A particle is launched from the surface of earth with speed v. For the particle to move as a satellite, which statement is correct?

$\frac{v_{e}}{\sqrt{2}} < v < v_{e}$

$v_e=\sqrt{\frac{2 G m}{r}}, \quad v_0=\sqrt{\frac{G m}{r}}$, we have

$v_0<v<v_{e}$

$\Rightarrow \frac{v_{e}}{\sqrt{2}}<v<v_{e}$

$\left\{∵ v_0=\sqrt{\frac{GM}{r}}  ~\text{and}~  v_{e}=\sqrt{\frac{2 GM}{r}}\right\}$