My dilemma

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22 years 2 months ago #2776 by Larry Burford
[ab]
Is there any consistent data on the Sun's motion wrt the Solar system
barycenter? Also, is there any difference in motion of the Sun's geometric centre and its magnetic field centre?

[tvf]
The Sun's motion wrt the solar system barycenter is calculated because the barycenter cannot be observed. In fact, its location is a matter of arbitrary definition, and not of physics. For example, if we include Alpha Centauri along with the Sun and its planets in our dynamical system, the barycenter moves half-way to Alpha Centauri without any observable consequences.

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This is rather unexpected. I'm intrigued.

Assuming that you are not pulling our leg, WHY would we want to allow for the possiblilty of including Alpha Centauri when determining the barycenter of "the Solar system"? Doesn't your example describe the approximate location of the barycenter of the Solar/Alpha Centauri "system"?

I've never seen a formal definition of barycenter - from context I had always assumed it was the technical term for center of mass. My CRC doesn't mention it and the Internet says "...center of mass...".

The location of a center of mass obviously depends on which masses you are talking about. Specifying "the Solar system" should exclude things like the Centauri triplets or the Sombrero Galaxy.

What am I missing here?

Regards,
LB


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22 years 2 months ago #3216 by Jim
Replied by Jim on topic Reply from
The barycenter is a model that balances the two mass centers as one would do on a balance scale. It is in common use today and no one thinks that is wrong because it has been in use for a few centuries. The error with this model is that in a dynamic system the static balance is not stable due to the fact the smaller mass is spinning way to fast to be offset by the slower and larger mass. The model is bogus.

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22 years 2 months ago #2777 by tvanflandern
<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Jim]: The moon then by this logic orbits 81 times faster than the Earth? So the GM=RV^2 rule must be false since it indicates the moon orbits 9 times faster.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

81 times faster is correct. The law you cite refers to the orbit of the Moon relative to the Earth, or to any real circular orbit and its center. It does not apply to motion around fictitious points such as the barycenter. No mass is located at the barycenter.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>:And is the moon tide very much bigger than the tide on Earth?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The Moon tide is nearly 1000 times larger than Earth tides. That is partly because Earth's mass is so much larger than the Moon's, and partly because the Moon does not rotate, so the "tide" (or bulge, if you prefer) is permanent. -|Tom|-

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22 years 2 months ago #2964 by tvanflandern
<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>WHY would we want to allow for the possiblilty of including Alpha Centauri when determining the barycenter of "the Solar system"? Doesn't your example describe the approximate location of the barycenter of the Solar/Alpha Centauri "system"?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The example is intended to illustrate how arbitrary "barycenter" is. It applies to all the masses under consideration. That line can be drawn wherever we please.

A "universe" (dynamical system) consisting of Sun, planets, and Alpha Centauri is just as valid as one consisting of Sun and planets only. Barycenter can be equated with "center of mass".

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Specifying "the Solar system" should exclude things like the Centauri triplets or the Sombrero Galaxy.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

My point is just as valid if I said "include the mass of hypothetical Planet X with a Jupiter-sized mass orbiting the Sun at a distance of 1000 au". That is certainly a legitimate part of the solar system, yet would drag the barycenter out to the Earth's orbit. The Earth sometimes would go right through it. But nothing we can observe changes. -|Tom|-

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22 years 2 months ago #2779 by Larry Burford
[tvf]
The example is intended to illustrate how arbitrary "barycenter" is. It applies to all the masses under consideration. That line can be drawn wherever we please.

A "universe" (dynamical system) consisting of Sun, planets, and Alpha Centauri is just as valid as one consisting of Sun and planets only. Barycenter can be equated with "center of mass".

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I guess I'm not making myself clear. I understand THAT we can include any mass in our definition of a dynamical system. But I'm not sure WHY we would consider adding some masses to some systems.

Rather than try to rephrase my original question, though, let me try a different approach. Just before AB asked his question about the barycenter of the solar system (to which you made your reply referencing Alpha Centauri) you had mentined the barycenter of the Earth-Moon system. When you specified "Earth-Moon" you clearly meant to exclude all other masses. True? In this case there is no ambiguity about the definition of the dynamical system or where the barycenter of that system is located. True?

AB specified the Solar system in his question. No specific masses were explicitly mentioned, so the definition of the dynamical system is ambiguous, and open to modification. True?

(Damn! You have been Tholenized! <img src=icon_smile.gif border=0 align=middle> Seriously though, it is important to be precise. Ambiguity leads to many misunderstandings and disagreements.)

AB's question was: "Is there any consistent data on the Sun's motion wrt the Solar system barycenter?" If this question were to be reworded thus: "Is there any consistent data on the Sun's motion wrt the Sol-Jupiter (or Sol-Jupiter-Saturn, etc.) system barycenter?", I'm guessing the ambiguity would go away. True?

On the topic of calculating vs observing the barycenter of a system. Aren't we observing the barycenter of a star system (the star and whatever mass is within its gravitational sphere of influence) when we use the star's wobble to detect things orbiting it?

We can also look at Sol and see it wobble. But in this case we can identify just about all of the mass causing that wobble.

Is there a different term for the center point of this wobble? Perhaps "wobblecenter"? Since this is an observable point in space, it would seem not to be the same in general as barycenter. Of course if you pick your dynamical system carefully it could be the same point.

Regards,
LB

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22 years 2 months ago #2780 by AgoraBasta
Replied by AgoraBasta on topic Reply from
So now my question would be - is the Sun wobbling consistently with the known composition of the Solar system? And how is the observed "visible" Sun, after the corrections to light transit times are made, placed wrt its magnetic field and its gravitational field?


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