Let's say there's some satellite revolving around the Earth. Its orbital velocity would be

$$v=\sqrt{\frac{GM}{r}}.$$

Evidently, this is independent of the distribution of the mass of the earth, and that implies that even if we manage to compress the Earth to the Schwarzschild Radius, it will not affect the motion of the satellite. But I find it hard to believe that there's a black hole right there but the satellite is revolving as usual. Am I going wrong somewhere?