Centripetal acceleration is given by the formula
[tex]a_{cen}= \frac{v^2}{r} [/tex]
Since we know the value of the acceleration is 9.8 m/s² and we know r, we can solve for the speed, which is the magnitude of v. Note the value of a is just the acceleration due to gravity, which is what makes the rocket orbit and not fly off into space.
[tex]9.8 \frac{m}{s^2}=\frac{v^2}{6.381 \times 10^6m} \\ \\ 9.8 \frac{m}{s^2} \times 6.381 \times 10^6m=v^2 \\ \\ v= \sqrt{9.8 \frac{m}{s^2} \times 6.381 \times 10^6m} =24755 \frac{m}{s} [/tex]
