Time Dilation & Visual Observation of Black Holes

[EskWIRED]

I'm under the impression that one sees clocks slow down when watching distant objects approaching strong sources of gravity, such black holes. And that objects in an elliptical orbit travel faster when they are near their attractor.

I can't quite figure out how these two phenomenon work together when an such an object travels close to a black hole.

If one were to watch a star orbiting a supermassive black hole, might it appear to slow down, rather than speed up at its closes approach, given sufficient time dilation close to the event horizon?

 

[PeterDonis]

If one were to watch a star orbiting a supermassive black hole, might it appear to slow down, rather than speed up at its closes approach, given sufficient time dilation close to the event horizon?

There are no stable orbits inside a radius of three times the horizon radius, and no free-fall orbits at all, even unstable ones, inside one and a half times the horizon radius. Even the latter radius is not close enough to the horizon for gravitational time dilation to counteract increasing orbital speed.

 

[EskWIRED]

Thanks.

Does time dilation need to be taken into account when observing or making calculations concerning stars orbiting the black hole at the center of the Milky Way? Or are they far enough away at all times that time dilation can be ignored?

 

[PeterDonis]

Does time dilation need to be taken into account when observing or making calculations concerning stars orbiting the black hole at the center of the Milky Way?

AFAIK, no. None of them are close enough for it to be a significant factor.