Question

A rocket in orbit just above the atmosphere is moving in uniform circular motion. The radius of the circle in which it moves is 6.381 × 106 m, and its centripetal acceleration is 9.8 m/s2 . What is the speed of the rocket?

Answer 1

The centripetal force for an object moving in circular motion is:

`F=m (v^2)/(r)`
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

`F=ma_c`
where
`a_c` is the centripetal acceleration. So we can find the centripetal acceleration by equalizing the two equations:

`a_c = (v^2)/(r)`
Since we know the value of the centripetal acceleration of the rocket,
`a_c = 9.8 m/s^2` , and the radius of the orbit,
`r=6.381 \cdot 10^6 m`, we can solve the previous formula for v, the speed of the rocket:

`v= √(a_c r)= √((9.81 m/s^2)(6.381 \cdot 10^6 m))=7912 m/s`