B Orbital parameters of stars orbiting Sagittarius A*

[tony873004]

Nice! I like glow of the stars.

 

[jimbo007]

Thanks for the link Loren I will check it out and yes would be to compare. I am going to try and create a more 3 dimensional perspective like Janus's and get the camera zoom around with some smoke/fog effects if I can ever figure out how to get it working. The smoke/fog is turning out to be a big CPU hog so have to try to work out some shortcuts

 

[m4r35n357]

I made it years ago for my original Gravity Simulator software. The version you see is the newer "browser" version. It uses the same data. So the data in my sim is at least 6-7 years old. It was orbital elements data. I converted it to Cartesian. Here's an online calculator I made that converts between the two:
http://orbitsimulator.com/formulas/OrbitalElements.html

Since my simulation is a web page, you can view the source and get all the cartesians in one glance. Search the code for "objMass[1] ="

There's probably more recent data. The Wikipedia link doesn't give enough data to make what I made. Over the weekend I'll see if I can find more complete and current data.

edit: I just saw the table in Janus' reply. Let me know if you need help making cartesians out of that.

Pardon the bump, but I was recently involved in another thread (which I now can't find) where someone else was asking for just this information and it did not seem to be available. I stumbled across this thread by accident!
I have a simulator suite that does black hole orbits and an (unadvertised) Newtonian n-body simulation, and the latter takes a list of Cartesian state vectors as its input (I already have data for the Solar System from NASA's Horizons facility).
Now I can start to look at the galactic centre . . .
[EDIT 1] OK I see it is Solar System data, but I hope there is galactic centre stuff somewhere in this thread if I dig deep enough.
[EDIT 2] Now looking at your simulator, precisely how does one pause it?

 

[tony873004]

[EDIT 2] Now looking at your simulator, precisely how does one pause it?

There is a [||] button on the left of the screen.

 

[m4r35n357]

I made a mistake above with E. I'll fix it in a minute.

on second thought, that's too much algebra for me tonight to isolate E. from that equation!

Ah, the only button I didn't click on for some reason ;) Thanks, will investigate now.
[EDIT] BTW do you have mass data for the bodies? If not I'll have to see if I can look it up somewhere.

 

[tony873004]

I don't have that data. I imagine you'll just have to approximate based on the color of the stars.

 

[m4r35n357]

Ah, sorry I didn't mean to post that, was just looking at the source! Yes I notice that only the BH seems to have mass. Does that mean you are doing some sort of n body Kepler analysis?

 

[m4r35n357]

Using my normal POV-Ray method, here's an animation that gives a more three dimensional perspective of the respective orbits.

Would it be possible for you to provide me a list of body masses, and a snapshot of their coordinates and velocities? I'd love to try this out.

 

[Yukterez]

the orbit simulator I have on my computer (Gravsim)

What metric does that simulator use, Newtonian or relativistic? Orbits around black holes can look much different under Einstein than they would under Newton as shown in this thread where the same initial conditions give very different results for Newton and Einstein: Black hole orbits
Since it says n-body in the description I guess it is Newtonian, but maybe it would be better to simulate the orbits as test particles in Schwarzschild metric to get the right eccentricity and perihelion shifts. But that depends on which effect is stronger: the mutial attraction of the orbiting stars reative to each other or the relativistic effect of curved spacetime generated by the central black hole (which is only the case if the orbits get close enough so that the ratio rs/r is not neglible).

 

[m4r35n357]

But that depends on which effect is stronger: the mutial attraction of the orbiting stars reative to each other or the relativistic effect of curved spacetime generated by the central black hole (which is only the case if the orbits get close enough so that the ratio rs/r is not neglible).

I think bearing in mind the very short observational period we are working with, any effects due to particles outside about $10R_s$ to $100R_s$ would be "lost in the noise", so I'm comfortable with a Newtonian approach. Not that I feel we have much choice in the matter ;)

 

[Yukterez]

I think bearing in mind the very short observational period we are working with, any effects due to particles outside about $10R_s$ to $100R_s$ would be "lost in the noise", so I'm comfortable with a Newtonian approach.

When the observed velocity at the perihelion at 10rs is for example 0.2236068c there would be a notable difference between the Newtonian and the relativistic orbit:

So if the closest perihelion were at that distance it might be better to neglect the mutual attraction of the orbiting stars and threat them as test particles, but therefore take the relativistic metric of the black hole into account, but if the closest perihelion were at 100rs it's surely better to stay with Newton.

Not that I feel we have much choice in the matter

We could simulate it in Schwarzschild metric (if the simulations we already have aren't already)

 

[Yukterez]

I see at Wikipedia that the lowest orbit has a semimajor axis of around 1000 Au while the rs of the black hole is only 0.1 Au. In that case there is no need for a relativistic simulation and Newton does the job.

 

[Janus]

I see at Wikipedia that the lowest orbit has a semimajor axis of around 1000 Au while the rs of the black hole is only 0.1 Au. In that case there is no need for a relativistic simulation and Newton does the job.

With the listed eccentricity, I get a precession of apsides of ~ 0.17 degrees per orbit. With a 14.53 year orbit, this works out to ~30500 years for the apsides to rotate a full 360 degrees. ( Compare this to the 43 seconds of arc per century precession for Mercury, which would take ~3,000,000 years to complete a full rotation.)

 

[m4r35n357]

When the observed velocity at the perihelion at 10rs is for example 0.2236068c there would be a notable difference between the Newtonian and the relativistic orbit:

Agreed, but my point was we don't have enough actual data to check our predictions accurately against (order of 15 year orbits).

So if the closest perihelion were at that distance it might be better to neglect the mutual attraction of the orbiting stars and threat them as test particles, but therefore take the relativistic metric of the black hole into account, but if the closest perihelion were at 100rs it's surely better to stay with Newton.We could simulate it in Schwarzschild metric (if the simulations we already have aren't already)

Yes, I suppose we could use the potential (with extra term due to GR) in a n-body simulation. We would also need to consider interactions between stars that pass nearby each other around the perihelion (we'd need to use that potential for all the stars), so I'd call that a modified Newtonian analysis really.
Then what if the black hole is spinning?

 

[jimbo007]

Interesting animations by Yukterez, unfortunately it's a bit beyond me to calculate relativistic orbits at the moment

Below is my 2nd attempt at a simulation using more stars