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.
If you are dealing with something that moves, at least something that does not move at an appreciable fraction of the speed of light, then Newton’s Laws of Motion are bound to be relevant. You can use them to understand the behaviour and trajectory of the objects in question.
In fact, the motion of virtually everything we deal with in normal life can be understood in terms of Newton’s Laws of Motion. Without them, the motion and behaviour of a great many objects in our world could not be properly understood.
They serve as the basis for much of physics, certainly much of the branch of physics known as mechanics. And have been important in several other branches of physics.
Until they were superseded by Einstein’s Relativity, his law of gravitation were used to understand the motions and behaviour of much of the celestial objects in our universe. Without an understanding of gravity as provided by Newton or Einstein’s equations, the behaviour of most of the objects in space cannot be understood.
But, the importance of this goes far beyond providing an understanding of the motion of Earthly and celestial objects. Newton was one of the first to show that many aspects of nature can be easily understood by the application of simple physical principles.
Not only that, he showed that the behaviour of these physical objects could be calculated and predicted using simple equations.
This made an immense case for the power of science, physics in particular, for understanding the universe and predicting its behaviour.
The work of Newton showed just how much of the real world could be understood and predicted using simple equations. But, not only this, it showed the immense power of induction.
This was key to Newtons immense success. He was a master of grasping the commonalities between seemingly disparate things such as rocks on Earth and comets in space and identifying general principles which applied to both kinds of entities.
We will talk further about induction in a later episode. But for now note that a key reason for Newton’s success at explaining so much of nature with a few simple principles, is his application of induction.
Another important aspect of Newton’s laws of motion is that his theory of calculus was crucial in helping to derive them. In fact, you can, as Newton did, use simple calculus to derive various of his laws of motion from previously established ones.
This illustrates the vital role mathematics plays in physics. Mathematics is the science of quantifying relationships between things. Physics of course deals with many such relationships.
What Newton did was start with something he knew to be true, such as his Second Law of Motion, and perform mathematical operations so that a consequence of this is that F equals mass times acceleration.