Is a Satellite free falling?

How about this then:

Free-fall is the same as being weightless. You are weightless if the only force acting on you is the force of gravity. That's it. Directions of velocities and accelerations don't matter.

Whether the satellite is falling exactly towards the planet, flying away from it, going sideways in circles or ellipses - none of it matters. As long as it is under the influence of gravity and only gravity, it's in free-fall.

If you add engines to the satellite and turn them on, or if you add the effects of atmospheric drag, you no longer have just gravity acting on the satellite, and it is no longer in free-fall.

 

Have you ever herd of the thought experiment with the bullet going faster and faster? Imagine firing a gun. The bullet goes really far but hits the ground eventually. If you could make a super powerful gun that fires the bullet really fast, the bullet would still be falling toward the ground, but the curvature of the earth would come into play (the ground would go "away" from the bullet) and thus the bullet keeps "falling" toward the ground, but we say it's in orbit. The velocity that governs this is given by the eqn:

v_orb= (GM/r)^^1/2
with G=big G
M= mass of earth
r= radius of earth

If you fire the bullet even faster (v_orb*2^^(1/2))eventually it will escape the gravitational pull of earth and go into intergalactic space, never to be seen again (like the satellite voyager).
I hope that helps, I never understood what people meant by things free falling until I learned of this thought experiment.

 

It might also help to consider the situation with a circular orbit. The satellite is always accelerating perpendicular to it's current direction. For an analogy, imagine driving a car in a circular path at constant speed, the car is always accelerating (centripetal acceleration) but it's speed never changes and the radius of the turn never changes (circular path).