[Dave Lev (OP)]

Particles are never connected.  Two things cannot touch.  None of Newtons laws about sets of objects require connectivity for this reason.

This is a sever mistake.
All particles on earth are fully connected due to gravity.
In the following law it is stated clearly:
http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/n2ext.html#c2
"The form of Newton's second law for a system of particles will be developed with the understanding that the result will apply to any extended object where the particles are in face connected to each other."
It is also stated:
"Since nothing we have done addressed whether the particles are connected or not, this result generally applies to a system of discrete particles or to an extended object consisting of connected mass elements."
So please - why don't you agree with those simple and clear evidences???

Let's set the whole Earth at the shape of spanner.
So, the Earth will look like an extended object with all of its mass while the length of each side is 10,000 Km. 
Based on Newton's Second Law for an Extended Object
http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/n2ext.html
"The motion of any real object may involve rotations as well as linear motion, but the motion of the center of mass of the object can be described by an application of Newton's second law in the following form:
F = M a

Yes, the motion of the center of mass will follow that law, just like it says.  I never said otherwise.

So, you agree that the center of mass of any kind of object at any shape (even if it is 20,000 Km spanner) must follow that law.
If so, you agree that there is only one center point of mass for any kind of object.
Therefore, there in nothing to disagree.
With only one center point of mass there is no way to get any extra thrust.
I hope that you agree with that.

Conclusions:
I didn't invent those laws.
You are more than welcome to call them at any name. However, those laws prove that there is one center of mass to any shape of object and at any offset.
Therefore, the assumption that there is an extra thrust due to offset contradicts those fundamental laws for gravity.
You didn't offer any alternative mathematic calculation in order to reject those laws and support the hypothetical idea of extra thrust due to bulges offset.
Hence, our scientists must look for better explanation why all the planets and moons are drifting outwards.
I'm specifically using the words "drifting" as I have proved that there is no extra thrust that can push them outwards.
I have no more questions about tidal friction.

With your permission, I would like to focus now on the Sun orbital cycle.

[Halc]

All particles on earth are fully connected due to gravity.

So is the moon.

In the following law it is stated clearly:
http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/n2ext.html#c2
"The form of Newton's second law for a system of particles will be developed with the understanding that the result will apply to any extended object where the particles are in face connected to each other."
It is also stated:
"Since nothing we have done addressed whether the particles are connected or not, this result generally applies to a system of discrete particles or to an extended object consisting of connected mass elements."
So please - why don't you agree with those simple and clear evidences???[/quote]
I totally agree with all that.  The former was an example (spanner) of a connected object, and the latter was an example of the same law working for unconnected objects.

I've never disagreed with any of that.  I disagree with the way you are using it.

So, you agree that the center of mass of any kind of object at any shape (even if it is 20,000 Km spanner) must follow that law.
If so, you agree that there is only one center point of mass for any kind of object.

Yes and yes.

Therefore, there in nothing to disagree.
With only one center point of mass there is no way to get any extra thrust.
I hope that you agree with that.

Where does any of the info on that page say that?   Why would you expect me to agree with that?

If I put forward force on my car, that's thrust.  F=ma.  The law is all about force and acceleration.  Of course it allows thrust.  If I put force on the spanner, or net force on the system of completely disconnected objects, that will move the center of gravity, which is thrust.

You make it sound like something on that page proves that nothing can change speed.

Conclusions:
I didn't invent those laws.
You are more than welcome to call them at any name.

Turns out they're all just different applications of Newton's second law of motion: F=ma.  They're not separate laws.

[/quote]However, those laws prove that there is one center of mass to any shape of object and at any offset.
Therefore, the assumption that there is an extra thrust due to offset contradicts those fundamental laws for gravity.[/quote]
I just love how you get the 2nd line from the first one.  The first line makes zero statement about what forces might exist or not on a system of objects.  It is just a statement that an object has a center of mass.  The lower line simply does not follow from it.
You keep repeating the same assertions over and over.  We're getting nowhere.

You didn't offer any alternative mathematic calculation in order to reject those laws and support the hypothetical idea of extra thrust due to bulges offset.

I never rejected the laws.  But I showed angular acceleration of an object where its center of mass never moved, and I showed acceleration of a set of objects without those objects ever not having a center of mass.  Tossing a handful of sand in the air illustrates it nicely.  At no point does that handful of sand not have a center of mass, and absent friction, that COM will even follow an elliptic trajectory until it hits the ground.  Plenty of thrust going on since the speed of the sand is always changing.

Hence, our scientists must look for better explanation why all the planets and moons are drifting outwards.

Or maybe you could actually understand what the material on you linked page means.

[Dave Lev (OP)]

I hope that you agree with the following:
1. The spanner has a center point of mass.
2. If we won't set an external force of the spanner there is no extra thrust.
3. In our case the spanner represents the Earth.
If you agree with all the above let's move to the following:

You claim that:

If I put force on the spanner, or net force on the system of completely disconnected objects, that will move the center of gravity, which is thrust.

Now
1. Let's use the idea that all the particles on Earth are connected.
In this case, we will assume that the tidal is so strong that it coverts totally the shape of the earth from ball shape into spanner. (Instead of just two bulges)
So, what?
The Earth in a spanner shape has exactly the same center point of mass as the Earth in ball shape (as all the particles are connected).
So, that external force (tidal) didn't change at all the location of the center point of mass (although it changed the earth shape).
Therefore, there is no way to set extra thrust on the moon.
Do you agree with that?

2. Let's assume that the particles on earth aren't connected.
So, the tidal is so strong that it split the earth into two totally separated objects.
Each object is represented by center point of mass. We can set those two center points of mass exactly where the bulges are located.
In this case I agree that the gravity force between each point to the moon is not equal. and the sum of their gravity force is different from just one central point of mass.
However, even in this case, there is no extra thrust.
(Assuming that we can hold those two points of center of mass at a constant distance and offset with regards to the moon, than the moon will orbit around those points without getting any sort of extra thrust.

3. We will split the Earth into infinite separated points of mass while we hold them at the same spot and the same offset from the moon.
Even in this case there is no thrust on the moon. However, the moon will orbit around infinite number of center of mass points instead of only one or two.

Maybe it is my limited understanding, but somehow I really don't see any way to transfer any thrust from the Earth to the moon due to tidal.
With your permission, let's move on.

[Halc]

I hope that you agree with the following:
1. The spanner has a center point of mass.
2. If we won't set an external force of the spanner there is no extra thrust.
3. In our case the spanner represents the Earth.

Agree.
#2 is true per Newton's first law.  If there is no force at all on the spanner, it will continue to move as an inertial object (stay stopped or move in a straight line).  This is true of the COM of the spanner, but not the rest of it.

If you agree with all the above let's move to the following:

You claim that:

If I put force on the spanner, or net force on the system of completely disconnected objects, that will move the center of gravity, which is thrust.

Thrust being acceleration in that context, yes.  F=ma.  Any net force must result in net acceleration, and any acceleration is thrust in the frame of the object with the force acting upon it.  It doesn't mean any particular portion of the object will accelerate, but it means the COM of the object must accelerate.

1. Let's use the idea that all the particles on Earth are connected.
In this case, we will assume that the tidal is so strong that it coverts totally the shape of the earth from ball shape into spanner. (Instead of just two bulges)
So, what?
The Earth in a spanner shape has exactly the same center point of mass as the Earth in ball shape (as all the particles are connected).

No.  The Earth in a spanner shape has exactly the same center point of mass as the Earth in ball shape, period.  The fact that it is connected or not is irrelevant to that.  Gluing two adjacent rocks together does not alter their mutual center of mass.
You can split Earth in two equal halves and move each chunk a lightyear in opposite directions, and the COM of Earth will remain exactly where it is now.  Any net force acting on either half will move that COM linearly as if the force was applied at that point, all per Newton's 2nd law.

So, that external force (tidal) didn't change at all the location of the center point of mass (although it changed the earth shape).

Yes

Therefore, there is no way to set extra thrust on the moon.

I love how you just suddenly assert this when the facts above do not in any way suggest it.  No, I've repeatedly said I don't agree with this.

If you want to make it easy, use a rigid 770,000 km dumbbell shaped object holding two massive earth-halves connected by a bar.  Give that object an offset of 2°, not 10 or 45, and give it a spin of say once per 400 hours. The acceleration on the moon will be so high it will rip apart.

2. Let's assume that the particles on earth aren't connected.
So, the tidal is so strong that it split the earth into two totally separated objects.
Each object is represented by center point of mass. We can set those two center points of mass exactly where the bulges are located.

They'll fall into each other.  The system isn't stable, so its immediate force on the moon will not be cumulative.  For the moon to split Earth in half, it would need to be far larger, enough to get Earth inside its Roche limit.  That's what is happening to Phobos right now.  It is cracking, almost ready to separate into two moons.

In this case I agree that the gravity force between each point to the moon is not equal. and the sum of their gravity force is different from just one central point of mass.
However, even in this case, there is no extra thrust.

Unstable, but that configuration for that moment very much produces a lot of thrust on the moon.  That will lessen as the two parts fall into each other, leaving an Earth back in once piece but a day that is many hundreds of hours long.

(Assuming that we can hold those two points of center of mass at a constant distance and offset with regards to the moon, than the moon will orbit around those points without getting any sort of extra thrust.

Now you're assuming an external application of angular momentum, which adds energy and momentum to the whole setup.  So much for conservation laws.  Newton's 3rd law says there needs to be a reaction to every action, so if there is angular momentum being added to the moon, it needs to come from somewhere.  You're supplying it with an external force holding these two Earth pieces in their unstable positions.

Anyway, if you don't see thrust from this obvious example, you need to take a class on doing vector arithmetic.  I did the math in post 40, where a positive force was computed for the forward component of forces acting on the moon.

3. We will split the Earth into infinite separated points of mass while we hold them at the same spot and the same offset from the moon.

What spot?  The two halves were at two spots.  I can't comment on this because I don't know what spot you're talking about.

Even in this case there is no thrust on the moon. However, the moon will orbit around infinite number of center of mass points instead of only one or two.

I think you mean different spots.  The moon will orbit the COM of the collection, just like it does now, assuming your arrangement doesn't change that COM.

I think you mean you slow the spin of Earth and have it turn once a month with the moon, holding the bulges out at their current offset.  External force will be needed to keep it like that, just like the example with two disconnected masses.

How do you expect a torque force to be exerted on the system and yet not have it gain angular energy?

Maybe it is my limited understanding, but somehow I really don't see any way to transfer any thrust from the Earth to the moon due to tidal.
With your permission, let's move on.

You need my permission?  If you don't understand vector arithmetic, I don't think your new question is something you're likely to get right.  The Earth/sun system is pretty simple.  We can approximate it with a circle.  If you wonder why the Earth orbital radius slowly increases, we're back to the tidal example that you clearly find a need to deny.

[Dave Lev (OP)]

Thanks halc

Let's agree that we don't agree on the idea that there is a constant thrust on the moon due to tidal bulges offset on the Earth.

[Dave Lev (OP)]

With regards to the Sun

Why are we so sure that during all of his life time the Sun had to keep the same orbital radius?
How could it be that all the moons and Planets are drifting outwards, (or inwards based on the tidal idea) while the sun is fixed at the same radius?
How could it be that in one hand our scientists claim that the SMBH increases its mass by eating stars and gas clouds, while on the other hand they don't consider an option that stars must migrate/drift inwards in order to supply the requested food for the SMBH monster?
If the SMBH has 4 x 10^6 sun mass, (while our scientists believe that this mass had been taken from the stars in the galaxy) than somehow 4 x 10^6  stars had to drift inwards.
So why our scientists are so sure that the Sun was always at the same distance from the center of the galaxy???
What makes our star so unique that it had to stay so far away from the monster at the galaxy center?

[Halc]

With regards to the Sun

Why are we so sure that during all of his life time the Sun had to keep the same orbital radius?

Well not at the exact same radius since it is under the effect of all the local stars and such.  But it is moving around the galaxy in a pretty good imitation of a circle (having done around 20 laps so far), and if it had been seriously deflected by some large passing object, it would very unlikely be deflected onto this fairly perfect orbit.  So it seems to have been free of that sort of thing the whole time.  That's a large reason why we're here: We've had a nice stable environment that wouldn't have existed if that large mass had gone through and disrupted the solar system.

How could it be that all the moons and Planets are drifting outwards, (or inwards based on the tidal idea) while the sun is fixed at the same radius?

We have no proof that the radius has been fixed all this time.  The clean orbit tells us that we've never had a large close encounter.  The stars that have had one typically become halo objects.
As for tides, you can't raise a tide on a black hole, and I don't think the tides raised by Sgr-A on the sun have any significant impact on its orbital radius.  Tidal forces follow a inverse-cube law, and that means Sgr-A probably has less tidal effect on the sun than I do.

Tides cannot pull our sun in.  The solar system has positive angular momentum (inclination +63°), so if any of that is affected by Sgr-A induced tides, it will push us further out.  Even if we had negative angular momentum, there isn't enough of it to drop us anywhere close to Sgr-A.

How could it be that in one hand our scientists claim that the SMBH increases its mass by eating stars and gas clouds, while on the other hand they don't consider an option that stars must migrate/drift inwards in order to supply the requested food for the SMBH monster?

4 million stars in 15 billion years is one every 4000 years.  Hardly a hungry monster.
Spacetime is bent near the SMBH, and things cannot orbit at all near them.  You need to move at lightspeed to orbit at a radius of 1.5 the radius of the event horizon.  Anything inside that is dragged in (or would need thrust to stay out), and stuff outside that but close still spirals in.  These are relativistic effects, not Newtonian effects.

If the SMBH has 4 x 10^6 sun mass, (while our scientists believe that this mass had been taken from the stars in the galaxy) than somehow 4 x 10^6  stars had to drift inwards.

A lot of that mass was already there before it formed into stars, but I suppose it all was outside the event horizon at some distant point, just like our solar system was all spread out before gravity pulled all that matter close enough together to make a star.

Things at the center of the galaxy are relatively congested.  Two stars pass close to each other and one goes faster and the other loses kinetic energy.  The slow star falls closer to the SMBH and the fast one shoots out and becomes a halo object.  Few things have a clean orbit that close in.

So why our scientists are so sure that the Sun was always at the same distance from the center of the galaxy???

They're not.  There is no history we can consult.  We seem to be on the road (a clean orbit) still, so that's evidence that we've not left it, because it is hard to get back if you fall off the road, or at least it takes a lot more than 20 orbits. That's pretty strong evidence, but not proof.

What makes our star so unique that it had to stay so far away from the monster at the galaxy center?

Most of the stars out this far are like that.  We're in the suburbs, and we're quite ordinary, not unique at all.  The big ones burn up faster, and the little ones burn much slower.  Scientists are not claiming that all the stars out here are heading for Sgr-A except us.
Look near Cassiopeia constellation for our doom.  That's the close encounter that will likely fling us out of our nice circular orbit in less time that it took life to evolve a human.

[Dave Lev (OP)]

There is no history we can consult.  We seem to be on the road (a clean orbit) still, so that's evidence that we've not left it, because it is hard to get back if you fall off the road, or at least it takes a lot more than 20 orbits. That's pretty strong evidence, but not proof.

The solar system has positive angular momentum (inclination +63°),

The Sun has currently positive angular momentum (inclination +63°). In other words, it is moving upwards from the Galactic Disc lane while it orbits around the center of the galaxy.
It is expected that once it gets to the pick it should get down and cross the galactic lane downwards.
Hence, the Sun is Bobbing up and down while it orbits the center of the galaxy.
This is not unique for the Sun. Actually all the stars in the galaxy bobbing up/down, in/out or in between.
If I understand it correctly, the Sun should move up and down at least four times before it set one complete orbital cycle.
So, how can we call it "clean orbit"?
Do you think that Newton or keler would accept that bobbing orbital activity as a "clean orbit"?
Can you please find one planet or moon that is bobbing up and down while it orbits around its main host (four times per cycle)?
How can we ignore that incredible positive angular momentum???
Actually you have already offered the answer for that bobbing activity"

Well not at the exact same radius since it is under the effect of all the local stars

So, you even claim that "it is under the effect of all the local stars".
Hence, why don't we accept the idea that what we see is due to the gravity impact of all the local stars?
We all know that gravity works locally.
As we stay on Earth, we are under the gravity force of the earth (Not the Sun, Not the moon and not under the gravity force of the whole galaxy ).
The moon also works under the gravity of the Earth (Although the Sun gravity on the Moon is stronger by at least twice)
The Earth (or actually - the Earth/moon center of mass) works under the gravity of the Sun (While it ignore the gravity of the whole galaxy, and so on.)
So, why the Sun doesn't orbit under the effect of all the local stars???
In other words, what is the real host of the Sun?
If the Sun goes up and down, could it be that it actually orbits around some sort of a center of mass which is the equivalent center of all the local stars? So, could it be that it doesn't directly orbit around the galaxy, but it orbits around a local center of mass while this local center of mass orbits around the galaxy.
It is the same phenomenon as the Moon orbits around the Sun (12 times per cycle).
If we shut down the light at the Earth, we might see that the moon orbits around the Sun while it's bobbing inwards and outwards. (As the Moon orbits almost horizontally to the earth/sun disc). If the Moon was orbiting vertically around the earth, we would see that it is bobbing up and down as it orbits around the Sun. Almost identical to the Sun bobbing activity.
So, why do we reject the idea that the bobbing activity shows clearly that the Sun doesn't orbit directly around the center of the galaxy, but around some local center of mass which had been set by the "effect of all the local stars"?

If you don't agree with this idea:
Would you kindly show the formula of gravity which can support that strange bobbing activity or "clean orbit" of the Sun?
I assume that you might claim that it is bobbing due to the gravity of the galactic disc lane. If so, please prove this hypothetical idea by real mathematics based only on Newton and kepler.

In my opinion, this bobbing activity is the smoking gun which we are looking for.
I really can't understand how can we ignore so important activity.
Once we agree that the Sun orbits around a local center of mass (Which is "under the effect of all the local stars" - as the Moon/sun orbit), we will get a clear answer for the Spiral galaxy enigma.

[Halc]

The solar system has positive angular momentum (inclination +63°),

The Sun has currently positive angular momentum (inclination +63°). In other words, it is moving upwards from the Galactic Disc lane while it orbits around the center of the galaxy.

Inclination is the tilt angle and has nothing to do with where we are going.  0° means the axis of the solar system is the same as the axis of the galaxy.  It isn't, it is off by 63°, which means it is more on its side than not.  Any inclination over 90° would give that solar system a negative angular momentum relative to the galactic axis.

What I said has nothing to do with us moving towards the center.  As I've said, our path is on average somewhat circular: the eccentricity is low enough to put us in the disk somewhere at a fairly narrow range of radius, but is otherwise pretty meaningless.  We take a wobbly path around the galaxy and have a speed somewhere between 225 and 250 km/sec most of the time.  The forces that change that are not tidal.

It is expected that once it gets to the pick it should get down and cross the galactic lane downwards.

I know of nobody (except you perhaps) that expects this sort of thing to ever happen.

Hence, the Sun is Bobbing up and down while it orbits the center of the galaxy.
This is not unique for the Sun. Actually all the stars in the galaxy bobbing up/down, in/out or in between.
So, how can you call it "clean orbit"?

You're right, its not very clean.  But we're in the plane and moving generally at the velocity needed to be at this current radius, so that's clean enough.

Do you think that Newton or keler would accept that orbit as a "clean orbit"?

The orbit is described as being non-Keplarian, so no.

If I understand it correctly, it should move up and down at least four times before it set one complete cycle.
Can you please find one planet or moon that is bobbing up and down while it orbits around its host (four times per cycle)?

Earth bobs up and down around 13 times each lap.  4 times?  No, I cannot think of one with that cycle.  I'd not heard of it for the galactic orbit.  Is there something nearby that we go around every 50 million years or so?  Is that a known thing?

How can you ignore that incredible positive angular momentum???

Same way I ignore the moon's incredible change in positive solar angular momentum every 14 days.  It all averages out in the end.

Actually you have already offered the answer for that bobbing activity"

Well not at the exact same radius since it is under the effect of all the local stars

So, you even claim that "it is under the effect of all the local stars".

Yes, that's right.  We don't exactly orbit Sgr-A, which is tiny compared to the mass of the galaxy inside our orbital radius.  Not at all like the Earth, dominated by that one huge mass in the middle with nothing but small objects giving minor but regular deflections from that perfect elliptical path.

The Earth works under the gravity of the Sun (While it ignore the gravity of the center of the galaxy, and so on.)

Earth accelerates due to the galaxy exactly as much as does the sun.  Gravity is never ignored.  We are inside the hill radius of the sun, so the galaxy in general isn't going to separate the two of us.  A single passing object might.

So, why the Sun doesn't orbit under the effect of all the local stars???

The sun is within the hill radius of no 'local' dominant mass.  Perhaps there is a cluster that holds together with mutual attraction, but then the orbit of the cluster still goes around the galaxy.  Earth has also made 20 trips around the galaxy, despite the continuous change in velocity.

In other words, what is the real host of the Sun?

Don't know.  Don't know if there is one before the galaxy as a whole.  Something must hold the galactic arms together, but that's not really an orbit.

If the Sun goes up and down, could it be that it actually orbits around some sort of a center of mass which is the equivalent center due to all the stars/SMBH in the galaxy?

That would be orbiting the galaxy, and it wouldn't go up and down due to that, except for normal orbital eccentricity just like Earth and every other planet.  Mercury radius changes an awful lot each orbit, but that is no indication that it is orbiting some mass other than the sun.

If there is some local mass around which all the nearby stars cling, then what really counts is the orbital speed and radius of the center of mass of that local group, and not the individual velocity of any particular object that is part of that group.

So, could it be that it is not directly orbits around the galaxy, but it orbits around a local center of mass while this local center of mass orbits around the galaxy.

Exactly.

It is the same phenomenon as the Moon orbits around the Sun (12 times per cycle).
If we shut down the light at the Earth, we might see that the moon orbits around the Sun while it's bobbing inwards and outwards. (As the Moon orbits almost horizontally to the earth/sun disc).

Right, but that bobbing in and out doesn't mean the moon has any chance of falling into the sun.  OK, it will, but only because the sun will come out here at grab it, not because the moon will fall in.

So, why do we reject the idea that the bobbing activity shows clearly that the Sun doesn't orbit directly around the center of the galaxy, but around some local center of mass which is under direct "effect of all the local stars"?

I didn't assert that one way or the other.  The local masses are pretty well known, and I don't know if our neighbors are always our neighbors, or if they're just nearby right now.  A good text would say.  I'm pretty sure this sort of thing is known. 
Not sure if our motion relative to this local mass would be considered 'orbital' since there is no central mass to stabilize it.  It is sort of a 3-body problem with similar masses: the movements of the masses is chaotic, not at all following the rules of orbital mechanics.  Any one of the bodies might get flung away from the group, bringing the remaining members of the group closer together.  New masses might come from outside and lose enough speed to become new members of the group.

If you don't agree:
Would you kindly show the formula of gravity which can support that strange bobbing activity or "clean orbit" of the Sun?

A=GM/r²
That describes the acceleration of any body given any number of masses spaced around it.

Prove your hypothetical idea for that bobbing activity by real mathematics based only on Newton and kepler.

Integrate the formula above and you get the bobbing activity.  Kepler doesn't much come into play here.  It's all that simple Newton formula.

In my opinion, this bobbing activity is the smoking gun which we are looking for.

Actually, I'm not really sure what you're looking for here.
Some single central mass (closer than SGr-A) around which we orbit?  No, we're not within any object's hill radius, so our local motion is not really best described as 'orbital'.

Once we agree that the Sun orbits around a local center of mass (Which is "under the effect of all the local stars" - as the Moon/sun orbit), we have got the answer for the Spiral galaxy enigma.

Enigma?  The 'bobbing' is quite expected.  There are masses nearby, but none close enough for an orbit.  A local center of gravity may well come into play, loosely holding a group of sister stars together, but our motion around that is chaotic, not orbital.
I call them sister stars because most of the the local ones are probably born of the same parent supernova, which explains their somewhat similar mutual velocity as a group.  We're a 2nd generation solar system.  The 1st generation ones lack planets like our inner ones.

[Dave Lev (OP)]

So, could it be that it is not directly orbits around the galaxy, but it orbits around a local center of mass while this local center of mass orbits around the galaxy.

Exactly.

Wow

If we agree that the sun orbits around a local center of mass while this local center of mass orbits around the galaxy, than we have to agree that all the stars in the spiral galaxy has a similar orbital motion.
Based on that, now we can get better understanding about the Spiral galaxy.
For example -
When we look at the nearby stars, we might see that each one is moving at a different direction and velocity.
We might think that very soon they all will get out from the spiral arm.
This is incorrect. all the nearby stars will stay with us. Each one of them orbits around it's unique center of mass, while the center of mass is moving with the arm. and that center of mass is a direct product of all the other nearby stars...
Let's look at S2.
We think that it orbits around the SMBH. That is big mistake.
If we look carefully, we also might find that it's orbital cycle isn't clean.
In other words, it also orbit around some center of mass with this center of mass orbits around the SMBH.
This is a very important issue.
Let's take the example of the Moon/sun orbital cycle.
If we ignore the earth, than just by monitoring the orbital cycle of the moon and its mass estimated, we might think that the Sun mass is very low.
So, we can't really extract the real mass of the sun directly from the moon orbit.
We must first find the mass of the earth, and then extract the Sun mass.
In the same token, if we want to extract the real mass of the SMBH we must first find the estimated mass of the S2 center of mass point and based on that data we can extract the real value of the SMBH.
We might find that the mass of the SMBH is significantly higher than our faulty calculation.
Do you agree with that?
 

[Halc]

So, could it be that it is not directly orbits around the galaxy, but it orbits around a local center of mass while this local center of mass orbits around the galaxy.

Exactly.

Wow

If we agree that the sun orbits around a local center of mass while this local center of mass orbits around the galaxy, than we have to agree that all the stars in the spiral galaxy has a similar orbital motion.

That's like saying that because we know about one white swan, we have to agree that all swans are white.  This is unlikely here.  Some stars are the biggest kahuna around and find nothing local around which it can orbit.
I doubt the sun's motion can be designated as an orbit.  It moves about the local center of mass, but doesn't follow any path as described by Kepler's laws, and this is IF the sun in fact is gravitationally bound to this local group.  I think there probably is such a thing, but I'm not sure.

Based on that, now we can get better understanding about the Spiral galaxy.
For example -
When we look at the nearby stars, we might see that each one is moving at a different direction and velocity.

Small differences, sure, but nothing that takes any of them out of the general path that takes them around the galaxy at the same pace as us.
So sure, the stars around us have different velocities, but a relative speed of only a few km/sec maybe.  As a group, we're all moving thataway at 230 km/sec ± that single digit variation.  The general path is therefore pretty much all the same way like a herd of sheep.

We might think that very soon they all will get out from the spiral arm.

I don't think anybody suggests that.  Depends on the definition of 'soon'.  Yes, it is forecast, but about 4 billion years away.  Wake me up. I want to watch.  Until then, we go around a bunch more times.

This is incorrect. all the nearby stars will stay with us. Each one of them orbits around it's unique center of mass, while the center of mass is moving with the arm. and that center of mass is a direct product of all the other nearby stars...

Right.  We go around as a group just like the planets don't leave the solar system despite every one of them having a different velocity than the sun at all times.

Let's look at S2.
We think that it orbits around the SMBH. That is big mistake.
If we look carefully, we also might find that it's orbital cycle isn't clean.
In other words, it also orbit around some center of mass with this center of mass orbits around the SMBH.

Pretty tall conjecture if you ask me.  They'd notice that in a moment.  They detect dark objects as S2 passes by them.  If it orbited one of them, it would have a regular deviation from its Keplerian path.  It doesn't.  So who's making the big mistake?

I find it impressive that they can watch it that well despite all the clutter between us and it that supposedly obscures the view of the galactic core.  Here also is the fastest known ballistic orbit of anything, and the gravity of the SMBH out where this star is is comparable to that of the moon.  Our black hole is a wuss...

This is a very important issue.
Let's take the example of the Moon/sun orbital cycle.
If we ignore the earth, than just by monitoring the orbital cycle of the moon and its mass estimated, we might think that the Sun mass is very low.
So, we can't really extract the real mass of the sun directly from the moon orbit.

Yes you can. The moon is about at the same orbital radius as Earth, and goes around in the same period.  That makes the Sun's mass perfectly consistent with the orbit of the moon about it, even if we were unaware of Earth being there.
If Earth was not actually there, the moon would go around in the same orbit (speed and radius) as Earth does now, just without the monthly wiggle since it would be one object instead of two.

We must first find the mass of the earth, and then extract the Sun mass.
In the same token, if we want to extract the real mass of the SMBH we must first find the estimated mass of the S2 center of mass point and based on that data we can extract the real value of the SMBH.
We might find that the mass of the SMBH is significantly higher than our faulty calculation.
Do you agree with that?

None of it.  It is based on the moon orbit not being consistent with the mass of the sun.  It matches perfectly, but it has a regular wiggle, meaning it orbits something, even if you can't see it.  S2 doesn't have a regular wiggle like that, and if it did, it would still go around SGr-A every 16 years like it does now.

[Halc]

Orbital speed is a function of 'reduced mass', which for any relationship except a binary star, is approximated by the mass of the primary.
V = √(Gμ/R) where G is the gravitationl constant, μ is the reduced mass of the pair of objects, and R is the radius.

Reduced mass μ for two objects is: μ = (m1^-1 + m2^-1)^-1 which is pretty much the mass of the sun for Earth's orbit, and SGr-A (plus a couple hundred dark objects) for S2. 

That means that the moon would orbit at about the same speed as Earth if it was by itself, and S2 would orbit at the same speed even if it was the only visible part of some larger object that it orbited.  None of these objects have enough mass to affect their respective reduced masses.

M31 (the object that is going to throw our sun on some totally new path) has a central SMBH designated as P2 with a mass that's around 10x that of Sgr-A.  'Nearby' orbits P1 which is the sort of cluster that you describe, a heavy collection of stars and such seemingly not held together with a single central mass.  It seems a strong enough gravity well to hold itself together, but it is far further from its SMBH than is S2.  If P1 were that close, tidal forces would separate the material into a ring.

[Dave Lev (OP)]

Orbital speed is a function of 'reduced mass', which for any relationship except a binary star, is approximated by the mass of the primary.
V = √(Gμ/R) where G is the gravitationl constant, μ is the reduced mass of the pair of objects, and R is the radius.

Reduced mass μ for two objects is: μ = (m1^-1 + m2^-1)^-1 which is pretty much the mass of the sun for Earth's orbit, and SGr-A (plus a couple hundred dark objects) for S2. 

That means that the moon would orbit at about the same speed as Earth if it was by itself, and S2 would orbit at the same speed even if it was the only visible part of some larger object that it orbited.  None of these objects have enough mass to affect their respective reduced masses.

Yes.
You are absolutely correct.
Sorry for my mistake.
However, with regards to the SMBH:
Why do we ignore the accretion disc?
Based on our measurements, the velocity of the plasma in that disc is 0.3 c (speed of light)
If we know the radius of the accretion disc (at the verified velocity), we can easily extract the real mass of the SMBH.
So, why do we insist on S2 which doesn't have a clean orbit instead of the accretion disc which has a perfect cycle orbit?

[Halc]

However, with regards to the SMBH:
Why do we ignore the accretion disc?
Based on our measurements, the velocity of the plasma in that disc is 0.3 c (speed of light)
If we know the radius of the accretion disc (at the verified velocity), we can easily extract the real mass of the SMBH.
So, why do we insist on S2 which doesn't have a clean orbit instead of the accretion disc which has a perfect cycle orbit?

They follow S2 because it is an object that can be followed.  If they measure velocity of plasma at a specific point, that doesn't indicate the orbit, just the speed of something at one moment.
By similar thinking, one could significantly overestimate our own sun from a distance if all we measured was the occasional comet when it grows a nice visible tail, and moves near Mercury orbit but far faster than mercury.  That observation might lead one to believe that the orbital speed at that radius is much higher than it is.  The can't follow the comet through a full orbit any more than we can follow the plasma through a full orbit.  With S2 we can.  Sure, it isn't a circular orbit, but that isn't needed to do the calculation.  It just makes the calculation a little less trivial.

They also follow S2 because they can see it deviate from its orbit, giving them an idea of the density of other dark objects that it passes, which is very useful information.  There is a lot of research going into dark matter, and these sorts of things help them estimate the MACHO component of dark matter (things that don't show light like Mars).

[Halc]

V = √(Gμ/R) where G is the gravitationl constant, μ is the reduced mass of the pair of objects, and R is the radius.

This is wrong. I substituted μ for the wrong mass.  μ is the reduced mass of the secondary, not the primary, so  V=√(GM/R), but skewed by greater acceleration (and hence speed) of the secondary. a=F/m so for orbital acceleration, a=F/μ.
 For small masses (pretty much everything except the moon and Charon), μ is essentially m.

[Dave Lev (OP)]

There is a lot of research going into dark matter, and these sorts of things help them estimate the MACHO component of dark matter (things that don't show light like Mars).

O.K.
As you have mentioned that issue - Dark Matter

Why Newton didn't add that brilliant idea of dark matter in his formulas?
Why he didn't say that any orbital system is based on dark matter?
Our science communities try to prove their hypothetical ideas by using Newton laws. As they have failed to explain the orbital velocity of our Sun, they came with this idea.
Now they even try to set more effort in order to show that this none realistic idea is realistic.
Let me give you an example -
Let's assume that we want to swim in a pool without water.
So, I will tell you that there is water, but the water is dark water.
You can't see it, you can't feel it, you can't smell it or drink it, but it is there because I said that it there. Would you believe me???

So, this is my personal opinion:
Dark matter is a solid proof for the failure of our scientists to show how spiral galaxy really works.
As they have failed to understand the real impact of none "clean orbit", as they have failed to understand the real impact of the Earth/moon "Drifting outwards", as they have failed to understand the real impact of the Ultra high magnetic power around the accretion disc, they couldn't explain how the gravity really works in Spiral galaxy.
I can do it.
I can explain how the whole universe works without any need for dark matter, for dark energy and for any sort of dark magic.
Based on Newton law I can easily explain:
How spiral galaxy really works?
Why there are spiral arms in spiral galaxy?
Why the stars in spiral arms have almost constant orbital velocity at any radius?
Why we see that all the far end galaxies are moving away from us at almost the speed of light, while our observable universe seems to be full with matter.
If we will come back 100,000 billion years (or even 10^Billion years) from now, we will see a similar universe with same density and almost the same numbers of galaxies per observable universe. We might not find our solar system, but there will be many similar.
Again - no need for dark matter or dark energy - just Newton law and simple common sense.
However, in order to do it I need the following basic understanding:
1. "Drifting" outwards
It's very difficult to verify a "drifting" outwards of few cm per cycle while the orbital radius is 1 Arc.  However, all the objects (assuming that they are far enough) are drifting outwards from their host. That is correct for all the objects including: Moons, planets, stars... There is no need for tidal support to explain this Phenomenon.
Therefore, any orbital cycle is by definition spiral shape cycle. So, even if it drifts 1 micro meter each cycle, it is still has spiral orbital shape.
2. Clean orbital cycle.
All the orbital cycles in the Universe must be clean. There is no room in our universe for none clean cycle (unless there is an interruption.)
So, the Sun must set a very clean orbital cycle around its center of mass. That must be correct for any star in the universe even if it is very massive star or object (unless there is no interruption).
3. The magnetic power around the accretion disc, push any matter upwards (or downwards) at a speed of 0.8 c (speed of light) that prevents from any gas cloud, star or even atom to drift inwards in order to be eaten by the SMBH monster.

That's all I need.
Based on those three elements, I can easily explain how our universe works without any sort of dark magic.
If you agree I will show how it works.

[Halc]

As you have mentioned that issue - Dark Matter

Why Newton didn't add that brilliant idea of dark matter in his formulas?
Why he didn't say that any orbital system is based on dark matter?

Newton didn't need to.  His formulas do not apply only to matter that emits light.  Jupiter will orbit the future white dwarf that the sun will become at the same radius as the black dwarf it will be even later on.  The latter is dark matter.

Our science communities try to prove their hypothetical ideas by using Newton laws. As they have failed to explain the orbital velocity of our Sun, they came with this idea.

The idea of there being burnt out stars and rouge planets is hardly new.  Nobody suspected these things didn't exist.  They measure the density of lit-up stars and conclude they don't have enough collective mass to explain the acceleration of the sun, so they know there must be more matter that is not young stars.

The new idea was not large objects (MACHO) like star cores, but small ones (WIMP).  Those are like neutrinos, except with much more mass.

Now they even try to set more effort in order to show that this none realistic idea is realistic.
Let me give you an example -
Let's assume that we want to swim in a pool without water.
So, I will tell you that there is water, but the water is dark water.
You can't see it, you can't feel it, you can't smell it or drink it, but it is there because I said that it there. Would you believe me???

Sure.  It explains how I can swim in a pool that is apparently lacking water.  OK, that probably means I can feel it since swimming involves applying thrust with my limbs, but in the same way the sun 'feels' the dark matter by its acceleration vector.

So, this is my personal opinion:
Dark matter is a solid proof for the failure of our scientists to show how spiral galaxy really works.

As they have failed to understand the real impact of none "clean orbit", as they have failed to understand the real impact of the Earth/moon "Drifting outwards", as they have failed to understand the real impact of the Ultra high magnetic power around the accretion disc, they couldn't explain how the gravity really works in Spiral galaxy.

Is there some pet alternative that you think explains the observations better?  Do I see a suggestion of magnetism there?  I've never seen magnetism work detectably beyond a few meters.

I can do it.
I can explain how the whole universe works without any need for dark matter, for dark energy and for any sort of dark magic.

OK, you do claim to have a pet explanation, all without having a basic grasp of the application of Newton's laws.

Based on Newton law I can easily explain:
How spiral galaxy really works?
Why there are spiral arms in spiral galaxy?
Why the stars in spiral arms have almost constant orbital velocity at any radius?

Why we see that all the far end galaxies are moving away from us at almost the speed of light, while our observable universe seems to be full with matter.
If we will come back 100,000 billion years (or even 10^Billion years) from now, we will see a similar universe with same density and almost the same numbers of galaxies per observable universe. We might not find our solar system, but there will be many similar.
Again - no need for dark matter or dark energy - just Newton law and simple common sense.

I don't think Newton's law predicts that.  1st law is that those receding galaxies will continue to recede, thus reducing the density of any given volume over time.  If your theory has new matter filling the gaps, that theory doesn't follow from Newton's laws.

However, in order to do it I need the following basic understanding:
1. "Drifting" outwards
It's very difficult to verify a "drifting" outwards of few cm per cycle while the orbital radius is 1 Arc.

What is 1 Arc?

However, all the objects (assuming that they are far enough) are drifting outwards from their host. That is correct for all the objects including: Moons, planets, stars... There is no need for tidal support to explain this Phenomenon.

You invoked Newton's laws.  Newton says the energy and momentum needed to do that has to come from somewhere.  Not all moons do this.  Most of Jupiters moons are not drifting outward, so the assertion is false.

Therefore, any orbital cycle is by definition spiral shape cycle. So, even if it drifts 1 micro meter each cycle, it is still has spiral orbital shape.

Agree, except for the 'by definition' part.  That spiral is a deviation from the 'by definition' elliptical model of ideal point masses.

2. Clean orbital cycle.
All the orbital cycles in the Universe must be clean. There is no room in our universe for none clean cycle (unless there is an interruption.)

What is clean?  A perfect ellipse?  You need to define that term, because I cannot think of anything that qualifies as having a clean orbital cycle, but maybe my concept of the term is different than yours.

So, the Sun must set a very clean orbital cycle around its center of mass.

The sun does not orbit itself.

3. The magnetic power around the accretion disc, push any matter upwards (or downwards) at a speed of 0.8 c (speed of light) that prevents from any gas cloud, star or even atom to drift inwards in order to be eaten by the SMBH monster.

One does not push at a speed.  One pushes with a force, or applies an acceleration.  This is a direct implication of Newton's 2nd law.  Where does the 0.8c come from? 

That's all I need.

You need somebody with a complete disregard for Newton's laws.  Yes, I suppose you could make that theory plausible to such a person.

Based on those three elements, I can easily explain how our universe works without any sort of dark magic.
If you agree I will show how it works.

I cannot agree with the points enumerated above, so don't bother.
You can't assert any of the things above.  Those should all be conclusions demonstrated by, or observations explained by application of the basic laws.

[Dave Lev (OP)]

Dark Matter

Newton didn't need to.  His formulas do not apply only to matter that emits light.  Jupiter will orbit the future white dwarf that the sun will become at the same radius as the black dwarf it will be even later on.  The latter is dark matter.

Based on Wiki:
https://en.wikipedia.org/wiki/Dark_matter
"Dark matter is a hypothetical form of matter that is thought to account for approximately 85% of the matter in the universe, and about a quarter of its total energy density."
"Many experiments to directly detect and study dark matter particles are being actively undertaken, but none has yet succeeded."
This is my opinion about the dark matter:
The galaxy rotation problem - We don't know how to explain that problem based on our current hypothesis/understanding how spiral galaxy works.
Hence, instead of reconsider our hypothetical ideas about spiral galaxies and some other issues, we have found a brilliant idea of dark matter.
However, unfortunately we didn't find any evidence for that unrealistic idea: "Many experiments to directly detect and study dark matter particles are being actively undertaken, but none has yet succeeded."
Therefore, we have two options:
1. Continue to hold our none realistic ideas about spiral galaxies and continue to look for that unrealistic dark matter.
2. Open our mind to different ideas which can perfectly explain the galaxy rotation problem and all the other unsolved issues without any need to dark matter.

However, if I understand it correctly - Our science community reject the idea that they might have a problem with understanding how spiral galaxy really works. Based on their point of view, they only need to find the evidence for that dark matter.
So, how long do we have to wait until they will claim - "Sorry, there is a chance that if we don't find it - it is not there?
One year, 10 Year? Or one billion years?
Why you don't even give a chance to look for a different concept about our universe?

[Halc]

Therefore, we have two options:
1. Continue to hold our none realistic ideas about spiral galaxies and continue to look for that unrealistic dark matter.
2. Open our mind to different ideas which can perfectly explain the galaxy rotation problem and all the other unsolved issues without any need to dark matter.

Both options are viable, but when noting that orbits seem to indicate that there is more stuff than what we see, it seems less magical to propose that there is more stuff we don't see than to discard Newtonian mechanics altogether and rewrite physics from scratch.
So is there a model supplied by such open-minded thinking?  Trust me, such a thing would be warmly greeted if it worked.

[Dave Lev (OP)]

So is there a model supplied by such open-minded thinking?  Trust me, such a thing would be warmly greeted if it worked.

Trust me.
There is a model that works by 100%.
However, I need your cooperation and good willing.
For just one moment try to forget all the wrong understanding/hypothetical ideas that we have about the galaxy (Including: Age of the Star/galaxy/Universe, dark matter/dark energy and so on).

There are three elements which are needed in this model.

1. The impact of gravity force due to local mass - The impact of gravity force due to local mass is stronger than the impact of gravity force of a very far end object. Therefore, the moon had selected to orbit around the Earth instead around the Sun, while the gravity force of the Sun/Moon is stronger by at least twice than the Earth/Moon gravity.
So, even if we shut down the light on Earth , the moon will continue to orbit around the Earth, while their mutual point of mass orbits around the Sun.
The outcome is as follow:
The moon orbits around a virtual host point (as we can't see the earth) while this virtual host point orbits around the Sun. So, the orbital cycle of the moon sets a clean orbital cycle around a virtual host point (Earth - which we can't see).
In the same token:
Every star in the galaxy must orbit around some host Point. It might be something that we see or something that we can't see. However, any star (at any size) must set a clean orbital cycle (in ellipse shape or a perfect cycle). If we can't see that host point, let's call it virtual host point. So, while the star orbits around that virtual host point, the host point orbits around the center of the galaxy. Therefore, we might think that the orbital cycle of a star around the galaxy is not clean.
With regards to our Sun
Please look at the following motion of the solar system in the galaxy:
http://www.biocab.org/Motions_of_the_Solar_System.jpg
http://www.biocab.org/coplanarity_solar_system_and_galaxy.html


The broken gray line shows exactly the virtual host point of the Sun while it orbits around the galaxy.
So, the Sun sets a clean orbital cycle around its virtual host point. This host point is a direct outcome of the local mass gravity (Due to the nearby mass in the Orion spiral arm).
So, the total orbital motion of the Sun is 217 Km/sec however, it also moves locally upwards/downwards to the galactic disc lane at 5-7 km/sec while it moves inwards/outwards at 20 km/sec.
Each star in the spiral arm has a similar orbital motion. Therefore, when we look at the nearby stars we see the following:
http://www.basicknowledge101.com/photos/2015/perception-of-time-rotation-of-galaxy.png
We might think that they move randomly relative to each other, but in reality, each one orbits around its virtual host point, while all their host points stay together in the arm and set a nice orbital motion of about 217 Km/sec around the galaxy.

Summery -
The orbital cycle around a virtual host point is a key element in my explanation.
Please try to accept this idea as is.
If you totally can't agree with that, you are more than welcome to prove it by mathematics.
However, please don't tell a story why this idea isn't logical based on our current understanding about the Galaxy
Agree?
If you have no objection - we will set the next element.