What does falling have to do with keeping a satellite in orbit?

Falling and Forward Motion Combine to Produce a Curved Path--The Heart of Satellite Orbits

The forward speed of the ball determines whether the path is only slightly curved or sharply curved. The relationship between forward speed and the curvature of the path is at the heart of satellite orbits.

Falling and Forward Motion are Independent

The key to understanding satellite motions is in recognizing that gravity acts only in the downward direction -- forward motion and falling are totally independent of each other.

If there were no gravity or frictional forces acting on the basketball in the figure, it would follow the straight line path forever. Gravity makes it drop down from this straight line path. The distance it falls from the straight line depends on the time it takes to travel to a given spot. If the ball is thrown at high speed along the path it will get to the net rapidly and have very little time to fall along the way. If the basketball is thrown more softly, it will have time to fall quite far before arriving at the basketball net.

How are the Falling Ball and the Falling Player Related?

The basketball player holding on the the net, has no forward motion. If he lets go of the net at the same time the other player releases the basketball, he will always catch the ball. A fast ball will hit him high up in the air because neither he nor the ball have had time to drop far. A slow ball will contact him further down in his fall.