How much mass does it take before photons will have a stable orbit?

[smorningstar]

This is my first post so I hope I'm putting it in the right section
I searched for similar questions but could not find one.

Edington preformed his experiment where he observed the bending of light around the sun due to gravity.
I have been thinking this past weekend about a hypothetical situation.

What would happen if we had an extremely large mass and tried putting light into its orbit?
A spaceship can orbit the Earth with the right speed and altitude. So why can't we do this with light? (besides for it being non-practical in size.) If so what would it look like. Would it look different, Would we be able to add more photons to it? Is there a limit to how much it can hold, similar to are atmosphere and the amount of satelites that can be placed in it. What would happen with any light escaping from the mass?
What are your thoughts?

Many thanks,
smorningstar

 

[vin300]

"photon sphere" in library items
https://www.physicsforums.com/library.php?do=view_item&itemid=268"]

 

[Born2bwire]

We already have something that can do this, a black hole, assuming that it's gravity potential is appropriately symmetric. Photons are bosons, multiple photons can exist in the same state. Not that orbiting photons could really be classified as a simple quantum state, we can extend the idea to that photons do not interact with each other very much. So I do not see that much of a limit to how many photons you pack into an orbit. Unlike an object with mass, they will not bump into each other nor will they generate their own gravity field (as far as I know) that will affect the entire system.

 

[smorningstar]

Thank you, now I understand it a little better.
However from what i read a black hole is always increasing its size up until a certain point. What if it was not a black hole that pulled everything in but was just a giant solid sphere of lead with a mass similar to a black hole? However the difference is one would be much more stable.

Or would it have such a high mass that it would collapse on itself?

Thanks

 

[Born2bwire]

Well, regardless of whatever it is, it is going to end up essentially being a black hole. The gravitational potential is going to be 1/r and light will always travel at a speed of c. If you have a strong enough gravitational potential at some radius R to give light a stable orbit, then obviously any radius less than R will be strong enough to pull light into the gravity well. If you have any kind of sphere of density and mass high enough to be similar to a black hole, then I doubt it is going to behave any differently from a true black hole.

 

[stevebd1]

The critical radius for an object of mass is considered to be r₀=9M/4 (or 2.25M) where M=Gm/c², which puts the radius inside the photon sphere (3M), based on this, some neutron stars on the brink of collapse are considered to have photon spheres (though based on the densities involved, they might be quark stars).