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 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:
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 ="
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.
Ah, the only button I didn't click on for some reason ;) Thanks, will investigate now.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!
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 orbitsthe orbit simulator I have on my computer (Gravsim)
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 ;)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).
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: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.
We could simulate it in Schwarzschild metric (if the simulations we already have aren't already)Not that I feel we have much choice in the matter
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.)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.
Agreed, but my point was we don't have enough actual data to check our predictions accurately against (order of 15 year orbits).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:
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.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)