[set fair (OP)]

This question has irked me for decades and I have never come across any reference to it. Even more so now that the existence of dark matter is in doubt.

Realising that gravity is not a force one could never the less draw lines, from a massive object, somewhat corresponding to electrical or magnetic lines that we are used to in diagrams.

So picture the supermassive blackhole at the centre of our galaxy with the Milky Way taken away. The lines would be straight going away from the blackhole. Now draw a second diagram with the Milky Way added. We are looking at the galaxy side on so the diagram looks like this
            -----------------------O----------------------
We ignore the lines from the stars just considering the lines from the blakhole. I think I could safely draw two straight lines - one going vertically up and one going vertically down. But because the stars in the galaxy are curving space the other lines must be drawn starting out going directly away from the blackhole but curving towards the galactic plane. The lines starting out nearly vertical would be nearly straight as we draw the lines getting moving from the vertical to the horizontal the lines would be progressively more curved towards the galactic plane.

Am I correct so far? I think this means additional gravity from the black hole the further you get from the blackhole. ie the stars at the edge of the galaxy not only get gravitational attraction from the other stars but also gravitational attraction from the blackhole but the latter would be greater than it would be if all the stars weren't there ie the gravity from the blackhole would be greater than that calculated using the inverse square rule

As I say, I have never come across reference to this. Is the effect negligible or is it nontrivial but taken into account but so rarely mentioned that I have never come across it?

[alancalverd]

I think this means additional gravity from the black hole the further you get from the blackhole. ie the stars at the edge of the galaxy not only get gravitational attraction from the other stars but also gravitational attraction from the blackhole but the latter would be greater than it would be if all the stars weren't there

There is no evidence of "gravitational shielding" AFAIK. Reduce the universe to a line from left to right. The gravitational field at a remote point on the right increases continuously with the total mass to the left of it.

[Halc]

Realising that gravity is not a force one could never the less draw lines, from a massive object, somewhat corresponding to electrical or magnetic lines that we are used to in diagrams.

It sounds like you want a diagram showing where a grid of plumb bobs would point if somehow held stationary relative to the galaxy. No, I've never seen a diagram of that, but it's not much different than if would be for any somewhat squashed mass.

So picture the supermassive blackhole

It is of negligible mass, only about 100,000th of the mass of the galaxy. It can be treated as just one more insignificant star until you get really close to it.

The lines would be straight going away from the blackhole.

They go straight out from Earth as well, but at large scales, both are just more mass.

Now draw a second diagram with the Milky Way added. We are looking at the galaxy side on so the diagram looks like this
            -----------------------O----------------------

The mass of the galaxy is not so flat as your diagram suggests. Much of the mass is away from the galactic plane.  Still, a portion of it spins, and that arranges some of the matter in the 'squashed' arrangement that makes it not spherically symmetrical.

But because the stars in the galaxy are curving space the other lines must be drawn starting out going directly away from the blackhole but curving towards the galactic plane.

The galactic plane is in all directions equally if you start at the center, so there's no direction to curve. Unclear where else you're starting your line from.  If you start a line right on the line somewhere offcenter, sure, it will point to the center of the galaxy since more mass is in that direction. Where else might you want to draw your arrow?  If you start near the line (say 1000 LY above the plane where we are, the line is diagonal, pulled to the side by the greater mass that way, but also pulled down by the bulk of the nearby visible matter so nearby.

Maybe you should draw a crude picture, something we could critique. Even a hand-drawing is fine. Just remember: the black hole is a blip of negligible mass, especially in our galaxy, it being notably underfed. Andromeda masses about what we do, but their black hole is around 10 times the mass, and it's still negligible compared to the galaxy it's in.

Also don't worry about the concepts of relativity (bent spacetime and such) since Newtonian concepts work fine for this sort of thing.  Newton's equations put a man on the moon despite relativity being around back then. Nobody did the calculations Einstein's way.

 The lines starting out nearly vertical would be nearly straight as we draw the lines getting moving from the vertical to the horizontal the lines would be progressively more curved towards the galactic plane.

ie the gravity from the blackhole would be greater than that culculated using the inverse square rule

At any large distance, the effect from any point object can be calculated using the inverse square rule. Near the edge of the galaxy, the gravity of the central black hole is utterly negligible, and all the stars out there are moving significantly faster than its escape velocity. It's all the other mass that keeps all those stars in orbit.

[evan_au]

Even more so now that the existence of dark matter is in doubt.

I think that the effects of Dark Matter are well accepted
- It is the nature of Dark Matter that is in doubt, since the LHC, cryogenic Xenon and several other approaches have not discovered anything significant, to date.
- there is still a small minority of cosmologists investigating various versions of MOND, but that is considered a real outlier, at present
- See: https://en.wikipedia.org/wiki/Dark_matter#Detection_of_dark_matter_particles

Now draw a second diagram with the Milky Way added. We are looking at the galaxy side on so the diagram looks like this:             -----------------------O----------------------

This diagram is intended to show the mass distribution of the galaxy
- the central "O" might represent the Milky Way's somewhat anemic galactic bulge, which has a greater mass than the central black hole itself.
- However, this diagram shows only around 20% of the Milky Way's mass; 80% of it is in the form of a Dark Matter halo, which is believed to be roughly spherical, and with the same centre as the "O" above
- Studies of gravitational lensing in other galaxies confirms that this mass exists far beyond the visible plane of a spiral galaxy
- The Euclid spacecraft is aiming to better map the distribution of Dark Matter around distant galaxies, focusing on a population of galaxies at a distance of about 10 billion light years.
- See https://en.wikipedia.org/wiki/Euclid_(spacecraft)#Scientific_objectives_and_methods

How much does the shape of the galaxy help keep the outer stars in place?

A lot.
It is the 80% of mass in the spherical Dark Matter halo which prevents the visible stars of our galactic disk from flying off into intergalactic space.

[Eternal Student]

Hi.

Looks like an intersting post but I'm not sure I fully undrestand what was being done.   What I think you were trying to do was use some ideas about the density of field lines in a diagram of an E-field or B-field to assess the strength or magnitude of the force at a given place.

Realising that gravity is not a force one could never the less draw lines, from a massive object, somewhat corresponding to electrical or magnetic lines that we are used to in diagrams.

   In the rest of your description, it does sound like your "lines" are field lines much as used to represent a magnetic / electrical field around various sources.

    We don't tend to use the same sort of diagrams for gravity because it has no sink for the field lines.  Electric fields have a positive and negative charge that are a source and sink for the field lines.   Magnetic fields have North and South poles that serve the same purpose.   There is no negative mass and therefore no sink for gravitational field lines, only sources.  However, that's not too much of a problem and you could draw field lines if you wanted to. 
    We would need to be careful to note that gravity is an attractive force.   When we say that an electric field originated from a +ve charge, we draw a field line with a direction that does come out from the source.   For gravity we may say that the gravity originated from a mass but the lines of force will always be directed into that source and not away from it.  We may imagine there is some "thing", some graviton particles maybe, that is coming out of that source but we'll usually draw the field line diagrams where the direction on the field lines indicates the direction of the force.

But because the stars in the galaxy are curving space the other lines must be drawn starting out going directly away from the blackhole but curving towards the galactic plane.

    That's a blend of ideas that you'd have to be carefull with.  If you use only Newtonian gravity as your model, then curving of space is not considered.  The stars can only be sources of the attractive force of gravity and not sinks.   We can find the net force at a place by adding the forces due to the BH and the star individually.  The field from the central BH was, let's say in   this  \    sort of diagonal direction on a diagram.    If you now add a star, the field originating from the star can only bend those field lines away from the galactic plane and not towards it.
   Here's a (badly sketched) diagram that shows some of the field lines you could draw.


field lines from BH and a star.jpg (75.13 kB . 1164x655 - viewed 669 times)

   If you use GR as your model of gravity, then you can consider the curving of space.   However, the details probably fall outside the scope of a short forum post.

Am I correct so far? I think this means additional gravity from the black hole the further you get from the blackhole.

   If the field lines from the BH were curved toward the galactic plane then the density of those field lines increases at that place.  However (with Newton) what you would identify as field lines originating from the BH seem to be cuved away from the galactic plane by the star.

Best Wishes.

[Eternal Student]

Here's a better diagram someone else has drawn (and I just copied from the internet).   This was for an electric field with charge Q ≈ 3 times the magnitude of charge P.    A gravitational field would have the arrows on the field lines pointing inwards to the sources.     The radial field lines that the big mass (or charge) would produce on its own are seen to be bent away from the other source.

field lines.jpg (31.85 kB . 440x331 - viewed 658 times)

[alancalverd]

Beg to differ! Whilst like charges repel, all known masses attract, so the gravitational field density between masses would look more like the electric  field lines between opposite charges.

[Eternal Student]

Hi.

   I would ask if you're sure but this might be an engineer thing, maybe you have a different set of conventions for fields and diagrams of field lines. 

Here's a diagram from Wikipedia:

  That diagram is the representation for the gravitational field of the Earth and Moon combined.   Blue lines are field lines,  orange lines are lines of equi-potential.
Further description available here:   https://en.wikipedia.org/wiki/Gravitational_field

Best Wishes.

[alancalverd]

That's better! The arrows are pointing towards the masses, and indicate a mutual attraction.

Fundamental rule of astronomy: gravity sucks! 

Unsolved problem of physics: why?

[Eternal Student]

Hi.

Fundamental rule of astronomy: gravity sucks!

   The fundamental rule for myself is that I can't draw diagrams well and borrow them.

Here's a better diagram someone else has drawn.....  A gravitational field would have the arrows on the field lines pointing inwards to the sources.

The arrows are pointing towards the masses, and indicate a mutual attraction.

   No they don't.  How do you see that?   
The moon and earth would seem to be pulled to themselves and not each other if they follow the field lines. 

Best Wishes.

[alancalverd]

Well at least there is a field line connecting the two barycenters, but I admit to being unable to devise an obvious  "mutual attraction" symbol consistent with the other field vectors!

[evan_au]

Blue lines are field lines,  orange lines are lines of equi-potential.

So the blue lines are the path taken by a 1kg test particle if you released it at that point (in the reference frame of the diagram).
And the orange lines are where a cloud of 1g test particles could wander if you released them with a range of small velocities  (in the reference frame of the diagram) (Correction from Eternal Student).

I admit to being unable to devise an obvious  "mutual attraction" symbol consistent with the other field vectors!

Perhaps the problem is that all field lines are shown as being equivalent?
- But a test particle 500km from the Earth feels a force 4 x greater than a test particle 1,000 km from the Earth.
- And the field line linking Earth and Moon is shown just as thick as the field line linking the Earth and Mars, when in fact the force of attraction between Earth and Moon is far greater and the force between Earth and Sun is greater again (even though Moon and Sun generate tides of similar height on Earth).

To show the strength of attraction, you might:
- Show the blue lines with greater thickness as you approach the Earth (representing the force on a 1kg test particle)
- Show the orange lines closer together as you approach the Earth (the closer the lines, the greater the force on a 1kg test particle)
- Recognise that most of space isn't populated with1kg test particles, and just draw in the blue lines between astronomical bodies, so you would have:
      - A thick line linking Earth & Moon
      - A thicker line linking Earth & Sun
      - A thinner line linking Earth and Mars
      - The thickness representing a Newtonian attractive Force
     - I suggest a logarithmic thickness, as the gravitational forces span many orders of magnitude!!

[Eternal Student]

Hi.

So the blue lines are the path taken by a 1kg test particle if you released it at that point (in the reference frame of the diagram).

   Yes.   That's the right idea.
   Formally, they show the (direction) of the force that woud act on a unit (1 Kg for gravity) test mass.
   
    A field line is constructed by starting at a point and then tracing a line through space that follows the direction of the vector field (the gravitational field in our example).  You take small steps in the direction of the field and then re-determine the direction of the vector field in this new place,   then take the next step in that direction  etc. etc.
     Take very small steps and many of them, this is how a computer would numerical solve the problem to create a field line diagram from a given vector field.  Analytically, the vector field F(x) will be tangent to the field line at every point x along the field line.

    Keeping in mind then that the gravitational field shows only the force that would act on a unit mass, we see that a particle won't neccessarily follow a path along those field lines,  it depends on what the initial velocity of the particle may have been. 
    If you dropped a particle into the space so that it started with 0 initial velocity,  then it certainly does proceed along the field lines for a while.   If you assume some drag (e.g. friction) or else stop it again quite often, then it would move along the field lines for ever (unless it hits something solid or the field line terminates).
   Informally we can and do say a test mass would move along the field lines if it was released there  (we just tacitly understand "released at 0 velocity").

And the orange lines are where a cloud of 1g test particles could wander if you released them with a range of small velocities  (in the reference frame of the diagram)

   Umm... I've never heard that description but it could work.   You may need to ask the dust particles to ignore any forces that act on them (and thus not to change their kinetic or potential energy at all).   If they agreed, then sure... they will only be able to wander off somewhere that stays on the same orange line they started on.
   If they insist on following the laws of physics, then they're going to go along the field lines.   Being only 1g won't help,  the force on them is less but their inertia is less in the same proportion.

And the field line linking Earth and Moon is shown just as thick...

   @alancalverd probably started this....   but you can't highlight every minor issue and I'm very grateful for all replies and contributions.

Well at least there is a field line connecting the two barycenters...

   Technically, there isn't any field line linking the earth to the moon in the diagram.   The point labelled P on the diagram is excluded  from any field line because the gravitational field vector there would be 0 and no unique direction can be allocated.  Specifically, the tangents we would want to calculate are undefined and we cannot include that point in any field line.

To show the strength of attraction, you might:
- Show the blue lines with greater thickness as you approach the Earth

     This is another absolutely outstanding idea.   Thank you for suggesting it.
     Diagrams with thicker or longer arrows already exist.   Different coloured plots can also be used.
They're usually called    "Vector field diagrams"  which isn't very different from what is being talked about here and usually called a  "Field line diagram".    Indeed the terms  "field line" would be exchanged with "streamline" if the vector field was representing some flow (of fluid) that exists in space instead of some force existing in space.
   The relationship between the two is apparent and there's hardly any need to have clearly different names for the diagrams.   Here's a diagram showing a 2-D vector field represented with red arrows and some streamlines (or field lines) shown in blue.   Hopefully, it illustrates the clear connection between the two.   Exactly as you suggested, in many ways the arrows tell you more than the field lines do.


 

Show the orange lines closer together as you approach the Earth (the closer the lines, the greater the force on a 1kg test particle)

    There is no fault to be found here, it's a great idea.
    It is exactly as you describe.  Draw the lines of equipotential at every 1 unit increment and everything will follow as described.   This is usually done.

Recognise that most of space isn't populated with1kg test particles, and just draw in the blue lines between astronomical bodies....

    We can certainly draw our own diagrams and illustrate things sensibly.   However it is not in my power to change the thing that is officially called a "Field line diagram" and add field lines where I please.

- - - - - - - -
Some more information that can be in a field line diagram
     Field line diagrams have a convention that can illustrate the strength of the field at places.   Although you could choose to start a field line (or streamline) anywhere and see where it goes,  you don't.    For simple situations, like the field lines originating from a point charge we have this:

  Where you can clearly see that the lines are getting closer together as you approach the charge.    The convention is to continue using the density (or closeness) of field lines as an indication of the field strength in that region.
   In the earth and moon example earlier,  this convention was followed and you can see the blue field lines are very far apart (low density) around the point labelled P.   The blue lines become much closer (high density) as you approach the earth.
    In some school physics classes (for about age 16 in the UK), you would be allowed to count the number of field lines crossing a patch of space as an estimate of the flux (they may not use terms like "flux").   For that, the convention must be strictly observed but it does give you a method to show the inverse square law for field strength quite easily.

    This is what I think, the OP  ( @set fair ) was asking about......

I think this  (... gravitational field lines curving in toward the galactic plane to form a high density of field lines...)   means additional gravity from the black hole the further you get from the blackhole

   All the italics  is my paraphrasing.

Best Wishes.

[evan_au]

You may need to ask the dust particles to ignore any forces that act on them (and thus not to change their kinetic or potential energy at all).

Oops! Thanks for pointing this egregious error!

I was thinking of what happens to a comet as it orbits the Sun. Dust released at a low velocity by the comet spreads out along the comet's orbit. But the comet's path does not follow equipotential lines around the Sun...

I'll mark up my post...

[alancalverd]

Gentlemen: the mass of the test particle is irrelevant as long as it is much less than the mass of the two principal bodies. All particles follow the same path with the same acceleration (Galileo).

As soon as the particle mass is significant, we run onto complicated 3-body dynamics, also known as observational astronomy!   

[Eternal Student]

Hi.

Thanks for your input @alancalverd .   You could be doing other things and we appreciate your time.   I'm fairly sure you make some comments just to give someone else something to discuss and that is a noble gesture.

As soon as the particle mass is significant, we run onto complicated 3-body dynamics

   No we don't.   By definition a "test mass" or "test particle" is an idealised concept and has no effect on the field.

the mass of the test particle is irrelevant as long as it is much less than the mass of the two principal bodies for almost everything.
   If we had a real particle with significant mass, we run onto complicated 3-body dynamics.....

I think we're waiting for some more input from the OP ( @set fair ) but it's a quiet day and rather than going outside and tagging my name on a bus shelter I'm going to read it again and maybe go in a different direction.

Best Wishes.

[alancalverd]

   No we don't.   By definition a "test mass" or "test particle" is an idealised concept and has no effect on the field.

A 1kg test mass, as specified by evan in reply #11 is not an idealised concept but a precisely machined lump of material, pretty much as used by Cavendish in establishing G.  A 1kg asteroid could eventually form the nucleus of a new planet, or wander off and become one hell of a meteor, depending on the outcome of random multi-body interactions.