Scientific Discovery and Kepler’s Laws of Planetary Motion Mr. Finn November, 2008

Background Greek astronomy Ptolemy Copernicus Tycho Brahe Johannes Kepler Mars

Greek Astronomy Planets –“little wanderers”  hard to explain Mars –red planet = “fiery one” –retrograde motion  hardest to explain Aristarchus –heliocentric system –explains retrograde motion

Retrograde Motion of Mars Download file: “marsmovie.gif” Save in same directory as PowerPoint. Click on image to open html file - Click on “OK” when prompted.

Ptolemaic System The Algamest –geocentric system –orbits = system of epicycles –explains retrograde motionretrograde motion –infinitely malleable adjusts to new data extremely accurate predictions

Copernican System Heliocentric system –planet orbits = circles –not centered on Sun, but points nearby –explains retrograde motionretrograde –simple but inaccurate not fully consistent with existing data retains some epicycles

Tycho Brahe Observational astronomer –best observatory in Europe at Hven ( ) –naked-eye observation telescope by Galileo in 1609 –20 years of data on planets Compromise system –Earth at center –other planets orbit sun

Johannes Kepler Mathematician –worked for Brahe inherited Brahe’s astronomical data Copernican system –Kepler strong believer Trials & Tribulations –repeatedly fled wars, religious persecution –mother on trial for witchcraft

Experimental Data Kepler’s “War on Mars” Brahe data on Mars –position relative to distant stars for 20yrs from Earth Data relative to moving Earth –find positions 1 Martian year apart –Mars at same point in orbit around Sun –seen from different perspectives on Earth Earth in different position in its orbit –where lines intersect = position of Mars Find orbit without any preconceptions –traces out ellipse!

Theory - Kepler’s Laws 1.Orbits of planets are ellipses with sun at one foci 2.Planets sweep out equal areas in equal times 3.Relationship between size of orbit & its period –P  a 3/2 –P 2 /a 3 = constant Harmonies in the Heavens

Kepler’s 1st Law Sun at one foci 2a2a a = semi-major axis perihelion aphelion

Kepler’s 2nd Law Equal Areas: A Equal Times: 1  2 3  4 planets move faster when closer to the sun Planet Sun

Kepler’s 3rd Law P  a 3/2 Unknown to Kepler

Newtonian Synthesis Newton’s Universal Law of Gravity Newton’s Laws of Motion –same laws explain heavenly and earthly motion –Aristotle believed two separate laws d Grand Synthesis #1 Grand Synthesis #1

Celestial Mechanics Pierre-Simon Laplace –Treatise on Celestial Mechanics (1799) Why is God missing?Napoleon - Why is God missing? –Laplace: “I have no need of that hypothesis.” “Je n’ai pas besoin de cette hypothèse.” Mechanical UniverseRise of the “Mechanical Universe”

Predictions Edmund Halley predicts return of comet Discovery of new planets –Neptune, Pluto Effect of planets on each other –precession of orbits –Mercury partially unexplained

Ptolemaic Cosmos

Ptolemy & Retrograde Motion

Copernican Cosmos

Copernicus & Retrograde Motion continued…

Retrograde Movie

Observatory at Hven

Tychonic System