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Imagine that we have a system that consists of a massive black hole, and the asteroid revolving around it on a stable orbit. What method can determine the distance to these asteroids observer who is still close to the event horizon?

The first thing that came to mind is to determine the signal propagation time to the asteroid and back. This time is equal to:

##\Delta \tau_{observer} = \sqrt{1-\dfrac{r_g}{r_{observer}}}

\int\dfrac{dr}{1-\frac{r_g}{r}}

##

But I do not know ##r_{observer}## and ##r_{asteroid}##

Need a different way.

The first thing that came to mind is to determine the signal propagation time to the asteroid and back. This time is equal to:

##\Delta \tau_{observer} = \sqrt{1-\dfrac{r_g}{r_{observer}}}

\int\dfrac{dr}{1-\frac{r_g}{r}}

##

But I do not know ##r_{observer}## and ##r_{asteroid}##

Need a different way.

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