Simple Nature - Light and Matter

a / An ellipse is circle that hasbeen distorted by shrinking andstretching along perpendicularaxes.b / An ellipse can be constructedby tying a string to twopins and drawing like this with apencil stretching the string taut.Each pin constitutes one focus ofthe ellipse.c / If the time interval takenby the planet to move from P to Qis equal to the time interval fromR to S, then according to Kepler’sequal-area law, the two shadedareas are equal. The planetis moving faster during timeinterval RS than it was duringPQ, because gravitational energyhas been transformed into kineticenergy.2.3 Gravitational PhenomenaCruise your radio dial today and try to find any popular song thatwould have been imaginable without Louis Armstrong. By introducingsolo improvisation into jazz, Armstrong took apart the jigsawpuzzle of popular music and fit the pieces back together in a differentway. In the same way, Newton reassembled our view of theuniverse. Consider the titles of some recent physics books writtenfor the general reader: The God Particle, Dreams of a FinalTheory. When the subatomic particle called the neutrino wasrecently proven for the first time to have mass, specialists in cosmologybegan discussing seriously what effect this would have oncalculations of the evolution of the universe from the Big Bang toits present state. Without the English physicist Isaac Newton, suchattempts at universal understanding would not merely have seemedambitious, they simply would not have occurred to anyone.This section is about Newton’s theory of gravity, which he usedto explain the motion of the planets as they orbited the sun. Newtontosses off a general treatment of motion in the first 20 pages of hisMathematical Principles of Natural Philosophy, and thenspends the next 130 discussing the motion of the planets. Clearlyhe saw this as the crucial scientific focus of his work. Why? Becausein it he showed that the same laws of nature applied to the heavensas to the earth, and that the gravitational interaction that madean apple fall was the same as the as the one that kept the earth’smotion from carrying it away from the sun.2.3.1 Kepler’s lawsNewton wouldn’t have been able to figure out why the planetsmove the way they do if it hadn’t been for the astronomer TychoBrahe (1546-1601) and his protege Johannes Kepler (1571-1630),who together came up with the first simple and accurate descriptionof how the planets actually do move. The difficulty of their task issuggested by the figure below, which shows how the relatively simpleorbital motions of the earth and Mars combine so that as seen fromearth Mars appears to be staggering in loops like a drunken sailor.Brahe, the last of the great naked-eye astronomers, collected extensivedata on the motions of the planets over a period of manyyears, taking the giant step from the previous observations’ accuracyof about 10 minutes of arc (10/60 of a degree) to an unprecedented1 minute. The quality of his work is all the more remarkable consideringthat his observatory consisted of four giant brass protractorsmounted upright in his castle in Denmark. Four different observerswould simultaneously measure the position of a planet in order tocheck for mistakes and reduce random errors.With Brahe’s death, it fell to his former assistant Kepler to tryto make some sense out of the volumes of data. After 900 pages of96 Chapter 2 Conservation of Energy