The only force acting on a satellite in its orbit around Earth is the force of gravity from Earth. Why does a satellite not fall down?

It is falling. It has to fall, that is the law of gravity. Otherwise, it would leave Earth in a straight line. But if it falls at exactly the rate it needs to fall to travel in an orbit, we call that "orbiting". If if falls faster than that, it crashes into Earth. If if falls less than that , it travels into space.

http://www.physicsclassroom.com/class/circles/u6l4b.cfm

A satellite in orbit around the Earth doesn't fall down because it is continuously moving around the Earth at a high speed. The force of gravity between the Earth and the satellite pulls the satellite towards the Earth, but its forward motion prevents it from falling. This is due to the concept of centripetal force and the balance between the gravitational force and the satellite's velocity.

To understand this in more detail, let's consider the following steps:

1. Newton's Law of Universal Gravitation states that every particle with mass exerts an attractive force on every other particle with mass. In the case of a satellite orbiting the Earth, the gravitational force is exerted by the Earth towards the satellite.

2. According to Newton's second law of motion, the force acting on an object is equal to the mass of the object multiplied by its acceleration. In the case of the satellite, the only force acting on it is the gravitational force exerted by the Earth.

3. When a satellite is in orbit, it constantly accelerates towards the Earth due to gravity. However, instead of falling down, the gravitational force causes the satellite to change direction. This change in direction is what keeps the satellite in a stable circular or elliptical orbit.

4. In order for the satellite to remain in orbit, it needs a centripetal force that constantly pulls it towards the center of the circular orbit. The centripetal force acts perpendicular to the satellite's velocity and keeps it moving in a circular path.

5. The force of gravity provides this centripetal force. The gravitational force between the Earth and the satellite is always directed towards the center of the Earth, providing the necessary inward force to keep the satellite in its orbit.

6. The satellite's velocity is crucial in maintaining its orbit. If the satellite were to slow down, the gravitational force would overpower the centripetal force, causing the satellite to move closer to the Earth. On the other hand, if the satellite were to speed up, the centripetal force would be greater than the gravitational force, causing the satellite to move farther away from the Earth.

In summary, a satellite in orbit around the Earth does not fall down because its velocity and the gravitational force of the Earth combine to create a balance between the centripetal force needed to keep the satellite in orbit and the gravitational force pulling it towards the Earth.