“It is odd, but on the infrequent occasions when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics. I believe that is probably because we respect the arts more than the sciences. The artists of the Renaissance said that man’s main concern should be for man, and yet there are other things of interest in the world. Even the artists appreciate sunsets, and the ocean waves, and the march of the stars across the heavens. There is then some reason to talk of other things sometimes. As we look into these things we get an aesthetic pleasure from them directly on observation. There is also a ”

“rhythm and a pattern between the phenomena of nature which is not apparent to the eye, but only to the eye of analysis; and it is these rhythms and patterns which we call Physical Laws. What I want to discuss in this series of lectures is the general characteristic of these Physical Laws; that is another level, if you will, of higher generality over the laws themselves. Really what I am considering is nature as seen as a result of detailed analysis, but mainly I wish to speak about only the most overall general qualities of nature.
Now such a topic has a tendency to become too philosophical because it becomes so general, and a person talks in such generalities, that everybody can understand him. It is then considered to be some deep philosophy. I would like to be rather more special, and I would like to be understood in an honest way rather than in a vague way. So in this first lecture I am going to try to give, instead of only the generalities, an example of physical law, so ”

“that you have at least one example of the things about which I am speaking generally. In this way I can use this example again and again to give an instance, or to make a reality out of something which will otherwise be too abstract. I have chosen for my special example of physical law the theory of gravitation, the phenomena of gravity. Why I chose gravity I do not know. Actually it was one of the first great laws to be discovered and it has an interesting history. You may say, ‘Yes, but then it is old hat, I would like to hear something about a more modern science’. More recent perhaps, but not more modern. Modern science is exactly in the same tradition as the discoveries of the Law of Gravitation. It is only more recent discoveries that we would be talking about. I do not feel at all bad about telling you about the Law of Gravitation because in describing its history and methods, the character of its discovery, its quality, I am being completely modern.
”

“This law has been called ‘the greatest generalization achieved by the human mind’, and you can guess already from my introduction that I am interested not so much in the human mind as in the marvel of a nature which can obey such an elegant and simple law as this law of gravitation. Therefore our main concentration will not be on how clever we are to have found it all out, but on how clever nature is to pay attention to it.
The Law of Gravitation is that two bodies exert a force upon each other which varies inversely as the square of the distance between them, and varies directly as the product of their masses. Mathematically we can write that great law down in the formula:”

“some kind of a constant multiplied by the product of the two masses, divided by the square of the distance. Now if I add the remark that a body reacts to ”

“a force by accelerating, or by changing its velocity every second to an extent inversely as its mass, or that it changes its velocity more if the mass is lower, inversely as the mass, then I have said everything about the Law of Gravitation that needs to be said. Everything else is a mathematical consequence of those two things. Now I know that you are not all mathematicians, and you caot immediately see all of the consequences of these two remarks, so what I would like to do here is to tell you briefly of the story of the discovery, what some of the consequences are, what effect this discovery had on the history of science, what kind of mysteries such a law entails, something about the refinements made by Einstein, and possibly the relation to the other laws of physics.
The history of the thing, briefly, is this. The ancients first observed the way the planets seemed to move in the sky and concluded that they all, along with the earth, went around the sun. This ”

“discovery was later made independently by Copernicus, after people had forgotten that it had already been made. Now the next question that came up for study was: exactly how do they go around the sun, that is, with exactly what kind of motion? Do they go with the sun as the centre of a circle, or do they go in some other kind of curve ? How fast do they move ? And so on. This discovery took longer to make. The times after Copernicus were times in which there were great debates about whether the planets in fact went around the sun along with the earth, or whether the earth was at the centre of the universe and so on. Then a man named Tycho Brahe* evolved a way of answering the question. He thought that it might perhaps be a good idea to look very very carefully and to record exactly where the planets appear in the sky, and then the alternative theories might be distinguished from one another. This is the key of modern science and it was the begiing of the true understanding of ”

“Nature – this idea to look at the thing, to record the details, and to hope that in the information thus obtained might lie a clue to one or another theoretical interpretation. So Tycho, a rich man who owned an island near Copenhagen, outfitted his island with great brass circles and special observing positions, and recorded night after night the position of the planets. It is only through such hard work that we can find out anything.
When all these data were collected they came into the hands of Kepler,* who then tried to analyse what kind of motion the planets made around the sun. And he did this by a method of trial and error. At one stage he thought he had it; he figured out that they went round the sun in circles with the sun off centre. Then Kepler noticed that one planet, I think it was Mars, was eight minutes of arc off, and he decided this was too big for Tycho Brahe to have made an error, and that this was not the right answer. So because of the precision of the experi”

“ments he was able to proceed to another trial and ultimately found out three things.
First, he found that the planets went in ellipses around the sun with the sun as a focus. An ellipse is a curve all artists know about because it is a foreshortened circle. Children also know because someone told them that if you put a ring on a piece of cord, anchored at each end, and then put a pencil in the ring, it will draw an ellipse (fig. 1).

Figure 1

The two points A and B are the foci. The orbit of a planet around the sun is an ellipse with the sun at one focus. The next question4s: In going around ”

“the ellipse, how does the planet go ? Does it go faster when it is near the sun ? Does it go slower when it is farther from the sun? Kepler found the answer to this too (fig. 2).

Figure 2

He found that, if you put down the position of a planet at two times, separated by some definite period, let us say three weeks – then in another place on its orbit two positions of the planet again separated by three weeks, and draw lines (technically called radius vectors) from the sun to the planet, then the area that is enclosed in the orbit of the planet and the two lines that are separated by the ”

“planet’s position three weeks apart is the same, in any part of the orbit. So that the planet has to go faster when it is closer to the sun, and slower when it is farther away, in order to show precisely the same area.”

Excerpt From: Richard P Feynman. “The Character of Physical Law.” iBooks.