A satellite moves in a circular orbit around the Earth of radius $r = 10000$ km. The acceleration due to gravity in this orbit is $g \approx 4$ m/s². Find the linear speed of the satellite.
The gravitational force acts as the centripetal force:
$$mg = \frac{mv^2}{r} \Rightarrow v = \sqrt{gr}$$
$$v = \sqrt{4 \cdot 10^7} = 2 \cdot 10^3 \cdot \sqrt{10} \approx 6325 \text{ m/s}$$
$v \approx 6325$ m/s