Dlux, you could use Keplers laws which are based on the laws of gravitation (obervation really), Newton could never prove gravitation, only observed that it exists.
The current thought is that the planet, if it where not for the Sun would speed through space, however the sun attracts the planet in, as it does this the planets speed increases, after it reaches its closest point to the Sun it is flung off and the whole thing repeats again.
HOWEVER what really seems to be the case is that the planet is seeking the shortest period of rotation, the Sun does not attract the planet inwards, infact the sun does totally the opposite, it exerts a force outwards. The planets are where they are and stay where they are because of the elements that they contain.
We can prove this via chemistry to. If you add energy to a atom its electrons jump shells (energy exterted outwards), however if you remove the heat source the electrons fall to lower orbital shells.... thus creating the illusion of gravity.
