Orbital parameters of stars orbiting Sagittarius A*

[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