Galactic Rotation, General Rule

[JMJones0424]

I find it just as important to know why I am incorrect as to know that I am incorrect.

 

I imagine a spherically symmetrical sphere. Take a plane passing through the center of the sphere. Any point on that plane has an equal gravitational pull from both hemispheres of the sphere above and below the plane, doesn't it, because the net force of gravity is towards the center of the sphere? So... if both of those hemispheres were removed, why wouldn't the shell theorem still apply to the circularly symmetrical disc formed by passing a plane through the center of the spherically symmetrical sphere?

 

After a few hours of thinking about it while tying trees (which gives plenty of time to let the mind wander), it became obvious to me where I messed up. If the shell theorem is correct, it cannot apply to a disk formed from passing a plane through the center of the sphere. My visualization works in the y and z axis, but fails in the x axis.

 

consider cutting the shell into rings

 

Indeed, this is how I realized I had messed up :)

I think the image below should show the obvious, various rings cut from symmetrical shell will not have the same mass ratio as the corresponding ring sections cut from the disk.

 

[athinker]

Bottom line fellas, If you think there is gravity in operation that has pull on an object in a ring then what is the direction and strength of the pull? (Second or third time i've asked that one). Is the ring pulling an object inside the ring to the center? In effect capable of causing an object to orbit the center as if there were mass there even though there is no mass there? Or is it accelerating all objects inside the ring towards the perimeter of the ring causing all objects inside a ring to go flying out

 

Obviously none of that is true. But those are the conclusions your model comes to. It either pulls out or in. If it does neither that's what I am saying. It has no effect and can be ignored.

 

So what say you? Out or in. Yes or no. Direct question. I admit I am completely ignorant of this. Enlighten me. Which way does it pull? Out or in.

[JMJones0424]

Bottom line fellas, If you think there is gravity in operation that has pull on an object in a ring then what is the direction and strength of the pull? (Second or third time i've asked that one).

OK, maybe my diagram isn't as obvious as I thought. Any point (except at the exact center) will be drawn towards the edge of the ring nearest it. If there was an object at the exact center, it would be balanced precariously like a marble at the top of a hill. I come to this conclusion because, working from the shell theorem, when one bisects a spherically symmetrical shell with a plane, creating a circularly symmetrical ring, the ratio of point masses at various angles and distances from any point (except the center) inside the sphere/ring changes. Therefore, given the shell theorem, the "ring theorem" must be false. Using my diagram, there is insufficient mass in the ring segment R₂ to prevent point A from moving outwards towards the edge of the ring. Using your diagram in post 12 there is insufficient mass in the outboard far mass section of the ring.

 

Obviously none of that is true.

Then obviously, you need to re-examine your proposition, because as CraigD has shown, it is false.

[LaurieAG]

Hi athinker, all,

 

Galaxies with uniform distribution of mass have a rotation curve sloping up from the center to the edge. Galaxies with a central bulge in the disk have a rotation curve sloping horizontaly flat from center to edge and objects with most of their mass concentrated in the center of their rotation disk, such as the Solar System of panets or the Jovian System of moons, have a rotation curve that slopes down from the center to the edge.

 

Thats very interesting but have you considered that nobody has ever observed half a spiral galaxy? All images of spiral galaxies are observed when the width of field is larger than the galaxies diameter of rotation.

 

Considering it has been calculated that our solar system has rotated around our galactic center 20 times in 4 billion years would you expect an observer, 200K light years away in a similarly proportioned solar system and galactic center, to be at the end point of a straight beam of light even though the point being observed has done one complete rotation around its galactic center?

 

If the solar system was 800K light years away would the path of light from our sun to the observer be similar to those in the attached diagram?

 

Better still, can anybody prove how the light paths between the two points could be expected to be straight.

[athinker]

LaurieAG,

 

Don't know what your point is. Suspect it may not be to the OP. The OP is about rotation. The rotation is determined by observations of red shift. If one side is red shifted less than the other then that side is rotating "toward" us. If a galaxy was stationary relative to us it would be blue shifted. But since most galaxies are moving away the shift isn't blue on the side moving "toward" us it is just less red shifted than the average shift of the galaxy. By taking the differance in red shift of one side to the other we can determing the rotational speed of that part of that galaxy. In high resolution red shift detection we are able to determine the rotational speed of parts of some galaxies (those that are close enough for the high resolution to seperate the shifts) so can determine the rotational curve of them.

 

JMJones0424,

 

I'm not ignoring your response. I'm waiting for Craig to post his response.

[LaurieAG]

Hi athinker,

 

I will wait your response but make one point for you to consider.

 

Are you seriously suggesting that the galaxies you describe look like the attached doppler image?

Edited June 3, 2011 by LaurieAG

[athinker]

Hi athinker,

 

I will wait your response but make one point for you to consider.

 

Are you seriously suggesting that the galaxies you describe look like the attached doppler image?

 

No...and yes but for different reasons.

 

But I think your question would be better answered in Q and A. It's just so far back in the prerequisites needed to understand this thread that it is really off topic for this thread. I'd be happy to help you in a different thread.

[CraigD]

Bottom line fellas, If you think there is gravity in operation that has pull on an object in a ring then what is the direction and strength of the pull?

OK, maybe my diagram isn't as obvious as I thought. Any point (except at the exact center) will be drawn towards the edge of the ring nearest it.

I agree with JM, and think his sketch explains this conclusion nicely. :thumbs_up

 

Since I’ve got my little program and some crude graphing tools on hand, I’ve attached some graphs of the force on a body as a function of radius at the inner edge of the annulus (a better term than ring, I think, as ring is used to describe many other geometric objects), and for annuli with fixed inner edge radii of 0.5 and 0.9 their outer.

 

We still haven’t actually written and evaluated the integral JM sketched, though the general results are clear from JMs sketch and my simulation. Since this whole “shell theorem applies not only to spherically symmetrical bodies but to circularly symmetrical ones” claim was athinker’s, I think he should have to do and post this calculus :) - and admit that this claim is wrong.

[athinker]

CraigD

 

The result of rings pulling all matter inside to the outside, throwing matter, including the matter of the inside part of the ring itself, out in all directions, is absurd. Rings would expand and disipate if that were the case. That conclusion is not confirmed by any observation what so ever.

 

I posted those conclusions to show how absurd that conclusion was. I had hoped that posting them would simply illustrate how absurd those conclusions are. Since you don't recognize, or are simply denying, the absurdity of those conclusions I don't think I could ever explain the true fact.

 

It is obvious that you pretensiously copy paste complicated formulai that you do not understand in an effort to muddy the water so as to obscure the exact nature of your ignorance from any other readers.

 

 

You are playing a game and I am done.

[ken hughes]

Well, I've been away from the site for a while now and things have certainly moved on haven't they.

 

The issues discussed since my last visit have to do with masses, forces, speeds and geometry. No one has picked up on my original proposal which involves temporal effects;-

 

- Time is dilated significantly toward the galactic centre and this will distort observed speeds making them seem slower than they actually are within their frame' (Redshift)

- There is only one point at which time runs the same as here in the solar system and that is at a similar galactic radius to ours in a galaxy of similar mass and distribution.

- Outboard of this point, speeds will be blueshifted and will seem faster than they actually are (within their own frame')

- Just about everything that has been discussed here will be affected by this phenomena, at least in terms of our observations.

- Why is no one interested in this? It is crucial to our understanding and purely physical arguments are meaningless without involving these very real temporal effects.

- For galaxies where curves continue to rise, this simply means the galactic mass is much smaller than ours and the "datum" point (where time passes the same as here) is very close to the centre and we observe continuing blueshift of rotaion speeds the further out we look. Time beyond these galaxies approaches intergalactic time much more closely. There is less of a "dent" in the time rate field.

- For galaxies which have more Newtonian-like rotation speeds and whose curves continue to fall with increasing radius, this simply means the galactic mass is much greater than ours and the time dilation effects put the "datum" position out beyond the observable mass of the galaxy.

 

This is a new area for cosmology and involves some original thinking. There won't be any programmes for this and we need to start by understanding the principles.

 

Has anyone any thoughts?

[CraigD]

Welcome back, Ken! :)

 

- Time is dilated significantly toward the galactic centre and this will distort observed speeds making them seem slower than they actually are within their frame' (Redshift)

- There is only one point at which time runs the same as here in the solar system and that is at a similar galactic radius to ours in a galaxy of similar mass and distribution.

- Outboard of this point, speeds will be blueshifted and will seem faster than they actually are (within their own frame')

This is true, but to offer this as a solution to the galactic rotation problem, we need to calculate now much points at various distances from galactic center are gravitationally time dilated.

 

I think you put this need well, Ken in about 2 months ago, when you wrote this:

We might re phrase the question;- "How can Newton's Law AND the observed rotation speeds, both hold?" After all, this is the best fit with known science if we can find an answer,

 

There is only one way for this to be the case and that involves the effects of time dilation. Now, our first reaction to this idea might be that time dilation is a very tiny phenomenon and would surely have no significant effect on rotation speeds. Well, that may or may not be the case but we should not throw in the towel just because the numbers MIGHT not work. Let's get the principles established first. The theory will stand or fall when we apply the correct math.

- though I think it’s better to think about principles and do math at the same time.

 

I, and I think others, got sidetracked from these fairly simple calculations responding to athinker’s more difficult to address claims that the shell theorem applies not only to spherically symmetrical bodies but to flattened disks (we’ve yet to offer a rigorous pure mathematical disproof, and like won’t, as approximate calculations and numeric methods disprove it well)

 

So let’s do the math for you suggestion (In physics, an idea’s usually not called a “theory” until after some math’s been done ;)) now.

 

Gravitational time dilation is given by:

 

[math]\frac{t_f}{t_s} = \sqrt{1 - \frac{2U}{c^2}}[/math]

 

where [imath]U[/imath] is the gravitational potential at the location of the time dilated clock measuring [imath]t_s[/imath].

 

For a very accurate calculation, we’d need to calculate [imath]U[/imath] using the mass and location of all the masses in the galaxy, so let’s make the simplifying assumption that the galaxy is a uniform density sphere radius a=15000 ly (about 1/3 the size of the visible disk of the Milky Way or Andromeda galaxy) and mass 1.4e42 kg (about that of the MW or Andromeda) It greatest [imath]U[/imath] is then at its center, and is given by

 

[math]U = \frac{-3GM}{2a}[/math]

 

For points outside of the sphere,

 

[math]U = \frac{-GM}{r}[/math]

 

(For discussion and links and references, see these posts)

 

We can now look at the “time dilation curve” of the galaxy , or rather, just a few points, as it’s pretty flat:

for r=0, [math]\frac{t_s}{t_f} = 0.999989624605919882 [/math];

for r=a= 15000 ly, [math]\frac{t_s}{t_f} = 0.999989624605919882 [/math];

for r= 50000 ly, [math]\frac{t_s}{t_f} = .999997924450906318 [/math]

 

If these time dilations are taken as red or blue shifts, the correspond to receding or approaching speeds of about 3110, 2074, and 622 m/s. The orbital speed of a typical star in our example galaxy – let’s use our own Sun’s – is 220000 m/s The GRP’s speed anomalies are on the order 100000 m/s.

 

So, even if all other problem with the explanation are ignored, GTD is about 100 times too small to explain the GRP.

 

To get a large [imath]\frac{t_f}{t_s}[/imath], [imath]M[/imath] must be large, and [imath]r[/imath] and [imath]a[/imath] small. This is only possible in the vicinity of compact objects like neutron stars and black holes.

 

2 other problem with explaining the RRP with gravitational time dilation are:

• The GRP anomaly is greater the further from galactic center the stars having their radial speed measured are, but GTD is greater the closer to galactic center they are.
  
• Although galactic rotation curves are usually drawn as graphs of speed vs radius, they’re actually obtained by measuring the spectral shift of stars on both sides of GC. On one side, they’re blueshifted, on the other, redshifted. GTD, however, results only in a small redshift.