Much of our thinking about gravitation has its origins in Isaac Newton’s thought experiment about firing a projectile from a high mountaintop at various speeds. If you are mathematically inclined you could read hisA Treatise of the System of the World
However, today with our computer technology it is possible to simulate the dynamics of his equations and watch them run in real time. Feel free to pick a speed for the cannon ball in the slider and then click on the ‘fire’ button to see what happens for different speeds. Click on the ‘clear’ button to clear the trails.
You will notice that up to 7000 metres/second the projectile falls back to the Earth. As you approach 7000 metres/second the curve of the trajectory approaches the curvature of the Earth. At 7100 m/s and above the projectile misses the Earth and so goes into orbit–a radical thought for someone to have in the mid-1600s.
This simulation is based on Daniel Schroeder's excellent tutorial on physics simulations using html5.