The Scientific Revolution: Tycho Brahe, Kepler, Galileo, and Newton - Prof. Alberto Daniel, Study notes of Astronomy

Download The Scientific Revolution: Tycho Brahe, Kepler, Galileo, and Newton - Prof. Alberto Daniel and more Study notes Astronomy in PDF only on Docsity! 2/5/2008 1 Lecture 3: Cosmology of the Scientific Revolution Tycho Brahe Kepler Galileo Newton http://www.physics.fsu.edu/users/Lind/AST1002/ 2/5/2008 2 Tycho Brahe (1546-1601) • Flamboyant and tyranical aristocrat, but devoted to science • Lived and observed on island off the coast of Denmark • Last of the great “naked eye” observers • Made planetary observations much more accurate than any previous • Observed “new star” (Tycho’s supernova) in 1572 • Demonstrated that comet was beyond Moon’s orbit • From parallax observations of new star, comet: • knew they were not in Earth’s atmosphere • evidence that heavens were not immutable 2/5/2008 5 Kepler’s first law Planets move around the Sun in ellipses, with the Sun at one focus. perihelion aphelion 2/5/2008 6 Solar system orbits Inner planets Outer planets + http://www.rasnz.org.nz/SolarSys/Orbits07.htm Note the low eccentricities! 2/5/2008 7 Kepler’s second law The line connecting the Sun and a given planet sweeps out equal areas in equal times. Therefore, planets move faster when they are nearer the Sun Consequence of angular momentum conservation. http://home.cvc.org/science/kepler.gif 2/5/2008 10 Kepler’s third law The square of the period P of the orbit is proportional to the cube of the semi-major axis R Period (P) = time it takes for planet to complete one orbit Semi-major axis (R) = half of the length of the “long” (i.e. major) axis of the ellipse. P2=constant × R3 P2=4π2/G(M+m) × R3 (Newton) 2/5/2008 11 For the Earth, we know that: P= 1 year = 3×107 seconds R= 150 million km (1 Astronomical Unit, A.U.) Kepler’s 3rd law says that, for other planets, 32 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛=⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ AU R yr P 2/5/2008 12 An imprecise version of Kepler’s laws Orbits are not circular A planet’s speed changes during its orbit There is a definite relationship between orbital period and the distance from the star 2/5/2008 15 http://www.astromax.org 2/5/2008 16 2/5/2008 17 Galileo’s lens, Florence 2/5/2008 20 Letter from Galileo reporting the discovery of Jupiter’s moons… SIDEREUS NUNCIUS 75 On the third, at the seventh hour, the stars were arranged in this sequence. The eastern one was I minute, 30 seconds from Jupiter; the closest western one 2 minutes; and the other western one was East * cs) cd oe West 10 minutes removed from this one. They were absolutely on the same straight line and of equal magnitude. On the fourth, at the second hour, there were four stars around | Jupiter, two to the east and two to the west, and arranged precisely East *x* eS * * West on a straight line, as in the adjoiming figure. The easternmost was distant 3 minutes from the next one, while this one was 40 seconds from Jupiter; Jupiter was 4 minutes from the nearest western one, and this one 6 minutes from the westernmost one. Their magnitudes were nearly equal; the one closest to Jupiter appeared a little smaller than the rest. But at the seventh hour the eastern stars were only jo seconds apart. Jupiter was 2 minutes from the nearer eastern East 3 ak @) * OF West one, while he was 4 minutes from the next western one, and this one was 3 minutes from the westernmost one. They were all equal and extended on the same straight line along the ecliptic. On the fifth, the sky was cloudy. On the sixth, only two stars appeared flanking Jupiter, as is seen East * ey * West in the adjoining figure. The eastern one was 2 minutes and the western one 3 minutes from Jupiter. They were on the same straight line with Jupiter and equal in magnitude. On the seventh, two stars stood near Jupiter, both to the east, arranged in this manner. 2/ 5/ 2008 Galilean Moons http://www. ladeltascience.com/astronomy/kisatchie04/ 21  Galilean moons ( from Galileo spacecraft !) 2/ 5/ 2008 35 2/5/2008 25 Phases of Venus: the test of the Heliocentric system http://www.telescope1609.com/Galileo.htm 2/5/2008 26 Galilean physics After 1633 trial, Galileo returned to work on physics of mechanics Published Discourses and mathematical demonstrations concerning the two new sciences (1642) Made experiments with inclined planes; concluded that distance d traveled under uniform acceleration a is d=a t2 Used “thought experiments” to conclude that all bodies, regardless of mass, fall at the same rate in a vacuum --contrary to Aristotle Now known as “equivalence principle” Realized full principle of inertia: body at rest remains at rest; body in motion remains in motion (force not required) Realized principle of relative motion (“Galilean invariance”): If everything is moving together at constant velocity, there can be no apparent difference from case when everything is at rest. Ball dropped from top of moving ship’s mast hits near bottom of mast, not behind on deck. 2/5/2008 27 Isaac Newton (1643-1727) Attended Cambridge University, originally intending to study law, but reading Kepler, Galileo, Descartes Began to study mathematics in 1663 While Cambridge was closed due to plague (1665- 1667), Newton went home and began to work out foundations of calculus realized (contrary to Aristotle) that white light is not a single entity, but composed of many colors began to formulate laws of motion and law of gravity Became professor of mathematics starting in 1669 (age 27!) Worked in optics, publishing “Opticks” (1704) invented reflecting telescope showed color spectrum from prism recombines into white light with a second prism analyzed diffraction phenomenon Isaac Newton in 1689, by Sir Godfrey Kneller. Father of modern physics and cosmology