# The Apple, The Cannonball and The Moon

# 2.1 The Apple, The Cannonball and The Moon

An apple falls straight down. The moon orbits Earth in a circle (almost). We know for a ''fact'' now that both motions are due to (the force of) gravity between Earth and the apple/moon. But this was not an obvious fact before Newton, simply because the motions looks so different.

In the modern day, if you ask a mathematician/physicist why the apple and the moon follow different paths despite both being acted by the same type of force, you will probably get a reply like:

''Oh yea gravity is Universal! It acts in the same way for both the apple and the Moon. It is just that the initial conditions were different, hence different paths exhibited.''

The reply probably would not enlighten many people. To visualise and make sense of the above, I'll borrow the story used by Leonhard Euler (1707-1783) in one of his letters to a German princess.

There is a cannon on a cliff, positioned such that it is parallel to the ground. If the cannonball is released without any firepower, the ball will fall straight down the cliff, much like how an apple falls down a tree. If however, the cannon shoots the ball with some firepower, the path will be a curve (projectile), and the ball will fall some distance away from the cliff. The more firepower one uses to shoot the ball, the greater the initial horizontal/tangential¹ speed of the ball, and the further away the ball will land.

Now we know that while our Earth looks flat locally, it is actually round. Suppose we have so much firepower at our expense, we can shoot the ball with so much initial tangential speed such that the ball goes almost round the Earth and fall right behind us! And if we were to be so silly to shoot with just a little more tangential speed, the ball will not land at all, but go round the Earth and hit us from behind!!

Perhaps we did shoot the cannonball with such an initial tangential speed, but we pack the cannon and move away while the cannonball circumnavigated the Earth. The ball will go round and round the Earth forever (assuming no air resistance), much like how the Moon orbits the Earth.