The centripetal force for an object moving in circular motion is:
[tex]F=m \frac{v^2}{r} [/tex]
where m is the mass, v the speed of the object and r the radius of the orbit. For Newton's second law, this is equal to
[tex]F=ma_c[/tex]
where [tex]a_c[/tex] is the centripetal acceleration. So we can find the centripetal acceleration by equalizing the two equations:
[tex]a_c = \frac{v^2}{r} [/tex]
Since we know the value of the centripetal acceleration of the rocket, [tex]a_c = 9.8 m/s^2[/tex] , and the radius of the orbit, [tex]r=6.381 \cdot 10^6 m[/tex], we can solve the previous formula for v, the speed of the rocket:
[tex]v= \sqrt{a_c r}= \sqrt{(9.81 m/s^2)(6.381 \cdot 10^6 m)}=7912 m/s [/tex]
