# Gravitational sphere

I was reading this article that mentions a blackhole as having a gravitational sphere of 4,000 light-years.

I'd not heard of the term (gravitational sphere) before so looked it up, and it looks like a simple definition is the same as sphere of influence and according to Wikipedia is

A sphere of influence (SOI) in astrodynamics and astronomy is the spherical region (actually is an oblate sphere) around a celestial body where the primary gravitational influence on an orbiting object is that body.

From the above, I take it to mean that an object could be tiny, but providing there are no objects anywhere near with another object with a bigger gravitational pull near them, then its sphere could be larger than a more massive object. i.e. I can't directly look at a gravitational sphere of 4000 light-years and think "that must be a huge object".

Is my understanding correct?

$r_h = \frac{G M_{BH}}{\sigma^2}$
where $\sigma$ is the stellar velocity dispersion, $G$ is the gravitational constant and $M_{BH}$ the mass of the BH. As you can see the radii of the SOI is dependent on the mass of the BH in this equation.