Newton is best known for the legendary book Philosophiæ Naturalis Principia Mathematica (Latin for Mathematical Principles of Natural Philosophy). Here he sets down the sum total of his considerable discoveries in mechanics.
This is a rigorous presentation of his well-known laws of mechanics and his theory of gravitation.
His law of universal gravitation states that everything in the universe attracts everything else in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
He used his theory of gravitation to prove Kepler’s laws of planetary motion, account for the tides, the trajectories of comets, the precession of the equinoxes and more.
He demonstrated that the motion of objects on Earth and celestial bodies in space could be accounted for by the same set of principles. This finally made sense of the heliocentric model of the universe and explained Kepler’s astronomical observations. Thus dismissing any serious doubt of the heliocentric model.
This was a crucial moment in physics! The importance of providing a single set of principles which explained the behaviour of both Earthly and celestial bodies can hardly be overstated.
Before Newton, it was customary to view the Heavens as a strange place very different from the Earth and not subject to the same kinds of laws. But Newton helped change this by showing that in fact the heavens and the Earth obeyed fundamentally the same equations.
This greatly demystified the heavens and helped to make the point that physic was a truly universal science which could explain everything, even the heavens.
But what about his other laws of motion? Chances are that if you have a science education, you have encountered these laws, even if you can’t remember them offhand. They are very simple laws which can be very easily understood and used by school children.
That is part of their beauty. They are not the sort of complicated, difficult to work with equations that take considerable mathematical expertise or computational tools to deal with. Which is more than can be said for several other equations in modern physics.
But, surely the worth of a theory is not in how elegantly simple to work with its mathematics is. Several aspects of the mathematics of quantum theory is much more difficult to work with. But that does not make it any less true or important. Regardless of what we think of the interpretations of the mathematics of quantum theory.