[Dave Lev (OP)]

Your gas cloud just got 33% less dense (33% increase of volume from a 10% increase in radius).  It would seem to require gas to be condensed to form stars, else they would already have been stars when the gas cloud was tighter.

Please see the following article about: Star Formation in gas cloud Around Suppermassive Black Holes:

https://arxiv.org/ftp/arxiv/papers/0810/0810.2723.pdf
"The presence of young massive stars orbiting on eccentric rings within a few tenths of a parsec of the suppermassive black hole in the Galactic centre is challenging for theories of star formation"

"The presence of young massive stars in the vicinity of the Galactic centre is difficult to reconcile with current models of star formation where turbulent molecular clouds produce a mostly clustered population of stars with a remarkably constant distribution of stellar masses, covering stars with masses from less than a tenth to greater than 100 times the mass of the sun (6)."

We have to understand the real meaning of: "turbulent molecular clouds".
In the article there is no real explanation. (Why they didn't trace that turbulent activity?)
However, I think that there is an order in that "turbulent".
I assume that it represents several/many internal orbital cycles.
If we could look carefully, we might find that around each orbital cycle there is an activity for new star forming.
So, deep in the gas cloud each star stars to orbit around a virtual center of mass.
All the virtual centers of new born stars are orbiting according to a multi star system under the impact of the nearby SMBH.
Therefore, deep in the gas cloud, each new born star gets a gift of orbiting around a virtual Host point.
That is correct to any star in the galaxy.
Actually, if we will trace S2, we might find that it set a bobbling activity as it orbits around the SMBH. That bobbling proves that even this star orbit around a virtual center of mass.
So, the gas cloud can set new stars as it drifts outwards. It just an issue of verifying the rate of outwards drifting VS the rate of new star forming.

[Dave Lev (OP)]

They've tracked it quite closely through more than a full orbit now.  It doesn't have any kind of regular bobbing activity.  S2 does seem to be the sort of object referred to in the article, being a large young star in a highly eccentric orbit about Sgr-A.  That one gets particularly close to it.

Yes it does.
S2 has a clear bobbling orbiting path.
Please look at the following diagram:
http://www.phy6.org/stargaze/Sblkhole.htm
We see clearly that the measured locations of S2 are not directly at the elliptical orbital cycle.
I do recall that in one of the articles it was stated that in 2002, the light of S2 was exactly at the same location as SMBH.
Our scientists were puzzled from this evidence.
They couldn't explain that verification. Therefore they had an idea of error in their instruments.
This was a big mistake.
There is no error in the data.
S2 orbits around a Virtual host point, while this VHP orbits around the SMBH.
Therefore, we see some Zig Zag in the location of S2 with reference to the expected orbital path.
Hence, S2 can even cross the location of the SMBH, while its VHP is moving exactly at the expected elliptical cycle.
I really don't understand why we have only few measured points on that image.
Technically we should know evry day where it is.
Why this information is not valid for all of us?
Why they hide this important information???

[Dave Lev (OP)]

S2 has a clear bobbling orbiting path.
Please look at the following diagram:
http://www.phy6.org/stargaze/Sblkhole.htm
We see clearly that the measured locations of S2 are not directly at the elliptical orbital cycle.

I don't see it.  I see an ellipse (viewed almost edge-on) and every measurement falling on it within the margin of error.  Nothing in the article suggests an irregularity to the orbit, or especially a regular one.

Sorry
This is the biggest mistake of our scientists!
In order to understand this important issue, let's look at the example of the Moon/Sun orbital cycle/
Let's assume that the Earth is invisible from outside. Therefore, it is actually a VHP for the Moon while this one orbits around the Sun.
So, if we try to monitor the Moon/Sun orbit, while we have no clue if the Earth is there, what shall we see?
The Moon/Earth orbital radius is:
R1 (Moon/Earth) = 384,400 Km.
The Earth/Sun orbital radius is
R2 (Earth/Sun) = 149,600,000 Km.
The ration is:
R1/R2 = 384,400 / 149,600,000 = 0.0025
In this example let's assume that the Moon/Earth orbital cycle is located at the same Earth/Sun orbital cycle.
Therefore, if we try to monitor the Moon/Sun orbital cycle, we might see that the moon is moving in almost a perfect cycle, with very minor error.
If we randomly monitor the location of the Moon, it is clear that the error fit is in the range of Zero to 0.0025.
Just if we monitor the moon while it is at its maximal/minimal distance from the sun (R2+R1 or R2-R1) we can get that maximal error fit of 0.0025.
From statistical point of view the chance to get randomly to the maximal 0.0025 Error is very low.
The error should be mainly greater than Zero and lower than 0.0025.
Now, please, let me remind you that in this example we don't know if the Earth (which is the VHP of the Moon) is there.
So, if we give those results to our scientists, what would be the answer?
Based on your answer, our scientists should reply:  "Every measurement falling on it within the margin of error"
So, based on this error margin, the Earth doesn't exist.
Now, let's go back to the S2 orbital cycle.
Please look again at the measured. What is the estimated error margin?
http://www.phy6.org/stargaze/Sblkhole.htm
We see clearly that many measured points are located outside the Fit orbital cycle.
If we look carefully, we clearly see that the maximal measured error point took place on 1995.36
It seems to me as an error which is significantly bigger than 0.0025.
If you also look carefully, we see that the SMBH is not located at the symmetrical point in that orbital cycle.
It is located too close to the left bottom side.
That is one more evidence that S2 doesn't orbit directly around the SMBH.
What about the orbital velocity? Did we try to verify if there are small variations in the measured velocities?
So, how our scientists could afford themselves to ignore those clear evidences of none fit?
I think that it is a fatal mistake to claim:  "Every measurement falling on it within the margin of error"!!!

[Halc]

This is the biggest mistake of our scientists!

The scientists know how to do vector arithmetic, and you don't, so the odds of them being the one making the mistakes are pretty low.

In order to understand this important issue, let's look at the example of the Moon/Sun orbital cycle/
Let's assume that the Earth is invisible from outside. Therefore, it is actually a VHP for the Moon while this one orbits around the Sun.

You just described dark matter, something you deny.

So, if we try to monitor the Moon/Sun orbit, while we have no clue if the Earth is there, what shall we see?
The Moon/Earth orbital radius is:
R1 (Moon/Earth) = 384,400 Km.
The Earth/Sun orbital radius is
R2 (Earth/Sun) = 149,600,000 Km.
The ration is:
R1/R2 = 384,400 / 149,600,000 = 0.0025

Yes, and if you run a Fourier transform on the data for the position of the moon over time, there would be two huge spikes for the periods of a month and a year.  The virtual host point would be glaringly obvious from that data.

In this example let's assume that the Moon/Earth orbital cycle is located at the same Earth/Sun orbital cycle.

I don't know what you mean by this.  A cycle doesn't have a location, and I don't think you are proposing that the Earth is where the sun is.  You want the moon to go around the Earth in one sidereal year?  That would put it at one of the Lagrange points, making it a trojan satellite, not really orbiting the Earth.

Therefore, if we try to monitor the Moon/Sun orbital cycle, we might see that the moon is moving in almost a perfect cycle, with very minor error.

No error at all in fact.

If we randomly monitor the location of the Moon, it is clear that the error fit is in the range of Zero to 0.0025.
Just if we monitor the moon while it is at its maximal/minimal distance from the sun (R2+R1 or R2-R1) we can get that maximal error fit of 0.0025.

We'd know the moon's position to far greater accuracy than that from the distance you indicate.
If you are appealing to margin of error, then it doesn't support your idea, it just says the data isn't accurate enough to make a determination.  No scientists are making mistakes then.  A regular perpetration would show up in a Fourier transform with enough data points, even with a margin of error far larger than the perpetration.

From statistical point of view the chance to get randomly to the maximal 0.0025 Error is very low.

OK, your knowledge of statistics is on par with your vector arithmetic prowess I see.  Statistics is exactly how you get an arbitrarily small margin of error from data points each of which has a large margin of error.

The error should be mainly greater than Zero and lower than 0.0025.
Now, please, let me remind you that in this example we don't know if the Earth (which is the VHP of the Moon) is there.
So, if we give those results to our scientists, what would be the answer?

If it goes around the Earth in the same period that it goes around the sun, then the dark Earth will be undetectable.  I'm not sure why you proposed that period, or even if that is what you meant.

Based on your answer, our scientists should reply:  "Every measurement falling on it within the margin of error"
So, based on this error margin, the Earth doesn't exist.[/quote]
If the moon has a period around Earth that is a month (something less than a year), and the measurements are all a worse margin of error than this 0.0025, then a sufficiently large sample of measurements would suffice to detect Earth, or the lack of it.

If you also look carefully, we see that the SMBH is not located at the symmetrical point in that orbital cycle.
It is located too close to the left bottom side.

That's because you're looking at an ellipse nearly edge-on which distorts where the focus points are.  Our vantage point is not perpendicular to the plane of S2's orbit, but you seem to assume so.

[Dave Lev (OP)]

In this example let's assume that the Moon/Earth orbital cycle is located at the same Earth/Sun orbital cycle.

Sorry if I was not clear.
The idea is:  The Moon/Earth orbital cycle disc plane is located at the same Earth/Sun orbital cycle disc plane.
Again - In this example we want to verify that just by monitoring the locations of the Sun & moon in one cycle (one year) we should find that the Earth is missing (assuming that we don't see it in our verification).

If the moon has a period around Earth that is a month (something less than a year), and the measurements are all a worse margin of error than this 0.0025, then a sufficiently large sample of measurements would suffice to detect Earth, or the lack of it.

O.K.
So, you understand the idea of this example. You also agree that if we see that our measurements of the moon has a small variations from the expected perfect orbital cycle (even if it is less than 0.0025) we should know that the moon must orbit around some other object. We call it Earth, but we can also call it VHP (as we don't see it in our example).
Therefore, I still don't understand why do you still support our scientists while they have clearly neglecting the variations of S2 locations from the expected perfect orbital cycle? They call those variations - Errors. But those variations are very important observations.
Let me use the example at a different perspective:
Let's assume that the  Moon/Earth orbital cycle disc plane is located vertically to the Earth/Sun orbital cycle disc plane and it orbits directly in the Earth/sun orbital cycle.
Let's also assume that our vantage point is perpendicular to the Earth/Sun orbital plane.
Therefore, it is clear that in all the verifications of the Moon location points we should see that it is perfectly located directly at the expected orbital cycle around the Sun.
So, without any variations (or errors) from the expected orbital cycle, we might think there is no need for the earth to explain a perfect orbital fit of the Moon around the Sun.
However, there is another key verification - Velocity.
"KEPLER’S SECOND LAW DESCRIBES THE WAY AN OBJECT’S SPEED VARIES ALONG ITS ORBIT
A planet’s orbital speed changes, depending on how far it is from the Sun. The closer a planet is to the Sun, the stronger the Sun’s gravitational pull on it, and the faster the planet moves. The farther it is from the Sun, the weaker the Sun’s gravitational pull, and the slower it moves in its orbit."
So, in a real elliptical orbit we should find that the velocity of the planet is decreasing smoothly as the farther it is from the Sun.
However, in this example, Due to the Moon/Earth orbital path, sometimes the moon orbits in the orbital Earth/sun direction, and sometimes on the opposite direction (I hope that you understand me correctly).
Therefore, we should find the moon is not smoothly increasing or decreasing its orbital velocity as it orbits around the sun.
So, we have two ways to verify if the Earth (or the VHP) is there.
One - By verify if there is variations (error) in the verified moon location with reference to the expected orbital elliptical cycle.
Two - By verify if there is none smoothly variations in the orbital velocity.
the location of the moon.
With regards to S2 - Even with the assumption that our vantage point is not perpendicular to the plane of S2's orbit, we clearly see that S2 Does not fulfill the two requirements.
Therefore, it shows that S2 must orbit around a VHP while this one might orbit the SMBH.
There is one more key evidence for that:
Please look at the following diagram:
https://en.wikipedia.org/wiki/S2_(star)#/media/File:Galactic_centre_orbits.svg
We see several S stars that orbit around the SMBH.
I assume that our vantage point is not perpendicular to any of those S planes of orbit.
There is good chance that each orbital cycle plane might be different from all the other.
However, if we try to estimate the requested location of the SMBH for each cycle (based on kepler law), we should find that each one needs the SMBH at a different location in space.
So, that also shows that those stars do not orbit directly around the same SMBH.
Each one of them orbits around a VHP while all of those VHP orbits around the SMBH.
Why can't you agree with something which is so clear to us?

[Halc]

The idea is:  The Moon/Earth orbital cycle disc plane is located at the same Earth/Sun orbital cycle disc plane.

Oh, OK.  It already is you know.  There is virtually no tilt to it, something not true in general.

Again - In this example we want to verify that just by monitoring the locations of the Sun & moon in one cycle (one year) we should find that the Earth is missing (assuming that we don't see it in our verification).

Earth would be detectable in this manner no matter what the tilt of the moon's orbit.

So, you understand the idea of this example. You also agree that if we see that our measurements of the moon has a small variations from the expected perfect orbital cycle (even if it is less than 0.0025) we should know that the moon must orbit around some other object.

It could have a very large variation (called eccentricity) and we'd still be able to detect the orbit, yes.

We call it Earth, but we can also call it VHP (as we don't see it in our example).

Yes, we presumably don't know it's there ahead of time, so we certainly don't know its name.

Therefore, I still don't understand why do you still support our scientists while they have clearly neglecting the variations of S2 locations from the expected perfect orbital cycle? They call those variations - Errors. But those variations are very important observations.

They've probably run a Fourier transform on the data and found no regular orbit to it.  That's why asked if you had done that.  You seem to be getting your data from pictures and conclusions written by somebody else, rather than from the actual measurements taken.  If you claim a pattern to the data, take the data and demonstrate it.

Let me use the example at a different perspective:
Let's assume that the  Moon/Earth orbital cycle disc plane is located vertically to the Earth/Sun orbital cycle disc plane and it orbits directly in the Earth/sun orbital cycle.

You mean perpendicular I presume.  A plane cannot be vertical to another one.

Let's also assume that our vantage point is perpendicular to the Earth/Sun orbital plane.
Therefore, it is clear that in all the verifications of the Moon location points we should see that it is perfectly located directly at the expected orbital cycle around the Sun.

No, it would move back and forth in one dimension but not in the other.  So assuming the axis runs right/left from that vantage, the motion you'd see from that vantage is a continuous up/down movement, which is towards and away from the sun when Earth is on the upper or lower side of the orbit, and forwards and backwards in its orbit when Earth is on either side.
If your measurements were good, you could also detect velocity towards and away from your vantage point, which would clue you in to motion in that dimension.  Good measurements are 3D and thus better than 2D pictures.

So, without any variations (or errors) from the expected orbital cycle, we might think there is no need for the earth to explain a perfect orbital fit of the Moon around the Sun.

I can think of no orientation of axes or vantage point that would make Earth undetectable in this way.

However, there is another key verification - Velocity.
"KEPLER’S SECOND LAW DESCRIBES THE WAY AN OBJECT’S SPEED VARIES ALONG ITS ORBIT
A planet’s orbital speed changes, depending on how far it is from the Sun. The closer a planet is to the Sun, the stronger the Sun’s gravitational pull on it, and the faster the planet moves. The farther it is from the Sun, the weaker the Sun’s gravitational pull, and the slower it moves in its orbit."
So, in a real elliptical orbit we should find that the velocity of the planet is decreasing smoothly as the farther it is from the Sun.
However, in this example, Due to the Moon/Earth orbital path, sometimes the moon orbits in the orbital Earth/sun direction, and sometimes on the opposite direction (I hope that you understand me correctly).
Therefore, we should find the moon is not smoothly increasing or decreasing its orbital velocity as it orbits around the sun.
So, we have two ways to verify if the Earth (or the VHP) is there.

They're actually the same way.  You variations are detectable despite any orientation of axes or vantage points.  So yes, there would be no way to hide the VHP if there was one.  Earth is not a VHP in that scenario.  It is a dark host mass.  It is a real mass, not a virtual one, and is dark, simply meaning we cannot see it.  For the moon or any other object to orbit an actual VHP would mean acceleration without any of the known forces to account for it.
So if scientists were to detect such regular motion, they'd know.  They detect this sort of motion for many stars, even when the motion is very subtle (less than the radius of the star), and use the motion to detect dark masses like gas giant planets.  Our own star exhibits this sort of motion about a host point, but its motion around it is not elliptical and thus really an orbit.  Sometimes the sun is incredibly close to its host point, and sometimes further away.  It's acceleration is not a function of its distance from that host point, and in the case of Keplerian orbit, it would be a function of that distance, per Kepler's 2nd law you quoted above which only applies to simple 2-body orbits.

One - By verify if there is variations (error) in the verified moon location with reference to the expected orbital elliptical cycle.
Two - By verify if there is none smoothly variations in the orbital velocity.

Same thing, since any variation in location or velocity would result in a variation of the other.

With regards to S2 - Even with the assumption that our vantage point is not perpendicular to the plane of S2's orbit, we clearly see that S2 Does not fulfill the two requirements.

You clearly see what you want to.  I don't see it at all, mostly because all I have is a lousy diagram and not actual data, but the perfect orbit path depicted hits every single one of the data points within the margin of error, meaning there many be deviation from that path, but said deviation is anything but clear.

Therefore, it shows that S2 must orbit around a VHP while this one might orbit the SMBH.

I told you how to clearly show that from the data set, or from a larger one.  You've not done that, so nothing has been shown.

There is one more key evidence for that:
Please look at the following diagram:
https://en.wikipedia.org/wiki/S2_(star)#/media/File:Galactic_centre_orbits.svg
We see several S stars that orbit around the SMBH.
I assume that our vantage point is not perpendicular to any of those S planes of orbit.
There is good chance that each orbital cycle plane might be different from all the other.
However, if we try to estimate the requested location of the SMBH for each cycle (based on kepler law), we should find that each one needs the SMBH at a different location in space.[/quote]
How so?  For it to appear be at one of the focus points of the elliptic paths, you need a perpendicular vantage point, and you admit that our vantage is anything but perpendicular.  The graph does not plot position, but rather ascension and declination, but you're interpreting the plot as position when presuming where the SMBH should be.

The graph is deceptive because they compare the appearance plot of these stars to a position plot of the orbit of several solar-system planets, none of which are presented as they appear to us, which would be nearly straight lines massively outside the narrow range of the diagram.

Anyway, have you ever watched elliptical motion from a non-perpendicular vantage point?  I have, at length even.  I had an entertaining screen saver that did just that, with a dozen objects in random orbits about a central mass, and each object left a trail behind it so the shape of the orbit was easy to see, and it looked exactly like that picture, except that your picture doesn't show where the motion is fast or slow, so you don't get a good feel for the actual point in the path where the approach to the center is closest.  S14 for instance is clearly closest on the far lower right of its path, not at the place where it goes behind the SMBH and appears to be in the same place.  It is a 2D plot of 3D motion, but you're interpreting it as 2D space when making these invalid claims.

Each one of them orbits around a VHP while all of those VHP orbits around the SMBH.
Why can't you agree with something which is so clear to us?

The moon's path around the sun is a wobbly ellipse.  None of those lines wobble.  Maybe they're simplified, but then they've hidden the evidence you seek.  I see nothing but clean ellipses depicted, so no VHPs.

[Dave Lev (OP)]

Quote
Therefore, I still don't understand why do you still support our scientists while they have clearly neglecting the variations of S2 locations from the expected perfect orbital cycle? They call those variations - Errors. But those variations are very important observations.
They've probably run a Fourier transform on the data and found no regular orbit to it.  That's why asked if you had done that.  You seem to be getting your data from pictures and conclusions written by somebody else, rather than from the actual measurements taken.  If you claim a pattern to the data, take the data and demonstrate it.

Our scientists can do it better.
Please look at fig 1.4 in pg. 20
Center of Mass at Offset Position
http://webdoc.sub.gwdg.de/ebook/dissts/Koeln/Mouawad2005.pdf
They claim clearly, that just based on the Red line they could set the Keplerian fit. Based on the Green line there is no fit.
However, they were also forced to shift the major axis in order to get the fit.
Please see pg 78 at Figure 7.6.
They specifically indicate that the shift in major axis was very critical to get the fit.
In the following examples the couldn't get the fit:
"Exemplary three non-fitting orbits. Example of 3 orbits with an error ≥ 5 σ corresponding to: (Left) the case of Western position, a fit with 3.3×106M point mass + 0.8×106M extended component (Middle) the case of Eastern position, a fit with 3.3×106M point mass + 0.4×106M extended component, and (Right) the case of Northern position, a fit with 2.7×106M point mass + 0.3×106M extended component."
Therefore, it is clear that without changing the position of the Major axis and specifically assume that it moves on the red line, there is no fit.
I don't have to prove it. It is written by our scientists.
So, how can we take an elliptical cycle and shift its major axis???
We know that our vantage point is not perpendicular to the plane of S2's orbit. But even if we try to place that elliptical cycle in space, there is no way to shift the major axis while we keep the shape of the elliptical cycle as is.
I have tried to do it without success.
This by itself proves that based on kepler there is no fit between S2 and the SMBH. Just after all those manipulations over manipulations they claim for a fit.
Sorry this is incorrect.
Why they so deeply insist for Fit???
Those none fits are more important than a fit.
The none fit gives us deep understanding about our galaxy.
It proves that S2 doesn't directly orbit around the SMBH.
That proves that there must be something between S2 and the SMBH.
In other words, S2 must orbit around some invisible object while that invisible object might orbit around the SMBH.
I call that invisible object a Virtual Host point - VHP.

  Gravity force is computed by GMm/r² and M is zero for a VHP, so the gravitational force exerted by a VHP is zero, and thus a VHP cannot pull a star into an orbital path by gravity.

I have never claimed that the VHP has Zero mass.
It all based on Multi star system, as you have explained:

Anyway, if you're talking only about the center of mass of multi-star solar systems, then this idea is not controversial.  Yes, that point exists, and the motions of the member stars does not move it one bit, but the point goes around the galaxy more or less as a unit.  The sun wiggles around its own point, with the point being inside the sun about half the time, and outside the other half.  The (quite predictable) path around that fixed point is anything but elliptical.  It resembles more of a scribble with no particular cycle to assign a period length.

I will explain it later on how it really works in the galaxy, and how that system can set all the unique features of the spiral galaxy without any need for dark matter.
Anyhow, it seems to me that you support our scientists by all means.
So, what ever I might offer and show, you have already took a discussion to support the current incorrect ideas for good.
Is it correct?

[Halc]

Our scientists can do it better.
Please look at fig 1.4 in pg. 20
Center of Mass at Offset Position
http://webdoc.sub.gwdg.de/ebook/dissts/Koeln/Mouawad2005.pdf
They claim clearly, that just based on the Red line they could set the Keplerian fit. Based on the Green line there is no fit.

Careful.  You make it sound like they're getting a Keplerian fit from looking at the red and green lines, but they're getting those fits from the data, and drawing the lines according to the fit.  You are doing it the opposite way.

Anyway, yes, the green line is an apparent better fit, and it plots a non-Keplerian orbit, which is to be expected since the center of the galaxy has far more than two bodies.  Keplerian orbits only occur with two body systems.
The title of the paper indicates that this is a study of mass distribution near the center of the galaxy, so of course it is going to be focusing on the deviations from that Keplerian orbit caused by the distribution of additional mass.

However, they were also forced to shift the major axis in order to get the fit.
Please see pg 78 at Figure 7.6.
They specifically indicate that the shift in major axis was very critical to get the fit.
In the following examples the couldn't get the fit:
"Exemplary three non-fitting orbits. Example of 3 orbits with an error ≥ 5 σ corresponding to: (Left) the case of Western position, a fit with 3.3×106M point mass + 0.8×106M extended component (Middle) the case of Eastern position, a fit with 3.3×106M point mass + 0.4×106M extended component, and (Right) the case of Northern position, a fit with 2.7×106M point mass + 0.3×106M extended component."
Therefore, it is clear that without changing the position of the Major axis and specifically assume that it moves on the red line, there is no fit.

There is no fit anyway.  I see three different attempts at a fit to the same data, each set apparently fitting a different subset of the measurements.  I don't see any assumption about assuming that a red line moves.

I don't have to prove it. It is written by our scientists.
So, how can we take an elliptical cycle and shift its major axis???

It isn't elliptical.  It wasn't expected to be, since it isn't a two body system.  The orbit of Uranus isn't elliptical, and measuring the deviations from a pure Keplerian orbit is exactly how they knew where to look for Neptune and eventually Pluto.  That's what they're doing in this paper is learning about the nature and density of other objects using the same techniques used to find additional planets.

We know that our vantage point is not perpendicular to the plane of S2's orbit. But even if we try to place that elliptical cycle in space, there is no way to shift the major axis while we keep the shape of the elliptical cycle as is.
I have tried to do it without success.

From just 2D point plots, it is actually quite effortless.  You can change the axis to almost anywhere you like.  From a 3D plot (one with temporal data), there is only one fit to the major axis.

This by itself proves that based on kepler there is no fit between S2 and the SMBH.

There is always a fit.  It is the line that most closely matches the data.  The fit need not match the actual path since that's not what a fit is.
That S2 does not perfectly follow a Keplerian orbit about the SMBH is expected.  It isn't a 2 body system.

Just after all those manipulations over manipulations they claim for a fit.
Sorry this is incorrect.
Why they so deeply insist for Fit???

It's them doing statistical analysis on the data.  It's what you do.  These guys know their statistics.

It proves that S2 doesn't directly orbit around the SMBH.

Depends on your definition of directly.  It doesn't orbit only the mass of the SMBH, yes.  There is other mass around which it orbits.  It is a crowded place down there.

That proves that there must be something between S2 and the SMBH.

Of course.  Why wouldn't there be??  This paper is trying to learn more about how much more something is between S2 and the SMBH, and the distribution of it, and not just prove that something is there.  It would be a far larger claim to say there was not something additional inside that orbit.

In other words, S2 must orbit around some invisible object while that invisible object might orbit around the SMBH.

That doesn't follow at all.  Just because Venus is inside our orbit doesn't mean we orbit it.  But Venus does make the orbit of the Earth/moon system non-Keplerian, just as we deviate the orbit of Venus despite not being inside its orbit.

I call that invisible object a Virtual Host point - VHP.

Oh, it's an object now. The story changes. How is it virtual if it's an object?  An invisible object is dark matter.

I have never claimed that the VHP has Zero mass.
It all based on Multi star system, as you have explained:

Our sun is not a multi-star system.  Such systems are quite common, but we're not one of them.
In a binary system, it is the gravity of the other object that pulls each object into a Keplerian orbit about the other.  The VHP (center of mass of the two) does not exert any force since it is massless.

If you story is now that the VHP has mass, then it is just a dark object and not at all the center of mass of any system.

I will explain it later on how it really works in the galaxy, and how that system can set all the unique features of the spiral galaxy without any need for dark matter.

You just posited dark matter being the unseen mass around which S2 orbits.  You just don't call it dark matter, but that's what it is: matter you can't see, and if S2 had such a secondary orbit, it would count as having been seen, just like all the other binary systems where only one of the two is luminous.

Anyhow, it seems to me that you support our scientists by all means.

They know how to do mathematics that is completely beyond my skill set.  You've displayed a need to review high-school mathematics, and sometimes even lower.  Your ideas work in your head because you don't have the mathematics skills to see the trivial violations with your assertions.

So, what ever I might offer and show, you have already took a discussion to support the current incorrect ideas for good.
Is it correct?

Not at all.  I'm just pointing out places where your idea doesn't hold water.  A new theory that works and makes falsifiable predictions would be warmly received.  But I've seen nothing but bad science from your postings: cherry picking data, drawing conclusions from diagrams that are not to scale instead of actual data, and complete denial of any evidence that counters your ideas.
If you want to get any attention, compute a curve of S2's path based on a VHP that matches the data points better than any the scientists have.  You'd need to find the period of the secondary orbit.  But none of the green non-Keplerian paths match a model with a secondary orbit.  You need to find that line.  Do the work, else you have zero evidence of the VHP thing.

I still have no idea why the VHP idea was necessary for the whole idea of matter being created at the SMBH and moving outward.  It seems that if it worked that way, it would work with or without everything needing a VHP.

[Dave Lev (OP)]

Please look at the following article:
http://en.es-static.us/upl/2018/03/S2-black-hole-orbit.png
We see clearly the orbital shape of S2 and some other S stars.
https://earthsky.org/space/star-s2-s0-2-single-milky-way-monster-black-hole
It is stated:
"Until now, it was thought that S0-2 might be a double star. Two stars orbiting each other would have complicated the upcoming gravity test
But a team of astronomers led by Devin Chu of Hilo, Hawaii – an astronomy grad student at UCLA – has found that S2 doesn’t have a companion"
The question is: Why our scientists consider that there are two orbiting stars?
Could it be that there is a difficulty to explain the orbital path of S2 just by one star?
Could it be that they also have thought on a possibility that based on the real verifications, S2 should orbit around some other object as I was expecting?
So, could it be that even our scientists understand that there is a problem with S2 orbital Path?

I still have no idea why the VHP idea was necessary for the whole idea of matter being created at the SMBH and moving outward.

You don't know, but it is clear to me that our scientists know why a companion star is needed!!!
As I was expecting:
There is no need for any real companion star (or object). The VHP by itself can give a perfect explanation for what we see.

It is also stated:
"[S2] orbits Sgr A* on an ellipse that takes about 15 years to complete. The diameter of its orbit is about 300 billion km [200 billion miles], which may sound like a lot, but we’re talking about a suppermassive black hole here! That’s close!
And it gets closer. Because the orbit is an ellipse, the star drops down to a mere 18 billion km [11 billion miles] from the black hole, a positively terrifying close approach. That’s only four times farther from the black hole than Neptune is from our sun."
I wonder if that information represents the S2 elliptical orbit cycle that we see.
It was stated that our vantage point is not perpendicular to the plane of S2's orbit.
So, what we see doesn't represent the real S2 orbital cycle.
Therefore, I would like to understand what we really see and what is the real orbital cycle (based on our understanding).
It was also stated that the major axis had been shifted to the left.
Unfortunately till now I couldn't understand how the Major axis could shift to the left while we see that S2 cycle set a nice Symmetrical elliptical shape.
So, our scientists must give us full information about the real S2 orbital cycle and how it is positioned in space in order to set the expected major axis shift in the nice elliptical cycle that we see.
This is very important information.

 

[Halc]

It is stated:
"Until now, it was thought that S0-2 might be a double star. Two stars orbiting each other would have complicated the upcoming gravity test
But a team of astronomers led by Devin Chu of Hilo, Hawaii – an astronomy grad student at UCLA – has found that S2 doesn’t have a companion"
The question is: Why our scientists consider that there are two orbiting stars?

That's kind of the default state.  Most stars come in pairs or larger groups.  The lone star like our own is in the minority.  So until verified one way or the other, a given star is likely to be in orbit about one or more companions.

Could it be that they also have thought on a possibility that based on the real verifications, S2 should orbit around some other object as I was expecting?

No.  The verification was finally done, and it turned up no other object.  S2 is by itself, or so says the article you quote.  Such a companion would have interfered with the smooth velocity change being measured, demonstrating relativistic red-shift.

As I was expecting:
There is no need for any real companion star (or object). The VHP by itself can give a perfect explanation for what we see.

1) We don't see this motion you claim.  2) A VHP by itself has no mass and cannot affect the path of a star.  It is the mass of one or more companion objects that makes a star's path have a semi-regular deviation from a clean path.  S2 does not have a clean path since it passes by many other objects during its 15 year circuit, but none of those objects orbit S2, and S2 does not orbit them.

It is also stated:
"[S2] orbits Sgr A* on an ellipse that takes about 15 years to complete. The diameter of its orbit is about 300 billion km [200 billion miles], which may sound like a lot, but we’re talking about a suppermassive black hole here! That’s close!
And it gets closer. Because the orbit is an ellipse, the star drops down to a mere 18 billion km [11 billion miles] from the black hole, a positively terrifying close approach. That’s only four times farther from the black hole than Neptune is from our sun."
I wonder if that information represents the S2 elliptical orbit cycle that we see.

If you're asking if that information describes the elliptical path we see from our vantage, then yes.

It was stated that our vantage point is not perpendicular to the plane of S2's orbit.

I think I said that, yes.  The article didn't bother to mention that.  We're not perpendicular to any of the orbits plotted in that picture, but we seem to be nearly edge-on to at least one of them (S14).

So, what we see doesn't represent the real S2 orbital cycle.

That we don't have a perpendicular vantage doesn't mean it isn't real.  Venus's orbit (or that of any of the planets for that matter) hardly looks like an ellipse from our vantage, but it is in fact nearly circular.  We very much can see its real orbital cycle without need for a perpendicular vantage.

It was also stated that the major axis had been shifted to the left.

OK.  To be expected.  It is precessing, even more so due to the relativistic component of its orbit.  Even Earth does this.

Unfortunately till now I couldn't understand how the Major axis could shift to the left while we see that S2 cycle set a nice Symmetrical elliptical shape.

It isn't a nice symmetrical ellipse.  You saw them trying to fit different curves to the data.  None of them was exact.  It is passing objects that deflect its path, as expected.  But the axis shift is probably more from precession than it is from random deflections from non-orbiting masses.

[Dave Lev (OP)]

So, what we see doesn't represent the real S2 orbital cycle.

That we don't have a perpendicular vantage doesn't mean it isn't real.  Venus's orbit (or that of any of the planets for that matter) hardly looks like an ellipse from our vantage, but it is in fact nearly circular.  We very much can see its real orbital cycle without need for a perpendicular vantage.

You do not answer the question!
What is the real Orbital cycle shape of S2???
What do you mean by: "We very much can see its real orbital cycle without need for a perpendicular vantage."
So, do you mean that what we see is almost the real orbital cycle of S2?
How can you set any sort of calculation on something that is almost correct?

OK.  To be expected.  It is precessing, even more so due to the relativistic component of its orbit.  Even Earth does this.
It isn't a nice symmetrical ellipse.  You saw them trying to fit different curves to the data.  None of them was exact.  It is passing objects that deflect its path, as expected.  But the axis shift is probably more from precession than it is from random deflections from non-orbiting masses.

The major axis shift is very dramatically.
How can you compare it to Earth?
Our scientists have to find the center of mass based on the orbital cycle of S2 (by ignoring the SMBH) and then find how far is it from the SMBH.
Than they have to prove by calculation, that without any need for a perpendicular vantage, we can move the calculated center to the location of the SMBH.
Sorry - you try to offer a solution to a problem without any real calculation.
I would expect from our scientists to offer real solution.

2) A VHP by itself has no mass and cannot affect the path of a star.  It is the mass of one or more companion objects that makes a star's path have a semi-regular deviation from a clean path.  S2 does not have a clean path since it passes by many other objects during its 15 year circuit, but none of those objects orbit S2, and S2 does not orbit them.

After all of our discussion, it seems that you have no clue what is the real meaning of the VHP.
So, let me explain it again for you:
The VHP is the center of mass for a star in a multi mega star system
Each star has a unique VHP.
As you have already explained:
"Anyway, if you're talking only about the center of mass of multi-star solar systems, then this idea is not controversial.  Yes, that point exists, and the motions of the member stars does not move it one bit, but the point goes around the galaxy more or less as a unit.  The sun wiggles around its own point, with the point being inside the sun about half the time, and outside the other half.  The (quite predictable) path around that fixed point is anything but elliptical.  It resembles more of a scribble with no particular cycle to assign a period length."
So, the VHP is a virtual point which represents the center of mass of multi star system.
There is no real object there.
But it is a virtual point in space which which is used as the center of mass for a specific star.
Therefore, each star in the galaxy (which is under a Multi star system) must have a unique VHP for itself.
Back to S2:
S2 orbital cycle is directly affected by the nearby multi star system.
Therefore, S2 must orbit around its unique VHP, while this VHP might orbit around the center of the galaxy or the SMBH.
Why is it so difficult for you to understand my simple message?
You can accept it or reject it.
But please, try to understand my explanation.
If you understand the explanation, let's see if it is feasible:
You claim that :
"S2 does not have a clean path since it passes by many other objects during its 15 year circuit, but none of those objects orbit S2, and S2 does not orbit them."
How can we verify if S2 orbits around other objects?
When we normally discuss about a multi star system - we mainly think about two, three, four...or maximal 16 stars.
If that was the case for S2, than we could easily find the other stars in the Multi star system.
However, in the center there are much more than few stars or even few thousands of stars.
Therefore, each S stars that we see must orbit around a unique VHP, while this VHP orbits according to the Multi Mega star system.
So, that multi mega star system is affected by all the nearby stars, by the SMBH and even by the 3KPC RING!!!
Yes, I do believe that this ring also has an important impact on the orbital cycles of the stars in the center.
Therefore, if we take in account all the gravities impacts we should find that S2 orbits perfectly around the impact of all the gravities and that there is no need for any dark matter.
Each S star orbits perfectly based only on real mass.
It is clear to me that you disagree with my explanation.
So, please - there is no need to argue about it.
The key point for me is to deliver the message about the VHP.
I hope that by now you understand what I mean by that word - VHP.

[Dave Lev (OP)]

Halo is a perfect example for the Multi mega star system:
https://scitechdaily.com/astronomers-make-shocking-discovery-about-stars-around-the-milky-way/
"These halo stars are grouped together in giant structures that orbit the center of our galaxy, above and below the flat disk of the Milky Way."
So, what kind of force keeps them together? How many stars there are in those giant structures?
It is clear to me that they all group together due to internal gravity force.
So, based on multi mega star system (as halo stars), each star must orbit around all the other stars, but it is impossible to verify a single orbit around a specific star or group of stars.
Therefore, if we will try to trace one star there, we will not be able to see that it orbits any other star (or group).
In the same token, S2 orbits due to the impact of all the mass in the center - (Multi mega stars system or giant structures), while we will not be able to verify that it actually orbits around any specific stars.

We call those giant star structures as halo stars because they have ejected from the disc of the spiral arm.
Actually, as long as they are in the disc, they must be connected to one of the spiral arms.
Let's look again at the Milky way diagram:
https://en.wikipedia.org/wiki/Milky_Way#/media/File:Milky_Way_Arms.svg
We see clearly that at the end of each spiral arm there are many points. It looks as a broken chain.
I assume that in each point of the chain there are Millions of stars.
Those millions of stars are grouped together due to gravity.
Each point in this chain set a local giant gravity.
Please look at the last chain in each arm.
This last chain holds itself to the one in front by gravity force.
As long as it is connected to the arm, it is part of the arm, It stays at the galactic disc plane and it follows the orbital path of the spiral arm.
However, it will not have the power to hold itself for long time.
The orbital velocity at that point is too high for the balanced gravity force in that last point of giant star structure.
Sooner or later, this last point in the chain will have to be disconnected from the arm.
However, once it is ejected from the arm, it is also ejected from the disc plane.
So, S2 which had been created at the core of the molecular cloud at the center of the galaxy must drift outwards over time.
One day S2 will arrive to the same radius from the center as the solar system.
At that time, our sun might get to the last point in the arm orbital chain.
Then, we will be ejected from the arm and be part of the Halo stars....

[Halc]

You do not answer the question!
What is the real Orbital cycle shape of S2???

Something approximated by an ellipse, about 970 AU long and around 450 wide.  That's the actual shape, not what it looks like from here.  Like all orbits, it precesses, so it doesn't trace the exact same path each time around, even without other objects perturbing it.

What do you mean by: "We very much can see its real orbital cycle without need for a perpendicular vantage."

I was talking about the orbit of Venus, which looks, from our vantage, like an almost flat ellipse with the sun nowhere near either foci.  That orbit is quite real, and yes, we see it, so if you mean something else when you ask if we see the real orbit, I don't get your question.
The image of S2 is delayed by over 25000 years, so in that sense it isn't real.  Maybe the thing has since been eaten and isn't real at all anymore.  Betelgeuse has the same problem.  Never sure if it is really there or we're just seeing an afterimage of a nonexistent star.

How can you set any sort of calculation on something that is almost correct?

Tell that to the weather prediction guys.  To be completely correct, you need a full description of its state.

The major axis shift is very dramatically.
How can you compare it to Earth?

Earth orbit is nearly circular.  OK, S2 is not as eccentric as say a comet, but it also has a relativistic orbit, and that might effect major axis shift.  I don't know how to compute that.  I know that relativity very much plays a role because they never were able to predict Mercury's orbit until all GR effects were accounted for.
S2 is also passing random objects, any of which can send it onto a new trajectory, a different ellipse.  That seems to happen multiple times per orbit, as shown by some of the pages you've been linking.

Our scientists have to find the center of mass based on the orbital cycle of S2 (by ignoring the SMBH) and then find how far is it from the SMBH.

Sorry, but I cannot figure out this statement.  What center of mass are they seeking?  S2?  Sgr-A?  Something else?  S2's CoM is where S2 is.  Ditto for Sgr-A.  Neither seems to be a binary object.

Sorry - you try to offer a solution to a problem without any real calculation.

Not sure what I was asked to calculate.  I certainly don't see any calculations from you, the guy who expects a different idea to be taken seriously.

After all of our discussion, it seems that you have no clue what is the real meaning of the VHP.
So, let me explain it again for you:
The VHP is the center of mass for a star in a multi mega star system
Each star has a unique VHP.

Why wouldn't all the stars in said mega-star system have the same VHP?  How does any particular star know which stars to include in the VHP calculation and which to leave off?  Our sun for instance has stars visible in every direction.  So how might I begin to guess which of those contribute to the VHP and which do not?  Most importantly, why would you expect motion about this VHP to be anything resembling something close to a familiar elliptic orbit?

Anyway, I don't deny that our star is potentially part of a group, and that the group sort of travels as a clump in a cleaner path than any individual mass.  I just don't think our motion within that group can be characterized as being in orbit around the group's center of mass or any other virtual point.  That only works for 2 body systems, not larger ones.
For even a simple 3-body system, barring symmetrical arrangements, none of the three biodies will accelerate towards the common center of mass.  In the most simple case of 3 equal masses with unequal spacing in a line, the middle mass will accelerate away from the common center of mass.  You seem to realize none of this.

The only VHP I see is the center of the galaxy.  We also are influenced by the disk, but forces from a disk are not characterized by an orbit.  The force of the disk actually grows with distance (to a point at least), unlike the force from a given point mass.  I think the disk force contributes to that 62 million year cycle thing, but I'm no expert.
The in/out motion you showed in one of your pictures might be due to the solar system having an eccentric orbit about the galactic center. It would have a ~200 million year period if it was that. Few objects seem to have really low eccentricity trajectories.

So, the VHP is a virtual point which represents the center of mass of multi star system.

I've already accepted this general idea, but in general, all stars in that group have essentially the same VHP then.

There is no real object there.
But it is a virtual point in space which which is used as the center of mass for a specific star.

It is the center of mass for all the stars in the set.  The center of mass for a specific star is the star itself.
You really need to choose whether you're talking about a virtual center of mass of a set of multiple objects, or the center of mass of a particular object, which tends to be the middle of said object.

Therefore, each star in the galaxy (which is under a Multi star system) must have a unique VHP for itself.

Yes, called its location.  That point isn't virtual, since the star is there.
Venus's center of mass is at its center, but Venus loosely orbits the center of mass of the solar system, and more accurately orbits the sun itself, but still not a perfect orbit around it.  No object's path can be accurately described by a clean orbit about a VHP which in turn orbits either the solar system or the sun.

Back to S2:
S2 orbital cycle is directly affected by the nearby multi star system.

What multi-star systems would that be?  There are other stars in that area, but none seem to form a system with S2, and nobody knows how many of these nearby objects are part of multi-object systems (stay with each other in their primary orbit).

Therefore, S2 must orbit around its unique VHP, while this VHP might orbit around the center of the galaxy or the SMBH.

They've actually eliminated this option as a possiblility.

Your logic is horrible.  S2 is affected by other masses, therefore it must orbit something other than its primary (the SMBH).  That simply doesn't follow.  Venus, for example, is affected by other masses (I cannot think of a mass that doesn't affect it), but it does not orbit any VHP.

Why is it so difficult for you to understand my simple message?
You can accept it or reject it.

I understand the message, but since it is based on nonsense, I cannot accept it.

How can we verify if S2 orbits around other objects?

I already told you this.  It would have a period to that orbit.  Orbits have periods.  Do the math that detects regular periods in the data. Making baseless assertions is not the way to go about it.

When we normally discuss about a multi star system - we mainly think about two, three, four...or maximal 16 stars.

I can think of much larger systems than that.

If that was the case for S2, than we could easily find the other stars in the Multi star system.
However, in the center there are much more than few stars or even few thousands of stars.
Therefore, each S stars that we see must orbit around a unique VHP, while this VHP orbits according to the Multi Mega star system.
So, that multi mega star system is affected by all the nearby stars, by the SMBH and even by the 3KPC RING!!!

Yes, all of this stuff has an effect, but none of it is a system that orbits as a unit, else all the other objects in the system would have the same 16 year period around Sgr-A, but we don't see that.  We see not one other object travelling with S2, else S2 would have a regular perturbation to its orbit.  You keep asserting a pattern that just isn't being seen.  Not saying it isn't possible, just that it isn't the case with this particular star.

Yes, I do believe that this ring also has an important impact on the orbital cycles of the stars in the center.

What impact would that be?  I mean, I agree there is one, but I suspect you haven't thought it through.  What impact would a ring have on Earth's orbit for instance?  Suppose it is out at the asteroid belt, but having the same mass in relation to the sun as the galactic ring does to our SMBH.  Our actual asteroid belt has almost no mass compared to the sun, so we'd need to imagine a more massive one.

Therefore, if we take in account all the gravities impacts we should find that S2 orbits perfectly around the impact of all the gravities and that there is no need for any dark matter.

But you haven't taken anything into account. You just imagine that if you did, this S2 orbit (and that of our own solar system for that matter) would fit. Imagining it isn't evidence at all.  You need to actually do the work and show how your idea makes the data fit better than the misguided ideas of all the professional astronomers who have to posit objects that cannot be seen in order to get the numbers to work.

[Halc]

Halo is a perfect example for the Multi mega star system:
https://scitechdaily.com/astronomers-make-shocking-discovery-about-stars-around-the-milky-way/
"These halo stars are grouped together in giant structures that orbit the center of our galaxy, above and below the flat disk of the Milky Way."
So, what kind of force keeps them together? How many stars there are in those giant structures?

The article doesn't say if they're kept together or still spreading apart or whatever.  It doesn't give a count either, but I'm sure the count depends heavily on what sort of object counts as a star and what doesn't.  There's not exactly a clean line defining that.

It is clear to me that they all group together due to internal gravity force.

If they stay together, then yes, gravity seems a lot more plausible than rubber bands or something.

So, based on multi mega star system (as halo stars), each star must orbit around all the other stars

Yet again, that doesn't follow.  Each star may tend to stay with the group, but it may also be ejected by chance.  The motion within the group is not necessarily anything that resembles the elliptical path of an orbit.

In the same token, S2 orbits due to the impact of all the mass in the center - (Multi mega stars system or giant structures), while we will not be able to verify that it actually orbits around any specific stars.

They've verified that it doesn't orbit any other specific stars.

We call those giant star structures as halo stars because they have ejected from the disc of the spiral arm.
Actually, as long as they are in the disc, they must be connected to one of the spiral arms.

Structures between the arms are still in the disk, so this is false.

Let's look again at the Milky way diagram:
https://en.wikipedia.org/wiki/Milky_Way#/media/File:Milky_Way_Arms.svg
We see clearly that at the end of each spiral arm there are many points. It looks as a broken chain.

Those broken lines are extrapolated arms, places that we cannot see at all.  They're not broken, but they're guesses as to what's there.  It is reasonable to assume the arms continue through the regions unseen, just like we can see in other galaxies.

Please look at the last chain in each arm.
This last chain holds itself to the one in front by gravity force.

I'm sorry, but you're asking me to consider gravity of a 'can't see it' designation on a diagram.  This makes no sense.  Those are not real clumps of stars that have been observed like that.  Read the text accompanying the diagram.

As long as it is connected to the arm, it is part of the arm, It stays at the galactic disc plane and it follows the orbital path of the spiral arm.

You're treating arms as objects, not as what they probably are, which is waves.  The arms do not move with the stars, else they'd have been smeared out a long time ago.  Our sun (and any star) is connected to no arm, and moves from one to the next as it orbits the galaxy at an entirely different rate than the apparent motion of the density waves that form the arms.

So, S2 which had been created at the core of the molecular cloud at the center of the galaxy must drift outwards over time.
One day S2 will arrive to the same radius from the center as the solar system.

It is a big star and even assuming it will drift like that, it will burn out long before it gets anywhere.  The big stars nearby (e.g. Betelgeuse) similarly could not have come from the center since they're far too young to have made the trip.  Either that or the big stars must drift outward at an incredible pace, making one wonder why S2 isn't getting any further away with each orbit.

Not claiming to know the answer myself.  The bar is a known stellar nursery, but I don't understand the dynamics of the bar.  S2 seems not to be part of that because it doesn't fall in that rotation curve of the galaxy that we were looking at.  I don't know anyone that can explain that curve and how it fits with named objects like S2.

[Dave Lev (OP)]

The bar is a known stellar nursery, but I don't understand the dynamics of the bar.

You don't know, but I know it for sure.
The center of the galaxy is the stellar nursery for most (or even all) the stars in the galaxy/Universe!!!
A star can be created ONLY in a Molecular gas cloud which orbiting around/near a massive object as a SMBH.
So, 99.9..9% of the stars in the Milky way galaxy had been created in that stellar nursery.
Each star have got all its Planets and moons in it's first day.
Therefore, the age of the Earth & Moon is identical to the age of our Sun.
All the objects in the Solar system had been created from the same matter at the same day.
The Earth and the Moon had been also created as a compact molecular gas object.
Their mass in the first day was heavier by more than 98 times than it is today.
The planets and moons in the solar system have got all the Water supply in their first day from the molecular gas cloud.
Over time, due to their compact size, they have lost most of the gas as Hydrogen and became rocky objects.
There was a time when water flows at the surface of Mars.
At that time, Mars was orbitting the Sun at the same radius as we are today and the Earth was much closer to the Sun while it's temp was quite higher.

The big stars nearby (e.g. Betelgeuse) similarly could not have come from the center since they're far too young to have made the trip.

As I have stated, all the stars (Yes - including Betelgeuse) had been formed at the center of the Milky Way galaxy.
Betelgeuse isn't a young star. It is as old as our sun.
You have a severe misunderstanding about the age of the stars in the galaxy.
We could set the calculation how long it might take to a star to drift from the center of the galaxy all the way to our current location.
Therefore, all the stars in the center are young stars.
As we move outwards, the stars get older.
So, there is a severe error in the way that our scientists estimate the age of the stars in the galaxy.

If they stay together, then yes, gravity seems a lot more plausible than rubber bands or something.

Thanks
Gravity keeps all the stars in the Halo stellar. In the same token, gravity keeps all the stars in spiral arms.

You're treating arms as objects, not as what they probably are, which is waves.

Yes, spiral arms are objects. All the stars in the arm are connected to each other by gravity force. The same gravity force which keeps the stars at the halo stellar also keeps the stars at the spiral arms.
However, as I have stated before, there are bridges and branches between the Arms.
Therefore, stars can migrate from arm to arm by those bridges and branches.
We can think about an arm as a highway while there are bridges between the arms.

Each star may tend to stay with the group, but it may also be ejected by chance.

That is correct!
As long as the star stay at the arm or cross to the next arm by bridge, it will save its location in the galactic disc.
However, if it will dare to move away from the arm or the bridge, it will be ejected as a rocket from the galactic disc for good.
Nothing can come back to the arm or the galactic disc.

why S2 isn't getting any further away with each orbit.

Yes, it is!
However, it is very difficult to monitor that drifting outwards.
S2 orbits around its unique VHP. (It is a host point - sorry if I used before the idea of center of mass).
So, S2 set a very clean orbit around its VHP while it increases its radius by only few cm or few m. per cycle.
However, this represents the S2 orbit around its orbital motion.
Let's look again at the following diagram of the Sun Motion:
http://www.biocab.org/Motions_of_the_Solar_System.jpg
In the same token, S2 apparent motion (blue dot points) orbits around its orbital motion (gray dashed line).
Please, you don't have to agree with that, just try to understand my message.
So, S2 orbits around a first level of VHP (let's call it VHP1) and set that nice apparent motion (Blue dot point)
Therefore, when we trace S2, we see that it doesn't move exactly on its orbital cycle:
http://www.phy6.org/stargaze/Kep3laws.htm
However, for this big orbital cycle (15 years), there is second level of VHP (Let's call it VHP2).
Therefore, if we assume that In each cycle, VHP1 drifts from VHP2 by few Km per cycle, than VHP2 drifts away from the SMBH by much more than that per cycle.
So far we have mainly discuss on this VHP (VHP2) but we have ignored the first VHP level (VHP1).
So, any star in the galaxy must orbit around a VHP1 which follows with him anywhere from its first day one in the Universe.
Therefore, when we look at the nearby stars, we shouldn't trace the physical location of the stars, but we must monitor the virtual locations of their VHP1.
If we do so, we should see that the distances between all the nearby VHP1' stars in the Orion arm are absolutely fixed!!!
So, all the VHP1 of the stars in the Sun' nearby area are moving exactly at the same velocity!!!
Therefore, no one is moving away from the arm!

[Dave Lev (OP)]

What is the real Orbital cycle shape of S2???

Something approximated by an ellipse, about 970 AU long and around 450 wide.  That's the actual shape, not what it looks like from here.

Thanks!
So, the ratio between the major axis to the shorter axis is about 1:2
I have just found a fantastic article:
https://www.slideshare.net/NUCLIO-PT/development-and-implementation-of-student-activity-to-find-mass-of-black-hole-by-naoki-matsumoto
Please look at at slide pg. 18
It is stated that the orbital inclination angle as viewed from the Earth of S2 is 45 degree. While after the correction to 90 degree we get the final results at the attached image.
However, it is quite clear to any first year student that the SgrA* (SMBH) can't be used as the host for this orbital cycle. No way!!!
Now, please look at slide in pg 20.
The calculated Periastron date is year 2002.25 + 0.05 = 2002.3
The calculated Apastoron date is year 1994.62
The full one orbital cycle Is:
P = 15.4 Year.
Based on that data, they have found the mass of the host should be (in pg 22)
3.4 * 10^6 Sun Mass.
So far so good.
I fully agree with this calculation!
However, they also claim that after the adjustment (which they do not explain), The estimated value of the SMBH mass is
SMBH = 4.1 * 10 ^6 Sun mass.
That is a severe mistake!!!
As I have stated, S2 does not orbit around the SMBH.
S2 orbits around its VPH1 which orbits around VHP2 which orbits around the SMBH (assuming that there are no more stages in between).
Therefore:
VHP2 (of S2) = 3.4 * 10^6 Sun Mass.
Now, we have to find the exact relationship between VHP2 and SMBH.
First, based on Kepler, we have to find the perfect location of VHP2 in that S2 orbital cycle of 15.4 years.
It is clear to me that it should be located high above the current location of the SMBH.
Than we have to find how long it takes to VHP2 to set one full cycle around the SMBH and the cycle shape (VHP2' Periastron and  Apastoron)
Just after getting this information we can extract the real value of SMBH.

There is a solid prove for my explanation.
Please look at the following article:
https://alchetron.com/S2-(star)#demo
https://alchetron.com/S2-(star)
If we look carefully, we should see that S2 doesn't set a full nice cycle. At the top of this image we clearly see that there is a shift in the orbital cycle (as an open loop).
This shift is a direct outcome of the orbital motion of VHP2 around the SMBH.
Therefore, The SMBH can stay in its place while VHP2 (of S2) orbits around it and set the same famous orbital motion as the Sun does.
Please look again at the following image:
http://www.biocab.org/Motions_of_the_Solar_System.jpg
Hence, S2 will never ever close one full cycle. It moves forwards due to the orbital motion of VHP2 around the SMBH and set some sort of open loop.
Based on this small shift we should find the orbital velocity of VHP2 around the SMBH.
This might help us to estimate the size of this orbital cycle and extract the real value of the SMBH.

[Halc]

Please look at at slide pg. 18
It is stated that the orbital inclination angle as viewed from the Earth of S2 is 45 degree. While after the correction to 90 degree we get the final results at the attached image.
However, it is quite clear to any first year student that the SgrA* (SMBH) can't be used as the host for this orbital cycle. No way!!!

I agree.  The rotation was not done on the correct axis, since if it was done correctly, SgrA would have been at the focus. 

Now, please look at slide in pg 20.
The calculated Periastron date is year 2002.25 + 0.05 = 2002.3
The calculated Apastoron date is year 1994.62
The full one orbital cycle Is:
P = 15.4 Year.
Based on that data, they have found the mass of the host should be (in pg 22)
3.4 * 10^6 Sun Mass.

Mass of host cannot be determined from just orbital period.  Jupiter has a sort of similar orbital period and yet orbits something of far less mass.  Anyway, yes, they measured the time for half an orbit and figured that the other half takes similar time.  Don't need to be a genius to figure that one out.

I fully agree with this calculation!

They didn't show their work.  There is a reference to a 'equation 4'.  The only math done on that slide is a conversion of units.

As I have stated, S2 does not orbit around the SMBH.
S2 orbits around its VPH1 which orbits around VHP2 which orbits around the SMBH (assuming that there are no more stages in between).
Therefore:
VHP2 (of S2) = 3.4 * 10^6 Sun Mass.

Therefore, if we take in account all the gravities impacts we should find that S2 orbits perfectly around the impact of all the gravities and that there is no need for any dark matter.

You just posited a VHP2 of mass similar to SgrA, which is a serious boat load of dark matter.  You are contradicting yourself.
I think they would notice if S2 was orbiting a second object that massive, but you seem to have other ideas.  How far away is VHP1 from this VHP2?  What period?

Now, we have to find the exact relationship between VHP2 and SMBH.

They're nearly the same mass and should be orbiting each other.  Other objects should be orbiting the combined mass of the two.

First, based on Kepler

You can't really quote Kepler.  You've denied his laws completely in the prior post, and Kepler's laws only apply to two-body systems and that isn't the case here.

we have to find the perfect location of VHP2 in that S2 orbital cycle of 15.4 years.
It is clear to me that it should be located high above the current location of the SMBH.

Which direction is 'high above'?  There's not exactly a clear direction that is 'above' out there.
You're just talking about a distance?  How much is 'high above' then?  How is SgrA not high above this VHP2, since it is so massive?  How far is VHP1 from VHP2?

There is a solid prove for my explanation.

Do you have even the slightest idea what constitutes evidence, let alone proof?

Please look at the following article:
https://alchetron.com/S2-(star)#demo
https://alchetron.com/S2-(star)

2nd link is dead.

If we look carefully, we should see that S2 doesn't set a full nice cycle. At the top of this image we clearly see that there is a shift in the orbital cycle (as an open loop).[/quote]
Yes.  Nobody claimed its motion is Keplerian, and this orbit also has a significant relativistic component.

This shift is a direct outcome of the orbital motion of VHP2 around the SMBH.

So you assert, but where's the proof of that?  You claimed there was a proof somewhere in it.

Please look again at the following image:
http://www.biocab.org/Motions_of_the_Solar_System.jpg

This image in no way reflects reality.  Nothing is to scale and the periods depicted do not reflect measured values.
Best I can tell from research, the 5-7 km/sec component has that 62 million year cycle (up and down about 3 times per trip around the galaxy, due to disk effects), and the 20 km/sec motion is one cycle per orbit, due to our eccentricity.  The blue dotted line is almost parallel with the grey line if it was drawn more correctly.

If we actually followed the blue dotted line as depicted (which is about 9x the length of the grey dashed line) and the 217 km/sec motion of the VHP was accurate, the sun would be moving at about 2000 km/sec, well above the escape velocity of the galaxy.  We'd just permanently shoot away.

Hence, S2 will never ever close one full cycle. It moves forwards due to the orbital motion of VHP2 around the SMBH and set some sort of open loop.

I cannot figure out what you mean to convey with this description.

[Dave Lev (OP)]

As I have stated, S2 does not orbit around the SMBH.
S2 orbits around its VPH1 which orbits around VHP2 which orbits around the SMBH (assuming that there are no more stages in between).
Therefore:
VHP2 (of S2) = 3.4 * 10^6 Sun Mass.

Therefore, if we take in account all the gravities impacts we should find that S2 orbits perfectly around the impact of all the gravities and that there is no need for any dark matter.
You just posited a VHP2 of mass similar to SgrA, which is a serious boat load of dark matter.  You are contradicting yourself.
I think they would notice if S2 was orbiting a second object that massive, but you seem to have other ideas.  How far away is VHP1 from this VHP2?  What period?

Now, we have to find the exact relationship between VHP2 and SMBH.

They're nearly the same mass and should be orbiting each other.  Other objects should be orbiting the combined mass of the two.

Dear Halc
After all our discussion, it seems to me that you still don't understand the real meaning of VHP.
Please, you don't have to agree with my explanation - but you have to understand my message.
So, let me explain it one more time for you:
1. VHP = Virtual Host Point
2. VHP is not a real object. It is a virtual object.
3. VHP1 - As I have already stated - ALL stars in the galaxy had been formed in a gas cloud near the SMBH. Each new born star must orbit around a virtual host point (VHP1) in the gas cloud in order to crystallize from molecular gas into real Star.
Therefore, the first level of virtual point (VHP1) is some sort of a gift which had been given to any star in the galaxy from the gas cloud in his first day. Hence, once the Star is out from the gas cloud its physical location is not relevant. We have to focus only on the Virtual point of his host (VPH1). Each star in the galaxy has a unique VHP1. This VHP1 goes with it anywhere it goes.
4. VHP can work over VHP. For example - The Moon orbits around the Earth, while The Earth orbits around the Sun. (Technically, the center of the Earth/Moon orbits around the Sun, but for this discussion, we can assume that the Earth orbits around the Sun. So, we see two levels or orbital cycles. In the same token - S2 orbits around VHP1, while this VHP1 orbits around another virtual host which is called VHP2. This VHP2 can technically orbits around other level of virtual host point - VHP3... and so on...
Therefore, if we focus on those Virtual points, we won't find any real object or any dark matter. All of them are virtual points. However, each Virtual Host Point represents mass. We can calculate the estimated mass of each VHP directly from the star mass and its orbital movement.
5. Dark matter - There is no dark matter and there is no need for dark matter. It is a pure fiction due to the simple outcome that our scientists have failed to understand how gravity really works at the galaxy.
6. Planets and Moons - They are all "by products" due to the process of  "new star creation" in the gas cloud. I can explain it later on if you wish. In any case, by definition - Each star in the galaxy gets also planets and moons as another gift from the gas cloud.

Final conclusion:
When we try to look at any nearby star, we shouldn't focus only on its real location and its mass. We have to focus on the location of its VHP1. Hence, by monitoring the movement of each star (physical location) in the galaxy, we can extract the location of its VHP1 and calculate its host mass (based on orbital cycle of the star and its mass).
From now on, this virtual host point and the calculated mass represents the first level of the orbital cycle of any real star in the galaxy. This is the most critical issue in the galaxy!!!
The shape of spiral galaxy is a direct product of VHP1 which is based on real object.

Is that all clear to you?
Please, let me know if you understand the message. Again, you don't have to agree with that. Just let me know if finely you understand the real meaning of VHP.

   

[Dave Lev (OP)]

Take 3 equal masses distributed in a triangle of sides 3, 5, and 7.  From that, you can find the center of mass of the three which is the same for all three of them.  We can call this VHPc.  In addition, each object X Y and Z has a sort of VHP that is halfway between the other two objects

That is good example.
So, it seems that you understand the meaning of VHP.
However, instead of three object, we must think on thousand, Millions or even billions objects.
Not just stars, but also gas clouds, SMBH and any other real object.
There is no dark matter in the galaxy.
This is a pure science fiction.
Our scientists had failed to understand how spiral galaxy really works, therefore, they came with this none realistic idea.
Based on the VHP idea we can get the spiral galaxy shape without any need for dark matter.

The motion of none of the objects (I have not given their velocities) cannot be modeled by any number of tiered VHP's, at least not according to Newtonian physics.

I disagree with that statement.
VHP over VHP is the key element in spiral galaxy which set the structure of spiral arm.
Please look again at the following image:
https://en.wikipedia.org/wiki/Milky_Way#/media/File:Milky_Way_Arms.svg
Please focus on the last chain point in the red spiral Arm (for example)
In this last chain point there might be thousands or millions stars.
As long as it is connected to the chain point in front, it will follow the orbital momentum of the spiral arm.
However, once it disconnected from the point in front, it will soon drift away from the disc plane.
Our scientists, ignore completely the meaning of the disc plane.
They think that this last chain point (with all the millions objects) orbits around the whole mass inwards the orbital cycle of that point. They have found that the real mass in the galaxy can't support its orbital velocity.  Therefore, they have got into conclusion that dark matter is needed.
As explained in the following:
https://www.quora.com/How-is-the-motion-of-stars-similar-to-the-motion-of-the-sun
"The stars don't reduce in orbital velocity as much as they should be doing... unless there's more mass than we can see.  Behold: meet the mysterious dark matter that must be responsible for this.  More mass due to dark matter can explain that."
That of course is a fatal mistake.
They actually ignore completely the disc plane.
Why suddenly at the end of the spiral arm the stars do not stay any more at the galactic disc?
in that article they show the different orbital cycles:
Disc star orbital - Yellow
Halo star orbits - Green
Bulge star orbits - Red.
So, only the Yellow represents the orbital star at the disc plane.
The dark matter can't give a clear explanation for that phenomenon.
Why suddenly at the end of spiral arms, the stars starts to orbits high above and below the disc (higher than the estimated disc width of about 1KLY.)
So, let me explain how it really works.
Let's assume that in this point there are 10,000 stars.
We see clearly that those stars are connected to each other.
Gravity force is the only force that can keep them all together.
In this activity, they all set a VHP which represents the center of mass of all this last chain point.
Let's call it VHP - m1 (m1 represents the total mass in the last chain point).
Now, for each point in this chain there must be also a represented total mass.
So, the one in front will be called - m2, the other one in front will be called m3 and so no.
Hence, we can see a long chain of points that are connected to each other.
m1 is connected to m2.
m2 is connected to m3.
m3 is connected to m4
mn is connected to mn+1.

However, when I say connected I mean gravity force.
In order to set a constant gravity force we must set an orbital cycle.
So, we actually have the following:
VHP m1 orbits around VHP m2.
VHP m2 orbits around VHP m3
VHP mn orbits around VHP mn+1
However, how could it be that we don't see any orbital cycle?
Because, the orbital velocity of VHP m1 around  VHP m2 is (almost) identical to the orbital velocity of VHP m2 around the galaxy.
Therefore, the orbital velocity of VHP mn around  VHP mn+1 is (almost) identical to the orbital velocity of VHP mn+1 around the galaxy.
I specifically say almost identical, as there is a room for this point to drift outwards. (As I have already explained - in real orbital cycles - orbital objects drift outwards from their host)
This is the basic idea of spiral arm and how VHP works over VHP.
However, at some point, the orbital velocity of VHPm1 can't trace any more the orbital velocity of VHP m2 around the galaxy.
Sooner or later, this last chain point should be disconnected from the spiral arm.
So, I give a clear explanation why the last chain point at the end of the spiral arm should be disconnected from the spiral arm and move away from the galactic disc in order to set the halo star.
The dark matter can't explain this phenomenon.
Do you agree that if the dark matter idea was correct, than the disc plane - or the spiral arm had to be continued further more (theoretically - to the infinity.)
I don't see any explanation why there is an end for the spiral arm based on this dark matter fiction.
So, I hope that by now you understand the idea of VHPmn over VHPmn+1 in the spiral arm which is needed to hold the stars in the arm (and on the disc plane).

[Dave Lev (OP)]

Rotation curve problem
Now we need to understand how could it be that the stars are connected to each other while we get the following rotation curve:
https://en.wikipedia.org/wiki/File:M33_rotation_curve_HI.gif
This is the rotation curve of M33 galaxy, but any spiral galaxy should have a similar rotation curve (more or less).
So what do we see.
Please focus only the observation graph.
The expected graph is none relevant as they assume that each star orbits around the galaxy by its own.
However, I claim that the stars are connected to each other.
So, if we think about a rigid disc, it is clear to us that the orbital velocity of a star at 20KLY from the center should be much higher than a star at a distance of 10KLY.
Actually as the radius in 20K is twice longer than in 10K the orbital ring is longer by:
2^2 = 4
Therefore, in a rigid disc, in order to keep itself in the arm, the orbital velocity at 20K should be four time faster than at 10K.
So, how can we explain this problem?
The answer is quite simple.
Spiral galaxy isn't a rigid disc.
The stars in the arm are connected to each other, but they also drift outwards.
Let's monitor few points:
At 5KLY - the orbital velocity is 70 Km/sec
At 10K - 90 Km/sec
At 20K - 110 Km/sec
So, let's assume that at t=0 we trace three stars at those located radius from the center.
If we will try to monitor the location of the stars after T
t=T
We should see that all of them had been drifted outwards.
Let's assume that T represents the time that is needed for a star to drift from 5KLY to 10KLY.
By this time there is high possibility that a star that was at 10KLY had been drifted to 20KLY.
due to the shape of the spiral arm, we should find that the total distance that the first star had to move from 5KLY to 10KLY might be a little bit shorter that the other star which had been drifted from 10KLY to 20KLY.
Therefore, there is no significant change in the orbital velocity as we trace stars that are located further away from the center (although - they are connected by spiral arms).
As I have already explained, new stars are formed in the center.
Those new stars replace the other stars which had been drifted out from in the spiral arms.
Therefore, at any given moment we see that all the arms are full with stars.
Therefore it is clear to me that our Sun is only temporary located at the current location.
As it drifts outwards, sooner or later it will get to the end of the spiral arm and then it will be ejected from the arm and the galactic plane.
So, the spiral galaxy acts as the biggest star sprinkler in the Universe.
Therefore, we see that for any star in the galaxy there is at least one outside.
Hence - all the stars that we see around our galaxy - in the Halo, in the dwarf galaxies... - all of them had been ejected from the galaxy.
One day we will be there too.