The velocity of a satellite in a circular orbit can be determined using the formula $v = \sqrt{g \cdot r}$, where $g$ is the acceleration due to gravity and $r$ is the distance from the center of the Earth. Given $g = 10\,\mathrm{ms^{-2}}$ and $r = 6.4 \times 10^{8} \, m$, substituting these values yields a velocity of approximately $8.0 \times 10^{4} \, \mathrm{ms^{-1}}$. This demonstrates the relationship between gravitational force and orbital velocity, highlighting how the distance from the Earth's center influences the speed required to maintain orbit.