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1. Feb 19, 2015

### GoBluePhysics

Hi there,

I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of $R_{min}=3R_s$ where $R_s$ is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you would need to be traveling at a velocity exceeding $c$. That's all good and dandy. However, wouldn't it be true that there exists a minimum orbit for any massive body due to the the velocity limit of c? In other words, if I am in an orbit around the earth such that my velocity is equal to $c$, what is my radius? Just something I thought up.

2. Feb 19, 2015

### Chronos

The short answer is It's the same as the photon sphere around a black hole [hint, less than the radius of earth].

3. Feb 19, 2015

### GoBluePhysics

When you say "photon sphere" do you mean the sphere created by a radius such that $r=1.5R_s$ (for a black hole)?

Wait. I think I understand. If I think of it in terms of Birkhoff's theorem, if the density of a black hole were expanded to have the density of another object (say, the earth) then the photon sphere and $R_s$ would be unmoved but they would also be inside of the object. Is that kind of the hand-wavy gist of it?

4. Feb 19, 2015

Yes.