Gravitational force \((F)\) provides the necessary centripetal force to keep the satellite in orbit,

\(\Rightarrow \frac{m v_0^2}{r} \propto F\)

\(\frac{m v_0^2}{r} \propto r^2\)

\(v_0 \rightarrow \text { Orbital speed }\)

\(r \rightarrow \text { Radius of orbit }\)

\(\Rightarrow v_0 \propto r^{3 / 2}\)