the solar system. You're instead talking about the barycenter of a system consisting of the solar system plus some distant quasar. No matter how big the lever arm, a distant quasar has precisely zero effect on the position of the barycenter of some group of objects that does not include that quasar. The center of mass of my car is not affected in the slightest by the nearby presence of the huge mass of the Earth.

Agreed, we choose which masses we want to sum to derive a c.g., and we usually only choose the ones that are actually connected, especially for objects that require lifting (eg cars). [The choice of objects was mentioned in my last sentence, which you may have been typing this post at the time I posted.]

This is true even though the center of mass of a system consisting of the Earth and my car together is nowhere near my car (and in fact almost exactly coincides with the center of the mass of the Earth by itself). The mass of the Earth doesn't move the center of mass of my car in exactly the same way that the mass of a distant quasar does not move the center of mass of the solar system.

Yes. But give the car wings and send it off in any direction and suddenly the Earth's c.g. becomes a big factor. We don't even care about the c.g. of the car, just as we don't really need the c.g. of Jupiter for the system's barycenter. I'm not disagreeing with anyone, semantics aside, but just scratching a mental itch with all that unuseful leverage, I suppose.

[Hornblower]

Agreed, we choose which masses we want to sum to derive a c.g., and we usually only choose the ones that are actually connected, especially for objects that require lifting (eg cars). [The choice of objects was mentioned in my last sentence, which you may have been typing this post at the time I posted.]

Yes. But give the car wings and send it off in any direction and suddenly the Earth's c.g. becomes a big factor. We don't even care about the c.g. of the car, just as we don't really need the c.g. of Jupiter for the system's barycenter. I'm not disagreeing with anyone, semantics aside, but just scratching a mental itch with all that unuseful leverage, I suppose.

My bold. This does appear to be about semantics. I'm sorry, but in my opinion you are quibbling with words when you insist that without orbital motion or whatever, there is no barycenter. When orbital mechanics people say "the barycenter is the center of mass of a set of bodies in orbit around one another", I interpret it as having co-opted a Greek word that literally means "heavy center". That gives them a single word from which an adjective can be derived for specifying a frame of reference, for example. It is a verbal convenience, not a fundamentally different concept. That center of mass does not go away if in a thought experiment we arrest the motions and mount the bodies on a rigid, massless structure of some sort. Its mathematical definition is the same as in any engineering application.

I stand by all I have said in previous posts.

[George]

My bold. This does appear to be about semantics. I'm sorry, but in my opinion you are quibbling with words when you insist that without orbital motion or whatever, there is no barycenter. When orbital mechanics people say "the barycenter is the center of mass of a set of bodies in orbit around one another", I interpret it as having co-opted a Greek word that literally means "heavy center". That gives them a single word from which an adjective can be derived for specifying a frame of reference, for example. It is a verbal convenience, not a fundamentally different concept. That center of mass does not go away if in a thought experiment we arrest the motions and mount the bodies on a rigid, massless structure of some sort.

I think there is a distinctive difference that should be considered. Calculate the c.g. points for both a solar system with and without a Planet 9. The difference is significant, especially if you stay in your static mode and don't apply dynamics (orbital periods, especially) to the question at hand. I suggest that it would be helpful to use both the c.g. term and the barycenter separately, since barycenter is a dynamic c.g. and not a static one.

Its mathematical definition is the same as in any engineering application.

Hence part of my confusions. I've done, long ago, a few hundred FBDs, all static. Leverage is much more intense in a mechanical, static free-body diagram. The tendency would be to put too much emphasis on the outer levers, especially since, in space, it is linear with distance and things get far away fast. I would curious how a class of junior-class mech. engineer students would respond with all this, frankly.

I stand by all I have said in previous posts.

Ok, but I'm only suggesting this for pedagogical reasons. Regardless, thanks much for your comments for they are, as usual, very helpful.

[grapes]

Or all of space is the trailer because the leverage effect is real, as Hornblower correctly argues.

It may (or may not) be true that the term "barycenter" is only used when talking about orbital motion, but it's still just the center of mass. How do you use the term "leverage" if there is no fulcrum?

The point I give is that when all those levers are applied, it really has little effect, which is why the barycenter commonly used works so well. The Planet 9 illustration in the other post might also help see this because it considers the time variable (ie angular velocities), which must be taken into account when calculating a barycenter from our choice of orbiting objects.

To extend Grey's example, the barycenter of the car/earth/sun is inside the sun, how does that change the view of the car/earth barycenter? It's just changing the gravitational forces that are included in the analysis.

[George]

It may (or may not) be true that the term "barycenter" is only used when talking about orbital motion, but it's still just the center of mass. How do you use the term "leverage" if there is no fulcrum?

Agreed. "Leverage" is hyperbole, so it's too strong a word since it suggests a force is being applied, and there is none. There is some sense of moment strength, perhaps, in considering an orbiting mass and the orbiting arm (barycenter to object). I was actually thinking there was more to this, apparently, and, giving this more thought than talk, I think I am confused.

Consider two examples:
1) US708 is traveling at about 1200kps. For simplicity, lets give it one solar mass and have it travel near us at 15000 a.u. In one year it would move about 1 deg. The barycenter between it and the Sun would be half-way between them. Would the Sun gain a new orbital vector around this encroaching star (and barycenter)? I've been thinking it would; simple moment math. But the answer is more likely, no, that gravity is the proper model. [Of course, it will gain a vector, but I am meaning a very strong tangential one matching that of US708 in a binary-type motion for that period, even though orbital acceleration must be considered, too.]

2) Saturn's Epimetheus and Janus exchange orbits close to every 4 years. As they near each other, excluding Saturn for a second, their mutual barycenter is easily determined, if we know their mass and locations, and we do. In a heavy-thinking (bull-headed) leverage model, the faster inner moon should swing past the slower moon and outward enough to become the outer orbiting moon. Vice-versa for the other moon. This is exactly what doesn't happen. And I don't think the kinematics improve by adding Saturn to this dynamic. The gravity/Kepler model, however, does work.

To extend Grey's example, the barycenter of the car/earth/sun is inside the sun, how does that change the view of the car/earth barycenter? It's just changing the gravitational forces that are included in the analysis.

Adding the Sun would only change how we plot the motions, which is where the barycenter comes in handy, if it is offset from the c.g. of the primary body. That's the point (no real difference) you both are making, I'm sure. A distant quasar to the solar system, or Milky Way, gives us only a superfluous barycenter; it's useless because there's no effective relative orbital motions. The car/Earth barycenter is also superfluous since the c.g. of Earth itself suffices. [There are exceptions -- my original hand-me-down was an old Old's 98, thus moving the Earth/car barycenter twice that of most others. ] The only purpose in giving the car wings is to get orbital motion's back into the picture for a barycenter term.

[publiusr]

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

The barycenter is perhaps closest to the core of the Sun when Jupiter and Saturn are in opposition

[Hornblower]

Agreed. "Leverage" is hyperbole, so it's too strong a word since it suggests a force is being applied, and there is none. There is some sense of moment strength, perhaps, in considering an orbiting mass and the orbiting arm (barycenter to object). I was actually thinking there was more to this, apparently, and, giving this more thought than talk, I think I am confused.

Perhaps your thought process is being cluttered up by concepts of moment arms and leverage, even though you have acknowledged that there actually is no leverage force involved in orbital motion. With the seesaw example for levers, there is gravity involved, but in a manner very different from that in orbital mechanics. With the seesaw, the gravitational forces are exerted crossways to the seesaw beam, and are of the same magnitude regardless of the positions of the bodies. Thus, when we move one body farther from the fulcrum, its torque about the fulcrum is increased, and the system becomes unbalanced unless we move the fulcrum accordingly. Note that the system is not in free fall.

Now consider a pair of bodies in free fall and orbiting one another. The line connecting them corresponds geometrically to the beam, but there actually is no beam present. The only forces acting on the bodies are gravitational ones on each one directed toward the other along the line, not crossways. The bodies have velocity vectors crossways and in opposite directions, and the gravitation causes the bodies to curve toward each other instead of flying off in straight lines. With just the right velocities they will be in a pair of stable orbits. The dynamics are such that the two bodies and the line connecting them show the same pattern of motion about a fixed point as with the seesaw, but for dynamically different reasons.

Consider two examples:
1) US708 is traveling at about 1200kps. For simplicity, lets give it one solar mass and have it travel near us at 15000 a.u. In one year it would move about 1 deg. The barycenter between it and the Sun would be half-way between them. Would the Sun gain a new orbital vector around this encroaching star (and barycenter)? I've been thinking it would; simple moment math. But the answer is more likely, no, that gravity is the proper model. [Of course, it will gain a vector, but I am meaning a very strong tangential one matching that of US708 in a binary-type motion for that period, even though orbital acceleration must be considered, too.]

2) Saturn's Epimetheus and Janus exchange orbits close to every 4 years. As they near each other, excluding Saturn for a second, their mutual barycenter is easily determined, if we know their mass and locations, and we do. In a heavy-thinking (bull-headed) leverage model, the faster inner moon should swing past the slower moon and outward enough to become the outer orbiting moon. Vice-versa for the other moon. This is exactly what doesn't happen. And I don't think the kinematics improve by adding Saturn to this dynamic. The gravity/Kepler model, however, does work.

Adding the Sun would only change how we plot the motions, which is where the barycenter comes in handy, if it is offset from the c.g. of the primary body. That's the point (no real difference) you both are making, I'm sure. A distant quasar to the solar system, or Milky Way, gives us only a superfluous barycenter; it's useless because there's no effective relative orbital motions. The car/Earth barycenter is also superfluous since the c.g. of Earth itself suffices. [There are exceptions -- my original hand-me-down was an old Old's 98, thus moving the Earth/car barycenter twice that of most others. ] The only purpose in giving the car wings is to get orbital motion's back into the picture for a barycenter term.

[Hornblower]

The barycenter is perhaps closest to the core of the Sun when Jupiter and Saturn are in opposition

Let's make sure we understand what you mean by opposition, which as seen from Jupiter could be interpreted as having the two planets on the same side of the Sun. That configuration, when viewed from the inner planet, is commonly called opposition. The barycenter is closest when they are on opposite sides of the Sun, which is superior conjunction as seen from Saturn and simply conjunction with the Sun as seen from Jupiter.

[grapes]

Agreed. "Leverage" is hyperbole, so it's too strong a word since it suggests a force is being applied, and there is none. There is some sense of moment strength, perhaps, in considering an orbiting mass and the orbiting arm (barycenter to object). I was actually thinking there was more to this, apparently, and, giving this more thought than talk, I think I am confused.

Consider two examples:
1) US708 is traveling at about 1200kps. For simplicity, lets give it one solar mass and have it travel near us at 15000 a.u. In one year it would move about 1 deg. The barycenter between it and the Sun would be half-way between them. Would the Sun gain a new orbital vector around this encroaching star (and barycenter)? I've been thinking it would; simple moment math. But the answer is more likely, no, that gravity is the proper model. [Of course, it will gain a vector, but I am meaning a very strong tangential one matching that of US708 in a binary-type motion for that period, even though orbital acceleration must be considered, too.]

I'd just say that, of course gravity is the proper model. The barycenter/CoM just gives us a convenient coordinate system, because (effects outside system ignored) it doesn't move.

2) Saturn's Epimetheus and Janus exchange orbits close to every 4 years. As they near each other, excluding Saturn for a second, their mutual barycenter is easily determined, if we know their mass and locations, and we do. In a heavy-thinking (bull-headed) leverage model, the faster inner moon should swing past the slower moon and outward enough to become the outer orbiting moon. Vice-versa for the other moon. This is exactly what doesn't happen. And I don't think the kinematics improve by adding Saturn to this dynamic. The gravity/Kepler model, however, does work.

I've never looked into that, what does happen when they exchange orbits?

Adding the Sun would only change how we plot the motions, which is where the barycenter comes in handy, if it is offset from the c.g. of the primary body. That's the point (no real difference) you both are making, I'm sure. A distant quasar to the solar system, or Milky Way, gives us only a superfluous barycenter; it's useless because there's no effective relative orbital motions. The car/Earth barycenter is also superfluous since the c.g. of Earth itself suffices. [There are exceptions -- my original hand-me-down was an old Old's 98, thus moving the Earth/car barycenter twice that of most others. ] The only purpose in giving the car wings is to get orbital motion's back into the picture for a barycenter term.

I knew there was a reason we were involved in this--a white '62 Olds 98, and a guy gave me a white '62 Olds 88 in lieu of taxi fare

I'm trying to understand why one is superfluous, but you think Planet Nine wouldn't be? I mean, other than gravity.

[Robert Tulip]

My bold. Sure, if someone misinterprets it in that incomplete quote as meaning the barycenter. In the complete final sentence in post #6 it should be clear that I was saying that the Sun is being jerked around by the giant planets.

In saying "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" I was explaining the issue in the same way you later summarised when you said "the barycenter location relative to the bodies at any given separation is an artifact of their mass ratio and is not a function of the strength of the gravitational interaction."

[Hornblower]

In saying "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" I was explaining the issue in the same way you later summarised when you said "the barycenter location relative to the bodies at any given separation is an artifact of their mass ratio and is not a function of the strength of the gravitational interaction."

In hindsight I think my use of "jerked around" was a bit of hyperbole. Suppose I say something like, "The combined gravitational actions of the planets gently nudge the Sun into a looping path around the stationary Solar System barycenter." Do you think that might be misleading to some of our fellow posters?

[Robert Tulip]

In hindsight I think my use of "jerked around" was a bit of hyperbole. Suppose I say something like, "The combined gravitational actions of the planets gently nudge the Sun into a looping path around the stationary Solar System barycenter." Do you think that might be misleading to some of our fellow posters?

The solar system barycenter has been one of my primary astronomical interests for many years. When I saw your statement about gravitational action, I immediately recalled my own first wrong assumption that the distance from the sun to the barycenter would vary as a direct function of each planet's gravitational attraction. As we saw in this thread, something like that seemed to be the assumption behind George's first listing of planets.

On your reformulation, I recall an enlightening comment from one of the expert astronomers on this site, that the path of the barycenter is a smooth arc around the galaxy. The barycenter-sun relation integrates the dynamic effects of all the mass of the solar system in this galactic path and is central to modelling the stable durable unity of the isolated astronomical location in which the earth has existed for more than four billion years. Description of the barycenter as stationary does not capture this dynamic trajectory of the sun and planets, which have circled the galaxy about seventeen times since the dawn of life on earth.

Modelling the solar system needs to be four dimensional. The simple two dimensional disk of an orrery, and for that matter the two dimensional flower representation of the solar radius distance from the center of mass, lacks the real complexity of the helical path that the sun follows in space and time.

[Robert Tulip]

Here is a set of diagrams I made to show the stable pattern of the sun's movement around the solar system barycenter.

These twelve diagrams each show 178.9 successive years of NASA JPL data, totalling 2148 years from 53 AD.

This stability is driven by the recurring triple conjunctions of Jupiter, Saturn and Neptune.

[Hornblower]

What do you mean by "This stability is driven..."? Are you suggesting that the system would be unstable without these triple conjunctions?

[Hornblower]

The solar system barycenter has been one of my primary astronomical interests for many years. When I saw your statement about gravitational action, I immediately recalled my own first wrong assumption that the distance from the sun to the barycenter would vary as a direct function of each planet's gravitational attraction. As we saw in this thread, something like that seemed to be the assumption behind George's first listing of planets.

On your reformulation, I recall an enlightening comment from one of the expert astronomers on this site, that the path of the barycenter is a smooth arc around the galaxy. The barycenter-sun relation integrates the dynamic effects of all the mass of the solar system in this galactic path and is central to modelling the stable durable unity of the isolated astronomical location in which the earth has existed for more than four billion years. Description of the barycenter as stationary does not capture this dynamic trajectory of the sun and planets, which have circled the galaxy about seventeen times since the dawn of life on earth.

Modelling the solar system needs to be four dimensional. The simple two dimensional disk of an orrery, and for that matter the two dimensional flower representation of the solar radius distance from the center of mass, lacks the real complexity of the helical path that the sun follows in space and time.

Yes, the Sun and the planets follow helical paths around the simple arc of the local barycenter's path around the core of the galaxy. Including this component of the overall motion in our analysis of the local relative patterns of motion and position is not needed to address the OP's question. It is scientifically valid to simplify that task by transforming to a frame of reference in which the local barycenter is treated as if stationary.

[Robert Tulip]

What do you mean by "This stability is driven..."? Are you suggesting that the system would be unstable without these triple conjunctions?

The stability I am describing is the specific recurring flower pattern seen in these twelve diagrams, each of which start from the time of a successive triple conjunction of the three planets which have most effect on the distance from the sun to the Solar System Barycenter.

On the Nice Model, the triple conjunction pattern of the gas giants has been stable since settling after the late heavy bombardment (model).

It is not an exact recurrence. Like the Saros Cycle of eclipses, these SSB flower patterns gradually emerge and dissipate in overlapping series. There are two overlapping 179 year cycles of the orbits of Jupiter, Saturn and Neptune. One is now ending in a wide triple conjunction around 2022, and one has a tighter conjunction in 2060. The last triple JSN conjunction was in 1881.

[Hornblower]

The stability I am describing is the specific recurring flower pattern seen in these twelve diagrams, each of which start from the time of a successive triple conjunction of the three planets which have most effect on the distance from the sun to the Solar System Barycenter.

On the Nice Model, the triple conjunction pattern of the gas giants has been stable since settling after the late heavy bombardment (model).

It is not an exact recurrence. Like the Saros Cycle of eclipses, these SSB flower patterns gradually emerge and dissipate in overlapping series. There are two overlapping 179 year cycles of the orbits of Jupiter, Saturn and Neptune. One is now ending in a wide triple conjunction around 2022, and one has a tighter conjunction in 2060. The last triple JSN conjunction was in 1881.

I understand that the orbits have been stable for a very long time, and I understand that there are recurring patterns of triple conjunctions of varying tightness. That does not answer my question of what you are saying, or perhaps trying to say, when you assert that "this stability is driven by the conjunctions."

[Robert Tulip]

I understand that the orbits have been stable for a very long time, and I understand that there are recurring patterns of triple conjunctions of varying tightness. That does not answer my question of what you are saying, or perhaps trying to say, when you assert that "this stability is driven by the conjunctions."

The source for your question, quoted again below, is speaking of the stability of the SSB pattern.

What I meant is that the SSB stability is driven by the triple conjunction pattern, not by the actual conjunction events.

Each successive 178.9 year wave function of the solar distance is almost exactly the same. This pattern stability of the SSB is solely because for any two dates separated by 178.9 years, Jupiter, Saturn and Neptune are in almost exactly the same relative positions, advanced by thirty degrees of arc, with the exactness of the triple conjunctions drifting in and out over overlapping periods of about two thousand years.

Twelve of these periods equal 2148 years, which by coincidence is a zodiac age, close to one twelfth of earth’s precession period of 25771 years.

Over each zodiac age, Jupiter, Saturn and Neptune form successive triple conjunctions in each of the twelve signs within each active conjunction family.

The triple conjunction next decade is part of a family that was tightest on 17-20 July 769 AD. Over the last 1250 years its conjunction period has increased from three days to about five years.

Here is a set of diagrams I made to show the stable pattern of the sun's movement around the solar system barycenter. These twelve diagrams each show 178.9 successive years of NASA JPL data, totalling 2148 years from 53 AD. This stability is driven by the recurring triple conjunctions of Jupiter, Saturn and Neptune.