1. UCLA Galactic Center Group: Animations

The movie shows a 3-dimensional visualization of the stellar orbits in the Galactic center based on data obtained by the W. M. Keck Telescopes between 1995 and 2012. Stars with the best determined orbits are shown with full ellipses and trails behind each star span ~15-20 years.

2. Originally Posted by mkline55
Dave Lee may not want an exposition, but I'm curious about the orbital path. I don't know if this is the right approach, but here's where I'd start. Take a cross-section of the ring and analyze it from there. Draw a circle to represent the cross-section. Put a dot in the center to represent the center of gravity. But remember that this is part of a ring, so the center of gravity will actually be offset either toward the center or toward the edge. Consider that at the outer edge of the ring all of the ring's mass is inward, and at the inner edge, some of the mass is inwards and some outwards. So move the dot appropriately. Since the ring is symetrical, if you then expand the cross-section into a ring again, the dot becomes a circle. Something orbiting the ring fairly close to the ring's surface and in a plane that is not exactly perpendicular to the ring's plane, might describe a path that circles the ring and simultaneously procedes around the ring.
If you just look at the optical parts of rotating sources (pure SR) you can use the constant speed of light and basic geometry to give you a solid platform for an observation model based on rotating sources (for 11-16 year cycles as well as billions of year cycles).

The image below shows the photon paths present, at the time of an observation, of the photons emitted and in transit between 2 identical sources that are rotating around a common center of mass and observers, at various angles to the plane of rotation, who are stationary with respect to the center of mass of the rotating sources. The distance between the observer and the sources cycle start locations 1,0 and 3,0 always equals (where is the angular velocity and the radius of rotation) after one complete rotation regardless of the angle of the observer to the plane of rotation of the sources. The observer may or may not be rotating around the common center of mass of the rotating sources to be considered stationary with respect to that center of mass. The scale shown in the images below is for .

Here's how to plot a 45 degree angle path over 4 quarters of rotation. You know the start and end points after each quarter, join them together and push them along to the observer.

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Originally Posted by Dave Lee
O.K.

If I understand it correctly, you claim that we don't need to verify the orbit plane due to the location of the central body.
So, as the location of the MBH doesn't meet a circular path, then we take it for granted that it is ellipse.
Hence, we didn't even try to verify the correct orbit plane for each star.

Is it correct?
We may not so much as verify the correct orbital plane as deduce its inclination.
And in addition to the line of orbit in sky, we also can follow the orbital speed.

4. At three pages I consider this now an extended discussion, and so the thread is moved from Q&A to Astronomy. Carry on...

5. Originally Posted by 01101001
You're wondering about a gnat within a swarm of gnats. The center of gnat-mass depends at every moment where all the gnats are right then. And a moment later the center moves.
I stand corrected. This professional science guy says: bees.

ESO: Unprecedented 16-Year Long Study Tracks Stars Orbiting Milky Way Black Hole

For the first time the number of known stellar orbits is now large enough to look for common properties among them. "The stars in the innermost region are in random orbits, like a swarm of bees," says Gillessen. "However, further out, six of the 28 stars orbit the black hole in a disc. In this respect the new study has also confirmed explicitly earlier work in which the disc had been found, but only in a statistical sense. Ordered motion outside the central light-month, randomly oriented orbits inside – that's how the dynamics of the young stars in the Galactic Centre are best described."
I always was weak in entomological etymology.

Anyone fear this 6-star disc will result in a trip down another garden path of other stars being inside or outside of the disc?

Don't get stung!

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Originally Posted by 01101001
I stand corrected. This professional science guy says: bees.
ESO: Unprecedented 16-Year Long Study Tracks Stars Orbiting Milky Way Black Hole
I always was weak in entomological etymology.
Anyone fear this 6-star disc will result in a trip down another garden path of other stars being inside or outside of the disc?
Don't get stung!
With regards to that article, it is stated:

"One particular star, known as S2, orbits the Milky Way's centre so fast that it completed one full revolution within the 16-year period of the study. Observing one complete orbit of S2 has been a crucial contribution to the high accuracy reached and to understanding this region. Yet the mystery still remains as to how these young stars came to be in the orbits they are observed to be in today. They are much too young to have migrated far, but it seems even more improbable that they formed in their current orbits where the tidal forces of the black hole act. Excitingly, future observations are already being planned to test several theoretical models that try to solve this riddle."

Hence, let's focus on S2 as it is quite important star.
In the other article the word "S2" repeats 88 times. (Quite significant with related to all the other stars.)
It is also stated:
"Our data set covers the pericenter passages of several stars. Particularly important to our analysis is the one of the star S2. The star is one of the brightest in the sample, and we observed a full orbit (see Figure 13). In 2002 S2 passed its pericenter, thus changing quickly in velocity throughout a period of a few months. These data are particularly useful for constraining the potential of the MBH. "
"Figure 13. Top: S2 orbital data plotted in the combined coordinate system and fitted with a Keplerian model in which the velocity of the central point mass and its position were free-fit parameters. "
So, In Figure 13 we see clearly the elliptical path of S2 as we see it from our location.
However, they don't say even one word about the real orbit plane of S2.
Therefore, technically, it could have a perfect circular orbit, while we see it as elliptical - as we might not have a direct top view location.
Please look at the following diagram rotation of S2:
https://en.wikipedia.org/wiki/Sagitt...tre_orbits.svg
The MBH is located just at the bottom side of this elliptical path.
Based on this diagram the distance from the MBH to the bottom side of the S2 elliptical orbit is about one square, while the distance from the MBH to the top side is more than 8 squares.
Therefore, I would expect to see significant change in R0. (Distance to MBH)
However, in "Table 4. Results for the Central Potential from Orbital Fitting":
There are six measurements of S2. The value of R0 is in between 8.80 Kpc (Measurement nu. 5) to 6.63Kpc (measurement nu. 6).
So, we really don't have any information about the top/bottom sides of S2 elliptical rotation path.
Can someone explain it?
How could it be that there is a relatively minor R0 change in the table (6.63 / 8.80), while there is a significant change in the diagram (1 / 8)?
Why they don't try to verify the real orbital plane of S2?
Last edited by Dave Lee; 2016-May-12 at 04:17 PM.

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Originally Posted by Dave Lee
So, let me ask the following:
1. What does the diagram represent? Is it what we see from our location, or does it represnt the real orbit plane of each star?
2. Do you mean that for each star they have verified the correct plane and based on that they have set the diagram? So they actually set a 3D rotation on 2D while each orbit represents a central top view.
3. Why it is not specify in the article what is the shift between each orbit plane to our location view?
1) Read the article. It says exactly what the diagram represents in the caption for it. "Stellar orbits of the stars in the central arcsecond for which we were able to determine orbits. In this illustrative figure, the coordinate system was chosen such that Sgr A* is at rest."
2) Read the article. It says exactly what the state vector representation of each orbit was.
3) Why would they? They have defined a co-ordinate system and used it. Why should they then provide transformations into arbitrary systems?

I have tried to verify the orbital plane in that article. The word "plane" is located in only 5 places in the whole article:
So? If you read a paper on domestic cats you probably won't find many examples of the word "Kitty". Use their terminology and read the paper - it explains the motion models used and how they turned them into orbits. You seem to have an image in your head about how they 'should' do it - I'd suggest you try to understand how they did do it rather than search fruitlessly for your own method in their paper.

I was quite surprised to discover that most of those stars orbits around some virtual center – which is not the MBH?
Why? People have been saying throughout this thread that the orbits are affected by more than just one object.

How could it be? Why they do not orbit around the MSB (which is located at 0)
Because there are other masses in the area. Can you rephrase your question? I must not be understanding it. You seem to be surprised that a body orbiting a cluster of objects doesn't orbit one of them.

How do we know for sure that this diagram represents the real orbit plane for each star?
Because ... I already told you. I pointed out how they had done this. I pointed out the models they had used. If you are confused then I'd suggest you point to sections of the paper you are struggling with - because the answers to your questions are all in it so far.

Therefore, technically, it could have a perfect circular orbit, while we see it as elliptical - as we do not have a direct top view location.
No. Because it would not be consistent with the data. Look at the 6DOF stuff they did. A circular orbit would simply not reproduce the results.

Why they don't try to verify the real orbital plane of S2?
They implicitly did via the orbit modelling. They just didn't use your non-standard approach.

8. Originally Posted by Shaula
1) Read the article. It says exactly what the diagram represents in the caption for it. "Stellar orbits of the stars in the central arcsecond for which we were able to determine orbits. In this illustrative figure, the coordinate system was chosen such that Sgr A* is at rest."
2) Read the article. It says exactly what the state vector representation of each orbit was.
3) Why would they? They have defined a co-ordinate system and used it. Why should they then provide transformations into arbitrary systems?

So? If you read a paper on domestic cats you probably won't find many examples of the word "Kitty". Use their terminology and read the paper - it explains the motion models used and how they turned them into orbits. You seem to have an image in your head about how they 'should' do it - I'd suggest you try to understand how they did do it rather than search fruitlessly for your own method in their paper.

Why? People have been saying throughout this thread that the orbits are affected by more than just one object.

Because there are other masses in the area. Can you rephrase your question? I must not be understanding it. You seem to be surprised that a body orbiting a cluster of objects doesn't orbit one of them.

Because ... I already told you. I pointed out how they had done this. I pointed out the models they had used. If you are confused then I'd suggest you point to sections of the paper you are struggling with - because the answers to your questions are all in it so far.

No. Because it would not be consistent with the data. Look at the 6DOF stuff they did. A circular orbit would simply not reproduce the results.

They implicitly did via the orbit modelling. They just didn't use your non-standard approach.
Let me add that in the region shown here, the total mass of the stars is a tiny fraction of that of the central black hole. Thus the orbits will be close approaches to Kepler orbits around the central mass, except in the rare cases of extremely close encounters with one another.

A circular orbit nearly edge on will look like an ellipse with the black hole at its geometric center, that is, the midpoint of its major axis. None of these orbits come even close. S13's true ellipse would have a minor axis about 90% of the length of the major axis, so a moderate inclination with an orientation that foreshortens the major axis but not the minor could make it look circular from this viewpoint.

Assuming that the calculated shape of S2's orbit is accurate, the star will spend most of its time between 6 and 8 squares from the origin, and it conceivably could have gone unobserved during the short interval during which it whipped around periapsis. Nevertheless, with sufficiently good data from the points at which it was observed, the experts working on this project could fit the ellipse as shown with reasonable confidence. I have no motive to second-guess them.

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Originally Posted by Shaula
1) Look at the 6DOF stuff they did. A circular orbit would simply not reproduce the results.
Can you please direct me to that info?

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With regards to my question:
"I was quite surprised to discover that most of those stars orbits around some virtual center – which is not the MBH?"

Originally Posted by Shaula
Why? People have been saying throughout this thread that the orbits are affected by more than just one object.
However, the total mass of the stars is a tiny fraction of that of the central black hole. Please see the following message:
Originally Posted by Hornblower
Let me add that in the region shown here, the total mass of the stars is a tiny fraction of that of the central black hole.
So, the MBH must have full control on all the stars in the aria.
We can use the solar system as an example - as all planets and moons in the solar system are a tiny fraction the sun mass.
So, all the Planets are orbiting the Sun, while the moons are orbiting the planets.
Therefore, let's look again on the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
How can we justify the local rotations of stars in this diagram (for example: S29, S97, S33 and many others?)
There is no visible central mass in the center of their orbit. (Not even anywhere inside the orbit cycle)
So, how can we justify those local orbits?
It is similar like a moon which orbits an invisible point in the solar system. Is it feasible?
So, the questions are as follow:
If the total mass of the stars is a tiny fraction of the central black hole, how could it be that those stars rotate around some invisible point in space?
Could it be that they rotates around some Black Hole?
If there are black holes, (and quite many of them), then could it be that the total mass of the stars + all the black holes aren't so tiny fraction with related to the MBH?

However, if there were BH then we had to see some strong gravity lensing in their spot (and maybe some sort of gravity interaction with the MBH.
Do we see it? If we don't see it, and there are no B.H. then how can we justify those local orbits???
Last edited by Dave Lee; 2016-May-12 at 07:38 PM.

11. Originally Posted by Dave Lee
With regards to my question:
"I was quite surprised to discover that most of those stars orbits around some virtual center – which is not the MBH?"

However, the total mass of the stars is a tiny fraction of that of the central black hole. Please see the following message:

So, the MBH must have full control on all the stars in the aria.
We can use the solar system as an example - as all planets and moons in the solar system are a tiny fraction the sun mass.
So, all the Planets are orbiting the Sun, while the moons are orbiting the planets.
Therefore, let's look again on the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
How can we justify the local rotations of stars in this diagram (for example: S29, S97, S33 and many others?)
There is no visible central mass in the center of their orbit. (Not even anywhere inside the orbit cycle)
So, how can we justify those local orbits?
It is similar like a moon which orbits an invisible point in the solar system. Is it feasible?
So, the questions are as follow:
If the total mass of the stars is a tiny fraction of the central black hole, how could it be that those stars rotate around some invisible point in space?
Could it be that they rotates around some Black Hole?
If there are black holes, (and quite many of them), then could it be that the total mass of the stars + all the black holes aren't so tiny fraction with related to the MBH?

However, if there were BH then we had to see some strong gravity lensing in their spot (and maybe some sort of gravity interaction with the MBH.
Do we see it? If we don't see it, and there are no B.H. then how can we justify those local orbits???
You appear to be interpreting those distorted ellipses on the display linked in post 70 as orbital motion of stars around some points other than the central black hole, when I cannot tell what that display is supposed to mean. It looks like a flat surface projection of the surface of an entire sphere. With no text and no links back to the source, I don't have the foggiest idea what to make of it. At least the display linked in post 60 is clearly a view of the small region around the black hole. Comparison with other sources linked in this thread corroborate this. The ellipses shown are consistent with Keplerian orbits around the central mass, with various amounts of inclination of the orbital planes and orientation of the lines of apsides. I stand by what I wrote in my previous post.

12. Your questions appear to be rooted in the same misconceptions that have been corrected over and over. There is no confusion between stars in elliptical orbits around a black hole and stars in circular orbits around "virtual centers", because the motions of stars in circular orbits are different, no perspective can make them appear the same, and stars don't choose to orbit random points in space. There is no assumption that we are viewing the orbits from above, and there is no requirement for it, the math they use does not assume an orbital plane, they fit for that as well as for the other orbital parameters.

You seem to again be trying to force everything into some conception of objects following circular orbits around "virtual centers". You may as well be trying to explain things in terms of a flat Earth. Your framework is broken, and you need to throw it away instead of trying to wedge everything into it.

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Originally Posted by Dave Lee
So, the MBH must have full control on all the stars in the aria.
Only if we ignore the existence of the rest of the galaxy, Dave Lee, as has been pointed out. For that matter why are you ignoring the effect of the other stars that orbit the MBH?
The MBH has a large mass compared to the stars. The MBH has a tiny mass compared t the rest of the galaxy. Looking at mass alone the rest of the galaxy "must have full control on all the stars in the aria". But gravitation does not depend on mass along! Gravitation also depends on distance (an inverse square law). What has the most influence over the stars is a complex issue. We have observed the stars for some decades, see that stars are in orbits around the MBH and thus are currently mostly influenced by the MBH. In the past the stars may have not orbited the MBH. In the future the stars may even stop orbiting the MBH.

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Originally Posted by Dave Lee
Therefore, let's look again on the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
How can we justify the local rotations of stars in this diagram (for example: S29, S97, S33 and many others?)
There are no "local rotations" in that diagram to justify because you give no context for the diagram. Not even a caption!

This is Figure 19 in MONITORING STELLAR ORBITS AROUND THE MASSIVE BLACK HOLE IN THE GALACTIC CENTER
Figure 19. Orientation of the orbital planes of those S-stars for which we were able to determine orbits. The orientation of the orbits in space is described by the orbital angular momentum vector, corresponding to a position in this all sky plot, in which the vertical dimension corresponds to the inclination i of the orbit and the horizontal dimension to the longitude of the ascending node Ω. A star in a face-on, clockwise orbit relative to the line of sight, for instance, would be located at the top of the graph, while a star with an edge-on seen orbit would be located on the equator of the plot. The error ellipses correspond to the statistical 1σ fit errors only, thus the area covered by each is 39% of the probability density function.
Those ellipses are error ellipses not "local rotations".

You may want to look at "Table 7. Orbital Parameters of Those S-stars for Which We Were Able to Determine Orbits" for measured eccentricities, etc.
Last edited by Reality Check; 2016-May-13 at 12:37 AM.

15. Reality Check, thank you so much for posting a link to the complete paper, rather than the uncaptioned figures which we had before.
Originally Posted by Hornblower
Assuming that the calculated shape of S2's orbit is accurate, the star will spend most of its time between 6 and 8 squares from the origin, and it conceivably could have gone unobserved during the short interval during which it whipped around periapsis. Nevertheless, with sufficiently good data from the points at which it was observed, the experts working on this project could fit the ellipse as shown with reasonable confidence. I have no motive to second-guess them.
I stand corrected. The paper shows clearly that they observed S2 through its pericenter passage, and that Dave Lee's material to which I had responded must have been incomplete and/or out of context.

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Originally Posted by Hornblower
Reality Check, thank you so much for posting a link to the complete paper, rather than the uncaptioned figures which we had before.
Actually the complete paper was linked to in the OP by Dave Lee - I just put the title in my link. As for S2's orbit - the paper is from 2009 so we have another 7 years of the orbit mapped and probably published somewhere.
Last edited by Reality Check; 2016-May-13 at 03:10 AM.

17. Originally Posted by Reality Check
Actually the complete paper was linked to in the OP by Dave Lee - I just put the title in my link.
I stand corrected again. This thread has gone through so many twists and turns that I had forgotten what was in the OP. Dumb me!

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Originally Posted by Dave Lee
Can you please direct me to that info?
Section 5 - Orbital Fitting. Section 6.4.

So, the MBH must have full control on all the stars in the aria.
The mass of the Sun is much larger than the mass of the Earth. So by your logic the Sun should have full control of the Moon. That is an extreme example but it covers the point I was making that you have ignored over and over. It is not a simple two body problem - there are other objects around.

The rest of your points have already been covered by other posters. You are hanging on to your own conceptual framework about how gravity works. And it is not a good enough one.

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Originally Posted by Reality Check
Only if we ignore the existence of the rest of the galaxy, Dave Lee, as has been pointed out. For that matter why are you ignoring the effect of the other stars that orbit the MBH?
The MBH has a large mass compared to the stars. The MBH has a tiny mass compared t the rest of the galaxy. Looking at mass alone the rest of the galaxy "must have full control on all the stars in the aria". But gravitation does not depend on mass along! Gravitation also depends on distance (an inverse square law). What has the most influence over the stars is a complex issue. We have observed the stars for some decades, see that stars are in orbits around the MBH and thus are currently mostly influenced by the MBH. In the past the stars may have not orbited the MBH. In the future the stars may even stop orbiting the MBH.
Thanks
Yes, this is an excellent explanation.
It is also correlated with the message from Shaula
Originally Posted by Shaula
It is not a simple two body problem - there are other objects
So,
1.It is not a simple two body problem - there are other objects which we shouldn't ignore.
2.We shouldn't ignore with the existence of the rest of the galaxy.
3.Gravitation also depends on distance (an inverse square law).
Therefore, let's look again on the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
If I understand it correctly there is no need to find any BH or some invisible mass in the center of those rotations. Each star orbits around the center of gravity which is a direct outcome from the mass in the galaxy including the MBH (but especially – from the close distance due to an inverse square law).
Is it correct?

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Originally Posted by Dave Lee
Each star orbits around the center of gravity which is a direct outcome from the mass in the galaxy including the MBH (but especially – from the close distance due to an inverse square law).
Is it correct?
... Only to first order, as was first said back in post 14 and in fact by the preceding 3 points you listed in the post. You are still trying to apply this simplistic two body solution to a problem that is much more complex.

They roughly orbit the centre of mass of the objects inside their orbits - but said orbit is perturbed by the non-spherical nature of said mass distribution, by nearby stars and other influences. The size and nature of the orbits depend on what is around them, what interactions they have had in the relatively recent past and so on.

You are over-simplifying the situation for the level of detail you seem to want to get in to.

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Originally Posted by Shaula
... Only to first order, as was first said back in post 14 and in fact by the preceding 3 points you listed in the post. You are still trying to apply this simplistic two body solution to a problem that is much more complex.

They roughly orbit the centre of mass of the objects inside their orbits - but said orbit is perturbed by the non-spherical nature of said mass distribution, by nearby stars and other influences. The size and nature of the orbits depend on what is around them, what interactions they have had in the relatively recent past and so on.

You are over-simplifying the situation for the level of detail you seem to want to get in to.
Thanks
However, would you kindly give a direct answer:

Is it correct that each star orbits around the center of gravity which is a direct outcome from the mass in the galaxy including the MBH (but especially – from the close distance due to an inverse square law).
Yes or no.

What do you mean by:

1. "... Only to first order" - What is the first order? order of what?
2. "They roughly orbit the centre of mass of the objects inside their orbits - but said orbit is perturbed by the non-spherical nature of said mass distribution, by nearby stars and other influences. The size and nature of the orbits depend on what is around them, what interactions they have had in the relatively recent past and so on." - I have no clue what does it mean. Please elaborate. Do you mean that only the mass inside the orbit has an effect on the center of Gravity?

22. Originally Posted by Dave Lee
Thanks
However, would you kindly give a direct answer:

Is it correct that each star orbits around the center of gravity which is a direct outcome from the mass in the galaxy including the MBH (but especially – from the close distance due to an inverse square law).
Yes or no.

What do you mean by:

1. "... Only to first order" - What is the first order? order of what?
2. "They roughly orbit the centre of mass of the objects inside their orbits - but said orbit is perturbed by the non-spherical nature of said mass distribution, by nearby stars and other influences. The size and nature of the orbits depend on what is around them, what interactions they have had in the relatively recent past and so on." - I have no clue what does it mean. Please elaborate. Do you mean that only the mass inside the orbit has an effect on the center of Gravity?

We will do well to break a response down into small chunks, so that if you encounter a point you do not understand for whatever reason, we can resolve it without first having to tease it out of a profusion of confusion we can get by trying to cover too much in one post.

We are studying a region with a radius of about 1/8 of a lightyear. Here we have a central black hole of several million solar masses, and a few dozen stars totaling at most a few hundred solar masses. This looks like a good analogy to our own solar system, with the black hole analogous to the Sun and the stars analogous to the planets. We know from observation that our planets move in close approximations to Kepler ellipses around the Sun, and that the orbits slowly drift because of perturbations by the relatively slight gravitational effects of the planets on each other. The Sun overwhelmingly dominates the action here. I feel safe in saying that the black hole does likewise in its close-in territory, which appears to be corroborated by the findings in the paper linked in this thread. Let me pause for comments and/or questions before going any farther.

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Originally Posted by Hornblower
We will do well to break a response down into small chunks, so that if you encounter a point you do not understand for whatever reason, we can resolve it without first having to tease it out of a profusion of confusion we can get by trying to cover too much in one post.

We are studying a region with a radius of about 1/8 of a lightyear. Here we have a central black hole of several million solar masses, and a few dozen stars totaling at most a few hundred solar masses. This looks like a good analogy to our own solar system, with the black hole analogous to the Sun and the stars analogous to the planets. We know from observation that our planets move in close approximations to Kepler ellipses around the Sun, and that the orbits slowly drift because of perturbations by the relatively slight gravitational effects of the planets on each other. The Sun overwhelmingly dominates the action here. I feel safe in saying that the black hole does likewise in its close-in territory, which appears to be corroborated by the findings in the paper linked in this thread. Let me pause for comments and/or questions before going any farther.
I read your answer, as well as Shaula's, and I have no clue what do you really want to say.

I must tell you a real story about an examination which I had in the University. It was very difficult question - and I didn't know the correct answer.
As it was very important examination, I have started to give a very complex and indirect answer. They were quite confused from my long and indirect answer that they didn't ask me any further question and moved on to the next student.

However, this isn't examination in the University.

So, please - Yes or no.
Why is it so difficult to give a simple answer? For example:
Yes - that is correct.
Or
No - it isn't correct due to...

In any case, let me try to guess what do you really mean by these indirect answers:
I assume that your answer is no. (Otherwise you would probably say - Yes.)

So, If it is no, and based on your understanding, what is the source for that "local" orbit rotation?
Last edited by Dave Lee; 2016-May-13 at 02:20 PM.

24. Originally Posted by Dave Lee
Thanks
However, would you kindly give a direct answer:

Is it correct that each star orbits around the center of gravity which is a direct outcome from the mass in the galaxy including the MBH (but especially – from the close distance due to an inverse square law).
Yes or no.

What do you mean by:

1. "... Only to first order" - What is the first order? order of what?
2. "They roughly orbit the centre of mass of the objects inside their orbits - but said orbit is perturbed by the non-spherical nature of said mass distribution, by nearby stars and other influences. The size and nature of the orbits depend on what is around them, what interactions they have had in the relatively recent past and so on." - I have no clue what does it mean. Please elaborate. Do you mean that only the mass inside the orbit has an effect on the center of Gravity?

I've read some of the responses, got more to read, but some of the confusion may come from this.

Objects do not typically orbit the center of mass, when the mass is extensive. As an extreme example, consider the satellites/modules in orbit around our moon, or earth. Their orbits are very far from centered around the center of mass of the earth/moon system. They'd have to be quite a ways away from both moon and earth in order for that to be the case.

25. Originally Posted by Dave Lee
So, If it is no, and based on your understanding, what is the source for that "local" orbit rotation?
What is a "local" orbit rotation?

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Originally Posted by 01101001
What is a "local" orbit rotation?
Please look again at the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
Please try to find S21 and S29 (as an example).
Do you see their orbit cycle?
Those stars do not rotate around the MBH. they rotate around some invisible point in space. (I call it - "local" orbit rotation).
Is it clear?
Last edited by Dave Lee; 2016-May-13 at 02:54 PM.

27. Originally Posted by Dave Lee
Please look again at the following diagram:
http://iopscience.iop.org/0004-637X/...e/apj297214f19
Please try to find S21 and S29 (as an example).
Do you see their orbit cycle?
Those stars do not rotate around the MBH. they rotate around some invisible point in space. (I call "local" orbit rotation).
Is it clear?
Does that link work for everyone else?

28. Banned
Join Date
Sep 2015
Posts
534
Originally Posted by grapes
I've read some of the responses, got more to read, but some of the confusion may come from this.

Objects do not typically orbit the center of mass, when the mass is extensive. As an extreme example, consider the satellites/modules in orbit around our moon, or earth. Their orbits are very far from centered around the center of mass of the earth/moon system. They'd have to be quite a ways away from both moon and earth in order for that to be the case.
Thanks
However, I don't understand how this example can offer a solution for the "local" orbit rotation. Would you kindly elaborate?

29. Originally Posted by grapes
Does that link work for everyone else?
It's a failed copy. Dave Lee means http://iopscience.iop.org/0004-637X/...e/apj297214f19

Originally Posted by Dave Lee
Do you see their orbit cycle?
What "orbit cycles"? The circles/ellipses/curves around the stars are not orbit cycles.

Originally Posted by Reality Check
Those ellipses are error ellipses not "local rotations".
What RC said.

30. Thanks for the revised link
Originally Posted by 01101001
What "orbit cycles"? The circles/ellipses/curves around the stars are not orbit cycles.

What RC said.
Does that resolve the issue, Dave Lee?

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