# Baricentre (barycenter) - does it 'wobble'?

by Nereid
Tags: baricentre, barycenter, wobble
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In another thread, in General Astronomy & Cosmology, the baricentre (or barycenter, for those in the US) was mentioned.

Here are the relevant statements:
 Let's simplify things a bit; let the mass of our BH be Msun, and let's write our distances as multiples of 100au. At a distance of 16 (= 1600 au), our BH would have an Einstein radius of 1" (and a crossing time of 40ks, ~11 hours).
 From context, I assume that "baricenter" is the center of the star being lensed, but since any star seen from Earth (other than sun) is a "point" I am not sure.
 The solar system baricentre (or barycenter, to those who live in the US) is its centre of mass. [...] How about you do a simple calculation for us, BillyT? Assume the only massive objects in the solar system are the Sun and Jupiter, that the mass ratio is 1:1000, and that the distance between the centres of these two objects is 800 million km. Where would the 'solar system baricentre' be?
 Thanks for the definition. Because of the 1:1000 ratio, the distance from the sun, I'll call it X, is approximately 0.8 Million Km along the line joining them, and dos ont move as both orbit it. More accurately, 1000X = (800 - X) is sovled to find the distance from the sun. [...] I note that in the two only object case you gave, the Baricenter does not "wobble" because these two are orbiting it, but has velocity relative to fixed stars as our solar system "orbits" the the galaxy center (Orbits in quotes as there must be very slight perturbations as other near by stars distrube this orbit.) If there were three (or more) objects it would bve rare that the baricenter was on the line joining any two, and never if the orbit planes were not the same.
 Indeed; the baricentre does not 'wobble', by definition!
 Either I don't understand you or you are wrong on this, assuming "baricenter" is just a new (to me) term for "center of mass." For example, in your two body case (Sun and Jupiter only), the baricenter is always in the plane of Jupiter's orbit; but now let us add Pluto, which is rarely in this plain. When Pluto is "above" (North or what ever is the correct term), then the baricenter is also slightly above (North) of the "Jupiter ecliptic." Conversely when Pluto is "below" (South), then the baricenter is also slightly South of the "Jupiter ecliptic." - This oscillation above and below the "Jupiter ecliptic" is what I was referring to as "wobble." Any third body, not in "Jupiter's ecliptic," will cause this wobble, Mercury with the shortest oscillatory period and the passing of a near by star, with such a long one that only a few oscillations have occurred in the history of the universe. I don't see how you can define away this real effect and yet keep the meaning of the "baricenter" the same as the "center of mass."
I think this is an interesting discussion, but completely OT for the original thread.

Does the baricentre 'wobble'? If so, how and why? If not, why not?
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 Quote by Nereid ....Does the baricentre 'wobble'? If so, how and why? If not, why not?
Until some one refutes my Sun, Jupiter, Pluto argument/example of baricenter "wobble" I will hold the view I expressed in the last quote of post 1.

I also note now for the first time, that the line of importance (assuming Earth based observations of black holes gravitational lens effects) is between the star with changing light curve and the Earth, not the baricenter, not that this fine distinction makes any significance difference, which is why I did not mention it in original thread, but this is a "clean start" so that fact should at least be noted.
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 Quote by Billy T Until some one refutes my Sun, Jupiter, Pluto argument/example of baricenter "wobble" I will hold the view I expressed in the last quote of post 1. I also note now for the first time, that the line of importance (assuming Earth based observations of black holes gravitational lens effects) is between the star with changing light curve and the Earth, not the baricenter, not that this fine distinction makes any significance difference, which is why I did not mention it in original thread, but this is a "clean start" so that fact should at least be noted.
If you are defining 'baricentre' as the centre of mass of the entire solar system, including all the comets, asteroids and Kuiper belt objects, then it cannot wobble unless there is some kind of time dependent force being applied to the solar system as a whole, which is not the case. But the baricentre of any two solar system objects that are in orbit around each other (eg. sun/earth) can 'wobble' due to the gravitational effects of other solar system masses.

AM

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## Baricentre (barycenter) - does it 'wobble'?

 Quote by Andrew Mason If you are defining 'baricentre' as the centre of mass of the entire solar system, including all the comets, asteroids and Kuiper belt objects, then it cannot wobble unless there is some kind of time dependent force being applied to the solar system as a whole, which is not the case. But the baricentre of any two solar system objects that are in orbit around each other (eg. sun/earth) can 'wobble' due to the gravitational effects of other solar system masses. AM
That is the way Nereid defined it for me, but lets imagine a solar system containing just three objects, which I will continue to call, Sun, Jupiter and Pluto with roughly their same great difference in masses, but to make the case more extreme, lets assume this "Pluto" has an orbit plane (Pluto's ecliptic if you like) that is perpendicular to the ecliptic of Jupiter.

(1) Do you agree that to first approximation, in this three object solar system, the baricenter is always in the ecliptic of Jupiter?

(2)Exactly so, to all orders, when Pluto is also in Jupiter's ecliptic, but when Pluto is climbing higher and higher above Jupiter's ecliptic the next order approximation shows the baricenter is moving farther and farther above the ecliptic of Jupiter also? (Motion is relative so it could well be, as you suggest, that the baricenter is fixed and Jupiter's ecliptic is moving "down.")

If you agree to these two (and I think you will) and continue to think that the baricenter is not moving, then it must be that the ecliptic of Jupiter is dropping farther and farther below the baricenter as Pluto climbs higher and higher above it.

What I don't understand is why, relative to a fixed baricenter, the ecliptic of Jupiter should move below the fixed baricenter despite the gravitational attraction of Pluto, weak as it may be, tending to lift the ecliptic plane of Jupiter.

I admit to having a strong inclination to agree that the baricenter is fixed, but am confused when I try to understand this three object solar system.

I also want to note that in my original post I did mention exactly your "time dependent force being applied to the solar system as a whole" by citing a passing star. (or black hole - see new thread Could a local black hole exists undetected?)
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 Quote by Billy T That is the way Nereid defined it for me, but lets imagine a solar system containing just three objects, which I will continue to call, Sun, Jupiter and Pluto with roughly their same great difference in masses, but to make the case more extreme, lets assume this "Pluto" has an orbit plane (Pluto's ecliptic if you like) that is perpendicular to the ecliptic of Jupiter. (1) Do you agree that to first approximation, in this three object solar system, the baricenter is always in the ecliptic of Jupiter?
No. It will be whereever $M_{sun}\vec r_{sun} + M_{jup}\vec r_{jup} + M_{sat}\vec r_{sat} + M_{plu}\vec r_{plu} = 0$

 What I don't understand is why, relative to a fixed baricenter, the ecliptic of Jupiter should move below the fixed baricenter despite the gravitational attraction of Pluto, weak as it may be, tending to lift the ecliptic plane of Jupiter.
Let's face it, Pluto won't have much effect on Jupiter. Jupiter's moons will have much more effect on Jupiter than Pluto. You cannot do this qualitatively. You have to work out the numbers. The planets will move in ways that will keep the barycentre in the same 'position' relative to the stars (ignoring of course the motion of that barycentre within the Milky Way and wrt to other galaxies).

 I also want to note that in my original post I did mention exactly your "time dependent force being applied to the solar system as a whole" by citing a passing star. (or black hole - see new thread Could a local black hole exists undetected?)
The only way to detect a black hole is to either see it or for matter to get close enough to it to be captured by it. A black hole with the mass of the sun would behave (gravitationally) just like the sun until matter got really close to it.

AM
 Sci Advisor P: 2,501 I think this discussion has skipped over the most basic question in all considerations of motion; "moving relative to what?". The Berry Center would indeed have the appearence of motion when viewed by any of the players in Billy T's theoretical model (the Sun, Jupiter, and Pluto). It is only to an outside observer, independant of Solar System dynamics, that it would be seen as constant, correct?

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