newtonian mechanics - Work in circular motions

Suppose that a satellite circles around a planet that exerts $2000N$ of gravitational force on the satellite.

I understand the fact that since the circular motion and the centripetal force are always perpendicular to each other, the work done by gravity is 0.

However, the satellite is being moved from one point to another, so Intuitively I am thinking "there must be some work done to move the satellite from point A to point B".

But besides the gravitational force, there is no force acting on the satellite.

Can some one explain me the gap with my logic and intuition?

Answer

I'll expand my comment here.

First, think of an object with no forces acting on it. According to $\vec{F} = m\vec{a}$ or to Newton's First Law, such an object will move in a straight line with constant velocity. This is a very important point: you do not need a force to mantain movement. Simply because an object moves from A to B doesn't mean you have to exert a force on it.

Astronauts on the ISS live in what is essentially a force-free environment (it isn't really, but it's as if it was), and if you've ever seen one of Chris Hadfield's videos, you can see that if you give anything the slightest push, it will keep on moving until it's stopped by something else.

This is all fine and dandy, but in your example there is a force acting on the object: the centripetal force which is required to mantain circular motion (remember, if the force disappeared, the object wouldn't stop; it would keep moving in a straight line). Which brings us to a subtler point: Work is defined as $\int \vec{F} \cdot d\vec{r}$, or, if you're not familiar with calculus, as $\vec{F} \cdot \vec{d}$, where $\vec{d}$ is the displacement vector.

What this tells us is that only the component of the force in the direction of motion is what matters. In the circular movement example, the force is always at right angles to the motion, and so there is no work, because two perpendicular vectors always have a dot product equal to zero.

How does this fit with the fact that the object is not moving in uniform motion but rather is being accelerated? Now we need to remember that work is the change in kinetic energy, defined as $\frac12 m v^2$. As you can see, the kinetic energy depends only on the magnitude of the velocity and not on its direction. In uniform circular motion, only the direction of the velocity is changing, because the force is at right angles to the movement. Since the speed (i.e. the magnitude of the velocity) is constant, no work is being done and the energy remains constant.

This is intuitively clear; if you put the satellite in orbit, it will keep on orbiting for all of eternity. If it was gaining energy each time it completes a full circle, very soon it would have enormous amounts of energy, and we know that's not the case, because the planets have been going around the Sun for a very long time, and we notice that their energy (in whatever form) doesn't seem to increase appreciably.