The Evolution of Astronomy: From Greek Theories to Kepler's Laws, Study notes of Astronomy

Download The Evolution of Astronomy: From Greek Theories to Kepler's Laws and more Study notes Astronomy in PDF only on Docsity! 2/2/05 Astr 121 Lecture 5, Prof Mohr The Origin of Modern Astronomy Western Development of a Model for the Heavens 2/2/05 Astr 121 Lecture 5, Prof Mohr Outline 1) Greek view of the Heavens 2) Ptolemaic Model of the Solar System 3) Copernican Model 4) Tycho Brahe, Johannes Kepler and Galileo Galilei 2/2/05 Astr 121 Lecture 5, Prof Mohr Ancient Greek View of the Heavens A model of heavenly motion from Plato and Eudoxus  Model based on spheres, regarded as the most perfect solid geometric form  Components of the Heavens modeled as spheres centered on the Earth  Adequate to explain motion of stars  Sun, Moon and planets more complicated  Introduce multiple spheres for each object  Eudoxus used 27 spheres to match observations of the day Earth is unmoving and at center of universe  A moving Earth should be perceptible  In motion of dropped object, jumping person Celestial realm is unchanging- infinite duration 2/2/05 Astr 121 Lecture 5, Prof Mohr Moving Earth Should Be Perceptible-- and It Is! Earth’s rotation is perceptible:  Foucault pendulum- first experimental demonstration of Earth’s rotation (1851)  Coriolis force-  Significant enough that it must be accounted for in firing artillery significant distances  Responsible for the preferred direction of rotation for storm systems Watch Earth from Moon, Shuttle or space probe (but some might suggest this is all a Hollywood hoax?) 2/2/05 Astr 121 Lecture 5, Prof Mohr Foucault Pendulum Fi gu re fr om 2 1s t C en tu ry A st ro no m y 2/2/05 Astr 121 Lecture 5, Prof Mohr Aristotle and the Mechanics of Motion Lived 384 to 322 BC Four elements  Earth, water, air and fire Natural motion  Earthly motion toward center of universe  Fire moves away from center  Water and air occupy the space between Objects of different composition fall at different rates  Air resistance posed serious conceptual hurdle Introduced concept of “force”  Causes deviation from natural motion  Constant force required to keep Earthly object moving  Heavenly objects move continuously (composed of ether- quintessence?) 2/2/05 Astr 121 Lecture 5, Prof Mohr Aristarchus of Samos: A Heliocentric Model Lived 310 to 230 BC Developed a heliocentric model of the heavens 1700 yrs before Copernicus Set out to solve Earth-Sun-Moon system using eclipse data  Moon is 1/3 size of Earth, estimated Earth-Moon distance  Estimated (incorrectly) that Earth-Sun distance was 20x Earth- Moon distance  Because Moon and Sun have same apparent size, Sun must be 20x larger  Sun at center because of larger size Never accepted:  No perceptible rotation of Earth  No parallax of stars 2/2/05 Astr 121 Lecture 5, Prof Mohr Stellar Parallax January March July Parallaxes are exceedingly small- the nearest star to the Sun moves only about an arcsec (1/3600 of degree) due to parallax. Typically stars appear to be larger than an arcsec on the sky, due to turbulence in the Earth’s atmosphere. 2/2/05 Astr 121 Lecture 5, Prof Mohr Toward Renaissance: Adoption of a Revised Ptolemaic System Astronomy stayed alive and well in the Islamic world after Greek civilization declined In Europe, theologians like Thomas Aquinas (1224-1274)  helped in adopting the Greek system Alterations made  Not infinite in duration- beginning with a Creator  Center of Earth the basest place… Hell  Celestial realm is the domain of angels  God or Creator above all Studies of Greek philosophy became standard part of education for the elite 2/2/05 Astr 121 Lecture 5, Prof Mohr Nicholas Copernicus: On the Revolution of Heavenly Spheres Lived in Poland from 1473 to 1543 (Re)introduced the heliocentric model  Apparently acquainted with the writings of Aristarchus Motivation for new model?  Complexity of the Ptolemaic system  Restore simplicity of circular orbits  Inaccuracy of Ptolemaic predictions 2/2/05 Astr 121 Lecture 5, Prof Mohr The Copernican Model Successes  Natural explanation for retrograde motion of Mars  If inner planets travel faster  Natural explanation for daily motion of stars and planets  Earth’s rotation  Natural explanation for seasonal changes  Given tilt of Earth’s rotation axis relative to axis of Earth’s orbit Problems  Parallax motion expected- unless stars at tremendous distances- but not observed  Predictions of planetary motion more inaccurate than in Ptolemaic system 2/2/05 Astr 121 Lecture 5, Prof Mohr Tycho Brahe: Improved Tracking of the Heavens Lived in Denmark and later in Prague (1546- 1601) Careful and systematic naked eye observer  Repeated measurements and used disagreement of multiple measurements to estimate errors (a new concept) His archive of observations underscored the shortcomings in the Ptolemaic system Rejected heliocentric model  Was unable to detect stellar parallax  Thought stars nearby because of apparent size (was not aware of the effects of atmospheric blurring or “seeing”) 2/2/05 Astr 121 Lecture 5, Prof Mohr Tycho’s Model of the Universe A mixed Ptolemaic-Copernican Model  Earth at center (no parallax)  Sun orbited Earth and Planets orbited Sun 2/2/05 Astr 121 Lecture 5, Prof Mohr Tycho’s Supernova Supernova in constellation Cassiopeia in 1572 Tycho studied it  No observable parallax  It couldn’t be an atmospheric phenomenon  Must be part of the “unchanging” realm of the stars Therefore, Heavens not immutable Tycho leaves for Prague in 1597 2/2/05 Astr 121 Lecture 5, Prof Mohr Ellipses An ellipse can be created using a string, two tacks and a pencil  Tacks mark each focus  Distance from a focus to any point on the ellipse and back to other focus is constant Eccentricity e of an ellipse is a measure of its departure from a circle  e~0 is close to circle (circle is special case of an ellipse where two foci are in same location)  Most planetary orbits have very low eccentricity (i.e. almost circular)  Often ellipses are characterized by the axial ratio or ratio of the minor to major axis, where a circle has an axial ratio of 1 2/2/05 Astr 121 Lecture 5, Prof Mohr Kepler’s 2nd Law Line from planet to Sun sweeps out equal area in equal time  Implies that planets travel fastest when they are closest to the Sun (called perihelion) and slowest when they are farthest from the Sun (called aphelion) In this figure the time for the planet (or comet, asteroid or space probe) to move from point A to point B is the same that it takes to move from point C to point D 2/2/05 Astr 121 Lecture 5, Prof Mohr Kepler’s 3rd Law The square of the period is equal to the cube of the semimajor axis  The form of Kepler’s 3rd law provides insight into exactly how the force of gravity weakens with distance from the source  Implies that planets in orbits nearer the Sun move at higher velocity in their orbits  We’ll see that Kepler’s law follows nicely from Newton’s law of universal gravitation, and that a generalized form can be developed that includes the mass of the central object  Note that Kepler’s 3rd Law applies to all orbits around the Sun-- even very eccentric orbits like those of the comets. ! P 2 = R 3 [period in years, distance in AU] ! v = 2"R P = 2"R R 3 2 = 2" R