[Wavytone]

You should study Newton's 'Principia', all is revealed. I have a copy, it is an amazing read and a magnificent glimpse into a beautiful mind.

You will need to be good at maths, specifically calculus at HSC (year 12) level.

Newton starts with the basic laws of motion then the postulate for gravity. From this the proof of elliptical orbits follows in straight word fashion. There are some interesting examples along the way, regarding the moon and tides as well.

It is available online as (obviously) its out of copyright.

It also shows how complex calculations were done in newtons day, and shows how the methods taught to kids these days have been dumbed-down and are quite primitive, thanks to calculators. Newtons methods are described in a book called 'The Trachtenberg System of Speed Mathematics'. Trachtenberg merely appropriate the methods Newton used and published under his own name. It's also the method that so-called 'geniuses' use to perform calculations on stage and TV.