…ellipse. It is, in fact, a hyperbola. And the correct orbits of objects around the sun is not an ellipse as Kepler thought, but the generalization to higher speeds is ellipse, parabola, or hyperbola. We didn't prove here that they were ellipses, parabolas,…

…It's 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 analyze what kinds of motions the planets made around the sun. And he did this by a method of…

…it's further from the Sun, and so on? We take away the other focus, we have the Sun then and the planet going around. And Kepler found the answer to this too. He found this, that if you put the position of the planet down at two times separated by…

…go around varies as a three-half power of the size, the square root of the cube of the size. So there's three laws of Kepler, which is a very complete description of the motion of the planets around the sun. The next question was, what makes them go…

…Or is there anything else to say? In the meantime, Galileo was investigating the laws of motion. Incidentally, at the time of Kepler, the problem of what drove the planets around the sun was answered by some people by saying that there were angels behind…

…vary inversely as the square of the distance. Now so far he hasn't said anything. Yes. Because he only said two things which Kepler said in a different language. One is exactly equivalent to the statement that the force is toward the sun, and the other…

…and Uranus were big planets that were known and the calculations were made as to how slightly different than the perfect ellipses of Kepler the planets ought to be going, Jupiter, Saturn, and Uranus, by the pull of one on each other. And when they were…