# Which force is required by a satellite revolving around the earth?

Since centripetal force is the inward force required to keep an object moving with a constant speed in circular path and centrifugal force is the apparent force that pulls an object from its centre or axis of rotation.

So...is a satellite revolving around the earth kept on its orbit by both centripetal and centrifugal force? Or only centripetal force

As I was taught back in school that a satellite requires both centrifugal and centripetal force, but personally, I think it should only be centripetal force, since the satellite still revolves around the earth, so where does centrifugal force come in?. Because the only reason a satellite could be pulled from its axis of rotation is if maybe an asteroid were to hit it or some other reasons.

## 4 Answers

Which force is required by a satellite revolving around the earth?

In the context of the currently accepted theory of gravity, General (theory of) Relativity, the answer is no force is required.

Consider the case of a ball forced into uniform circular motion due to a string. According to an accelerometer attached to the ball, there is a constant magnitude acceleration directed towards the center of the circular path; this is the centripetal acceleration required for uniform circular motion. The centripetal force responsible for the acceleration is from the tension in the string.

Now, consider an accelerometer attached to a ball in a circular orbit around the Earth. We might expect that the accelerometer on the ball reads the centripetal acceleration but, in fact, the accelerometer (ideally) reads zero! Evidently, there is no net force acting on the orbiting ball. Why then does the ball follow a circular path?

On the GR view, the ball is following an unaccelerated path (geodesic) in spacetime that is curved by the mass of the Earth (Spacetime tells matter how to move; matter tells spacetime how to curve).

The truth is that for a satellite revolving around the earth ,both centripital and centrifugal forces are required . Because while the body moves in a circular path its velocity at a point is along the tengent drawn from that point which gives rise to the centrifugal force and in the case of a satellite the centripital force is given by the gravity of earth and centrifugal force is given by its velocity. And if there was no centrifugal force the sattelite must fall on earth .

• I appreciate your answer but is there a way you could back up your answer with a reference? – Prince Nov 24 '16 at 15:12

True, there is only the centripetal force, which is the gravitational force keeping the body in orbit. The body is continuously falling due to the force, but it also has momentum perpendicular to the radial direction, so it orbits (I assume you know these details).

The centrifugal force is added in analysis if you are in the frame of reference of the body, or frame of reference where it moves in a straight line It is then an non-inertial (accelerating) frame which does not follow Newton's second law,ie, the centripetal force is acting on the body, but it is not moving towards it (in it's frame)! To counter this, a fictitious force is added, equal and opposite to the real centripetal force, and that is the centrifugal force.

The case is similar to how the direction of cyclones rotating is explained by the coriolis force in the Earth's frame of reference. Is is more convenient than taking the real intertial frame and studying the earth's rotation explicitly.

To put it simply, it's centripetal force that is keeping the satellite in orbit.

But let's understand the terminology a little bit more. The satellite is in space, and it's being pulled by Earth's gravity. The direction of this gravitational force that the Earth exerts on the satellite is center seeking, and we dub this force the centripetal (meaning center seeking) force.

But if you're on the satellite, you feel weightless. You look out and you see Earth. You say: "Hmm, Earth's there, so gravity should be there". So being a good Newtonian physicist you draw a free body diagram. But you realise that the only way you can be weightless is that there must be an outward seeking force, dubbed as centrifugal force, that is canceling the gravitational force. But the cause of this force is not known, if it's there at all. It turns out that being in the accelerating satellite means that you are not in an inertial frame, and this centrifugal force is a fictitious force.

When to use which terminology depends on your frame of reference. You have to be very clear on which frame of reference you are working in, but personally I just stick to the centripetal force interpretation.