My dilemma

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[LB]: I'm not sure WHY we would consider adding some masses to some systems.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I was illustrating arbitrariness and lack of physical significance for the point called “barycenter”. All real systems have slightly uncertain masses and the possibility of other, unknown masses. These change the barycenter, but not the physics.

I have some correspondents who attach physical significance to “barycenter”, and who derive things such as the centrifugal forces on various points on Earth’s surface due to their differing motions with respect to the Earth-Moon barycenter. This is physical nonsense. The motion of Earth with respect to the Earth-Moon barycenter has no more physical significance than its motion with respect to any other arbitrary point in space, such as the point midway between Earth and Moon.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

True. To the extent that “barycenter” is a computed point, its location is never ambiguous. The ambiguity arises from not knowing any masses exactly or completely, or where to draw the line about what to include.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

There cannot be “data” about a barycenter for any system of masses because a barycenter is not a physical, observable point. It is a purely mathematical one. If you specify the masses, then the computation should be exact. But so what?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>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?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

No, we are just observing the relative motion of two bodies, as we always are. Once we have enough data to estimate the separate masses, we become able to compute an estimated barycenter location. But we have no way to observe that location. And if we later discover another planet or a distant dwarf star in the same system, so that the barycenter jumps, that does not invalidate our previous work.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Is there a different term for the center point of this wobble?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

No, same term.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Since this is an observable point in space, it would seem not to be the same in general as barycenter.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

It is not observable. It is inferable. We observe the relative motion between bodies. As we do so, we may learn of a short-period orbiter soon. As time goes on, we may learn of more and more orbiting bodies contributing to the wobble.

In my “Planet X” example, the Sun and all known planets may have a huge-but-very-slow wobble with amplitude of 1 au. But there would be almost no relative wobble, so we would remain unaware of the existence of a large, undiscovered mass in our own solar system. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[AB]: is the Sun wobbling consistently with the known composition of the Solar system?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

By definition, yes. If the Sun had some unexplained wobble, that would lead us to infer additional mass in the system. The most accurate data measuring this “wobble” is pulsar timing data. If the Sun moves in some direction, pulses in that direction arrive earlier than expected, and pulses from the opposite direction arrive later than expected.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>And how is the observed "visible" Sun, after the corrections light transit times are made, placed wrt its magnetic field and its gravitational field?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

The Sun’s magnetic field is far too weak to detect from Earth. Inferences about it are made based on splitting of certain spectral lines.

The visible and gravitational Sun differ because of the light transit time, and nothing else. That merely means that any undiscovered mass is distant enough to affect Sun and Earth only very slowly and almost identically. -|Tom|-

So presumably, the only real barycenter is somewhere at the "center" of the universe, and this will have a tendency to wander about a lot!<img src=icon_smile_big.gif border=0 align=middle>

Now that the barycenter is clarified I am still puzzled about tidal force and the gravity statement GM=rv2. The moon is moving 81 times faster than the Earth I assume. Then the moon is not putting out anywhere the force it should according to GM=rv2. Since both masses are at the same distance only v2 can balance GM, and since Mm/Me is 1/81 then logically v2e/v2m=81 and v for Earth is 9 if v for moon is 1. The fact that the Earth v is 81/1 leads me to think there is something causing the Earth to be very much slower than it should be which is 9/1.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Now that the barycenter is clarified I am still puzzled about tidal force and the gravity statement GM=rv2. The moon is moving 81 times faster than the Earth I assume. Then the moon is not putting out anywhere the force it should according to GM=rv2.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

In GM = rv^2, M = mass of (Earth + Moon), r is mutual distance, and v is velocity of either body relative to the other. So there is only one value of M, r, and v, not two different values.

Earlier, I agree that the Moon's speed relative to the barycenter was 81 times greater than Earth's, but then hastened to mention that no mass exists at the barycenter, so motion relative to the barycenter has no physical meaning. The law you cite defoinitely does not apply to motion with respect to any fictitious points such as the barycenter. It only applies to motions of real masses relative to one another. -|Tom|-

The moon has mass of it's own and it has a gravity field of it's own that moves the Earth according to GM=rv2. I think you are ignoring this obvious fact and adding the two masses together is only proper when the system is examined from another point in the universe outside the system itself. Doing this addition within the system gets the wrong result if you are looking to see the real effects the gravity fields induce in each other. The use of centers of mass needs to be seen as two centers-one at the Earth center-one at the moon center.