# Why are orbits around a black hole not elliptic?

Most of the pictures of a black hole are like this:

Source: https://cdn.mos.cms.futurecdn.net/HsDtpFEHbDpae6wBuW5wQo-970-80.jpg.webp

Why are the orbits around it not elliptic? Is there any other force in addition to centripetal force?

• The answers are correct, but also: the two-body problem, with gravity as centripetal force, results in orbits that are any conic section, not just circles. Circles are more like a special case of the elliptical orbits. Feb 5 at 20:35
• I that's your thing you can watch this video by Veritasium for an explanation of what you're seeing there. Feb 5 at 22:38
• Note that the image in the question is an artists rendition, not a product of astronomical imaging. Feb 6 at 15:56
• @ErinAnne then again, we're definitely not dealing with a two-body problem here. Feb 6 at 17:52
• @U.Windl It is, but probably based on simulations such as this one that model the conditions near black holes. As far as I know, no one has yet taken a real photograph with enough resolution to see these effects. Feb 8 at 21:52

What this image depicts is the gravitational lensing created by the black hole. Light that passes close to a strong gravity source is distorted by it into characteristic ring-like shapes. (You can see many visualizations and examples on the linked page.)

The actual shape of the accretion disc shown in the image is, well, a disc, made up of particles orbiting in the normal elliptical way. In the foreground, you can see the structure of the accretion disc as it really is, a large flat cloud made up of distinct bands, like a planetary ring formation.

In the background, the disc has the same shape, but the observer's view of it is distorted by the black hole's gravity. The more distant parts of the disc, which are less distorted, are still identifiable as continuous rings, albeit bent. The nearer parts, which are more heavily distorted, are seen as a classic Einstein ring. The large segment that appears almost detached from the disc is actually a heavily distorted view of the material that's directly behind the black hole (from the observer's perspective).

• Cool. Is there anything to say on where the asymmetry comes from? I.e., the disk on the right-hand side is very bright compared to the left-hand side in this image. Is this just artistic freedom, or does this represent some physical aspect?
– AnoE
Feb 6 at 10:07
• @AnoE the disk on the bright side is moving towards the observer, whilst that on the dim side is moving away Feb 6 at 10:47

What you are seeing "bent" around the black hole is light from the accretion disk the path of which is warped by traveling close to the black hole. We see a distorted view of what is "behind" the black hole or really any light that passes near the even horizon. The black hole acts as a gravitational lens; it's not that the orbits are not ellipses (at least in the non-relativistic limit) or that the accretion disk is not flat, but our view of them is distorted.

The illustrations you reference are based on computer simulations, but they match with actual observations from the Event Horizon Telescope.

• Besides light being bent I think the matter around a black hole is either in a non-circular orbit or even has its orbit changed as it goes around. The vicinity close to a black hole is a pretty dynamic place as the plasma interacts with other plasma and the strong magnetic fields. This was seen in the recently released second photo of the M87 black hole which was taken in 2018, a year after the first image. Feb 5 at 14:44

# Photon Ring

While other answers describe the gravitational lensing effects of a black hole, the full picture is far more dramatic. Lensing, as the name implies, only affects an image that is already headed in roughly your direction to begin with. The lens focuses additional light rays that would otherwise pass you by but are still from a singular source.

As you likely know, light itself cannot escape a black hole, which means there is a radius at which it is perfectly balanced between escaping and falling into the hole. This is called the photon sphere. What this also means is that light from some source outside the BH may approach it and be deflected to any arbitrary angle via a partial orbit. It also means that when you see a photon from the region of the sphere, you actually have no idea where it came from. It might have come from a source on the opposite side of the BH, as in an Einstein ring, or it may have come from a completely orthogonal direction, like your left side, orbiting a quarter turn and then hitting your eyeball. You may collect a bundle of photons over an arbitrarily small solid angle that come from all different directions. As you can imagine, this goes well beyond what is possible with conventional "gravitational lensing".

If you were to hover near the photon ring (facing tangent to the photon sphere), it is theoretically possible to shine a light on the back of your head, whereupon the photons orbit the BH, and enter your eye. Thus, you could see the entire back of your body without the aid of any mirrors.

Note that I call it a "photon ring" as that is often used in non-technical descriptions because that is how we presume it would appear. Photons would, of course, orbit all around the black hole in every direction as a sphere; but from any given vantage point, none of the photons from the sphere would appear to come from the "interior" of the sphere. Hence, it would appear visually as a ring. And, of course, outside the ring you would see all the "normal" gravitational lensing effects typical of a very dense object.

• The "you could see the entire back of your body" is overly theoretical – if you are near the event horizon, you can't really hover. For small black holes, you'd be spaghettified already, for bigger ones the light orbiting around has such a large distance that what you see is smaller than your eye can percept (and be mixed up by all kinds of other light). Feb 6 at 20:30
• It's not just partial orbits. Photon trajectories just outside the photon sphere may orbit the black hole multiple times before escaping. Such paths aren't possible in Newtonian gravity: you'd just get a hyperbola. Here's an example of 600° deflection around a Schwarzschild BH, computed with high precision arithmetic using an elliptic integral. Distance is in Schwarzschild radius units. i.stack.imgur.com/2kiPb.png I have some details (& more diagrams) at physics.stackexchange.com/a/680961/123208 Feb 14 at 2:32

All the other answers do a good job of addressing the main point of the question, which is why the image of an accretion disk looks the way it does. But it is also true that orbits around a black hole are noticeably different from ellipses, provided they are close enough. They are still in a plane, so you wouldn't notice the difference in an image of an accretion disk. And the orbit is still like an ellipse, but it precesses; the point farthest from the black hole moves a little bit forward each orbit. So it's kind of a flower appearance, rather than a simple ellipse.

This phenomenon doesn't only appear with black holes. Mercury is close enough to the sun that this precession phenomenon was detected in the 1800s and helped convince Einstein he was on the right track with general relativity. But, with black holes, it's possible to get close enough for this phenomenon to be very pronounced.

I don't know whether the picture you posted is supposed to be a realistic simulation. I suggest reading this article which contains pictures from a realistic simulation. I think this picture from the article explains things well. Like many others have commented, gravitation bends the path of the light, so what you see does not represent the true orbit of the matter around the black hole.