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Statement

$1.3.21.$ At what speed should a satellite fly in order to move in a circle while "falling" to the Earth with acceleration $g$? Assume the orbit radius $R = 6400$ km and $g = 10$ $\frac{m}{s^2}$.

Solution

Equilibrium condition: centrifugal force compensates for gravitational force

$$ mg = \frac{mv^2}{R} $$

Where, the desired speed

$$v = \sqrt{gR}=8\text{ km/s}$$

Answer

$$v = \sqrt{gR}=8\text{ km/s}$$