Tycho Brahe and Johannes Kepler

ASTRONOMY 9: HISTORYOF COSMOLOGY Handout #14 Tycho Brahe and Johannes Kepler I. Tycho Drahe (1546 1601. Denmark) The "i2stronomer Prince", a very eccentric character, pompous and arrogant nobleman l35i: Studies law in Copenhagen (age 13) 1358: Witnesses partial solar eclipse. amazed that astrono~nicalevents are prcdzc2ablc, devotes self to astronom?Dispute with relative over who mas best at math 3 duel, nose sliced off and replaced with silver! Inlportant recognition: astronomy needs continuing observations of greater precision and accuracy Builds improl-ed instruments. becomes greatest pre-telescopic observational astronomer Positional data accurate to 2' (1130th of a degree)! Important astronomical events in Tycho's life A) 1558: Partial solar eclipse l3) 15i2: Superno\-a in Cassiopeia - No measured parallav 3 well beyond the moon in Aristotle's celestial realm - Heavenly change, contradicts Aristotelian cos~nos C) 1 5 i i : Conlet - Limits on parallax 3 at least 6x farther than Moon - No mere "atmospheric phenomenon"! King Frederick I1 gives Tycho the entire island of Hveen! Tycho builds grandiose observatory Uraniborg. "Castle of the Hea3-ens" Rules the island in grand dictatorial style T?;cho's cosmolog?; - Compromise between geocentric and Copernican ideas - Earth remains notion less at cos~niccenter (plausible, since fixed stars did not ha\-e measurable parallax) - Sun goes round earth as in geocentric model - But other planets go round Sun, as in Copernican model! - Note: Tycho's model breaks the "celestial spheres" Beconles "Imperial illatliematicus" to Rudolph I1 in Prague (1596) 1601: Dies of uremia after dinner with the Rosenbergs. "let me not seem to ha\-e lived in vain" 11. Joliannes Kepler (1571 1630, b. Germany) Founded '~astrophysics" Search for mathematical law-s to describe natural phenomena (planetary motion) Nightmarish childhood Attended Lutheran seminary from age 13 17 Prof of math and astronomy at Gratz by age 231 Kepler deeply influenced by Pythagorean thought - Beauty of geometr?; and mathematics - Harnlony of the spheres - Co~ivinced tliat cos~llosmust be geo~netricallybeautiful - Mystical inspiration for work Kepler's .'day job':: astrology! - 1601: w-rites treatise tliat breaks with principles of Ptolemaic astrology - Tries to make astrology more "certain", based on harmonies - Importance a t imperial court of Hal?- Roman Emp. Rudolph I1 Thought souls interacted with planets, "the hidden cause" Kepler's main obsession: significance of the fact that there were six known planets - Toda?- vie knom7 that pla~lets formed out of gravitational instability in a disk-shaped nebula 5 billion years ago - Fact that there are 9 is an '.accident" of the initial conditions of the nebula (rarity of such a configuration is unknown so far other solar s?-stems look very different, but vie can't detect similar ones to our own for another decade or two) - For Kepler. six planets nus st be related to the fil-e regular polyhedra (Platon%c solids) - Solids with regular polygons as faces and all vertices look the same - Can prove that only five exist: A ) Tetrahedron: 4 triangular faces. 3 edges a t each vertex B) Octahedron: 8 triangular faces, 4 edges at each vertex C ) Icosahedron: 20 triangular faces, 5 edges at each vertex D ) Cube: 4 square faces, 3 edges at each vertex E ) Dodecahedron: 12 pentagonal faces. 3 edges at each vertex - Kepler thought that planets moved 011 six spheres circumscribed and inscribed around the five solids - Finall?- failed t o reconcile w-ith observations, though fit to within about 5%)error - l:er?- modern scientific innovation: if theory doesn't fit the observations, nlust discard it! "Under a calamitous sky", Kepler marries a rich widow, "simple of mind and fat of body" with a "stupid, sulking, lonely, melancl~olycomplexion" l:er?; personal and amusing (though obscure) writings, unusual record of the blind alleys and frustrations in scientific thought 139i: Mysteri7~mC08mographicum (Secret of the Uniuersc) - Presents Kepler's cosmology in\-olving Platonic solids - First outspoken defense of Copernicus (50 ?-rs after death!) - Search for the physical causes of planetary motion Kepler recognizes that he needs good data 3 Tycho 1600: Tycho invites Kepler to join him; rocky relationship. constant arguing Tycho know-s Kepler has theoretical brilliance to interpret his data, but jealously guards his data After Tycho's death, Kepler gets Tycho's title and data Struggles long and hard trying to understand the motion of Mars Heliocentric model of orbit of Mars using circles leads to a stubborn error of 8'. even wit11 use of equant "Because these 8' could not be ignored. they alone have led to a total refor~nationof astronomy." 1609: Astronomia Noua (Neur Astronomy) - Problem of orbit shape; spends years trying all kinds of ovals and epicycles, finall?- stumbles across answer - First 2 of Kepler's t h r e e laws: 1. Planetary orbits are ellipses with Sun a t one focus 2. Orbits sweep out equal areas in equal times - Finall?- smashes the dogma of unifornl circular motion! - No more epicycles - First precise, verifiable natural laurs - Work on magnetisnl at this time by William Gilbert (1544 1603, physician to Elizabeth I ) - Kepler thinks the planets are held in their orbits by "magnetic" force from Sun ahich "diminishes in ratio to distance as does the force of light" - Comlection of Earthly with celestial - Tantalizingly close to idea of u~liversalgravity, but doesn't quite get it - Kepler's cosmos and the Holy Trinity: Father Sun at center, Son Sphere of stars at circumference, Holy Ghost force from Sun in intervening space 1619: Harmonice Mundi (Harmony of the Worlds) - Importance of Pythagorean harmony and geometr?- - - Compares ratio of min/mau distances of each planet from Sun rz-it11 musical harmonies; music of the heavens! After much trial and error, stumbles onto T h i r d law: P L cx a3 r P = period of planet (how long to go around Sun) r a = semi-major &xis of ellipse (for special case of circle, radius) r If P in years. a in A.U., then constant is 1: r A.U. = astronomical unit = Earth-Sun distance = 1.5 x 1U"m 1621: Epzlomc of Copcrnzcan Astronomy - Generalization of 3 laws t o all planets - First textbook of Copernican astronomy - Placed on Index of forbidden books . . . 162i: Rudolphznc Tablcs - Use of 3 laws t o predict planetar?- motions Kepler still does not understand physical reasons why his laws exist ... S o m n i u m : last published work - First real modern science fiction story - Dream of a journey to the moon Dies sickly and poor, unable to collect monies owed to him