Question

In a Star Trek episode, the Enterprise is in a circular orbit around a planet when something happens to the engines. Spock then tells Kirk that the ship will spiral into the planet’s surface unless they can fix the engines. Is this scientifically correct? Why?

Answer 1

No, it is not scientifically correct. When the engine is not working, the enterprise will be moving with constant speed in a circular orbit. The gravitational pull from the earth will provide the centripetal force which will keep the enterprise is the same circular orbit becuase the speed of the enterprise won't change. Hence, if the speed does not change then the radius of the orbit will also stay constant.

m = mass of enterprise, g = gravitational pull of planet, r = radius of orbit and v = speed of enterprise

Since, the centripetal force is always perpendicular to the velocity, it won't change the magnitude od the velocity and, moreover there is no force to change the magnitude of the velocity. Hence, the enterprise will stay in the same orbit. Take an example of moon going in a circular orbit. It does not have any engine and still remains in the same circular orbit. Hence, in the same way the enterprise will stay in the circular orbit around the planet.