In orbit

Imagine a very tall, pointed tower and a ball which is thrown horizontally from the top (see pictures below).
In the sketches below, the trajectory of the ball is shown for different initial velocities (without air friction). The faster the ball is thrown, the longer its flight lasts.
Can you imagine the trajectory of the ball, if the Earth is flat (picture above) or spherical (picture below)?

At a certain velocity the ball is completely revolving around the Earth.

The ball is falling towards the Earth the whole time but never reaches it because of the Earth's spherical form (see picture below).

If friction does not matter (for example outside the Earth's atmosphere), the orbital velocity remains constant. The ball is permanently revolving around the Earth without propulsion.

A spaceship revolves around the Earth in the same way. Itself and its astronauts always fall in free fall towards the Earth.