Phys 8-70 Astronomy The danger to which the success of revolutions is most exposed, is that of attempting them before the principles on which they proceed, and the advantages to result from them, are sufficiently seen and understood. Thomas Paine - American Revolutionary Anyone in a free society where the laws are unjust has an obligation to break the law. Henry David Thoreau - American Philosopher (rěv ə-lōō shən)). n A drastic and far-reaching change in ways of thinking and behaving.. n Orbital motion about a point, the planetary revolution about the sun. 4 The Copernican Revolution There are problems with the Ptolemaic Model Problems with Ptolemy 47-54 5 The solar system according to the Ptolemaic Model from 00 A.D. to 500 6
Features Deferent Circles Epicycles on the Deferents Inferior planets are never more than 47º from the sun Retrograde motion of mars is explained Features As the precision of astronomical measurements grew the need for adjustments to the model called for additional epicycles. In 5 King Alfonso X of Castile funded a 0 year project by Arab and Jewish astronomers to calculate extensive tables. Calculations became horrendously complicated and even Alfonso suggested that the model should by simpler if it was to have any truth in it. 7 8 Multiplicity ought not be posited without necessity. William Occam English Scholar - 40 Copernican Theory Keep it simple, stupid. Anonymous 0 th Century Philosopher The motions of the planets would be more easily explained if the sun were at the center. This principle is known as Occam s Razor 9 0 DeRevolutionibus, 54 Going Further Venus and Mercury revolve around the sun and cannot go nearer or further from it than the circles of their orbits permit If, acting upon this supposition, we connect Saturn, Jupiter and Mars with the same center, keeping in mind the greater extent of their orbits we cannot fail to see the explanation of the regular order of their motions. This proves sufficiently that their center belongs to the sun The extent of the universe is so great that [the earth] disappears when compared to the sphere of the fixed stars. Although this may appear incomprehensible and contrary to the opinion of many, I shall, if God wills, make it clearer than the sun, at least to those who are not ignorant of mathematics.
that fool who would reverse the entire art of astronomy Joshua bade the SUN and not the earth to stand still. Martin Luther - 59 Under very real threat of persecution, Copernicus changed the title of his book and its publication was finished only in the final days of his life. 546-60 Royal Astronomer of Denmark Tycho UraniborgBrahe Observations with the naked eye Measured parallax of planets Observed a supernova (57) Realized that Ptolemy was not right but denied Copernicus Proposed a model with the earth at the center and the sun revolving around it, but all of the other planets revolved around the sun Collected the best data available 4 Johannes Kepler 57-60 Kepler Deeply religious believer in astrology Mathematics was evidence of God Subscriber to the Copernican theory Hired by Tycho to prove the earth centered model Convinced that a mathematical harmony existed for the planets Inherited Tycho s fine data KEPLER! 5 Analyzed data regarding mars 6 Kepler s Laws. Each planet moves in an ellipse, with the sun at one focus. This orbit is in the Ellipses shape of an ellipse. and Areas. The line between the sun and the planet sweeps out equal areas in equal times.. The ratio of the cube of the average radius of a planets orbit to the square of its orbital period of revolution is the same for each planet. (Harmonic Law) Kepler s laws 7 The area A AB = The Area A CD 8
A P d R = A = d R ( ) = ( ) v t R v t R A P P A A P P A A vr = vr Law of Conservation of p P A A Angular Momentum 9 0 The Harmonic Law: Harmonic Law k a = a k P P = a = Average radius of planet s orbit P = The orbital period of the planet k = A constant for all objects orbiting the sun Consider the earth Harmonic Constant a P = ( AU ) ( yr) = = This is true for all planets no matter what the radius of their orbit. Retrograde Retrograde motion explained Motion at long last How does Kepler know the time periods of planets other than the earth? Consider You can t go to mars You can t watch mars go round Every so often, mars exhibits retrograde motion Retrograde motion is caused by the passing of mars by the earth at various points in their orbits. How does Kepler know times? 4 4
Working late on this lecture, the clock strikes midnight And the hands line up. A little scratch work and some calculations A little while later And they aren t lined up at all. I notice that they line up again sometime around :05 am. Is there some sort of a math rule that can predict when the hands will align? 5 Big deal 6 If I use the hands of the clock as an analogy Time for period the motion of the mars planets Radius of mars orbit 7 8 Measurement IMPORTANT Occam s Razor Copernicus Law of Ellipses Law of Areas Harmonic Law 9 0 5
EndNEXT TIME: Newton s Law of Universal Gravitation 6