Kepler

Mountains on the Moon Galileo observed the mountains of the Moon with his telescope Estimated their elevation correctly

Artsy eyepiece sketches Galileo was trained as an artist This allowed him to correctly reason that these patterns represent a rugged surface

Aristotle easily falsified by experiment – but emphasis was not on observation How people thought about projectiles up until the Renaissance: the cannonball moves in almost a straight line, until it runs out of impetus and falls on the house. WRONG!

Galileo gets it right Strobe photograph Galileo Galilei’s notebook In fact, all projectiles fall in exactly the same way, regardless of what they are or weigh!

Tycho Brahe – The Data Taker Key question: Where are things? Catalogued positions of planets in Uraniborg and Prague Working without telescope Data ten times as accurate as before Died at banquet binge drinking TYCHO BRAHE (Danish) collects detailed and accurate (1-2 arcmin accuracy) observations of stellar and planetary positions over a period of 20 years shows that comets and novas are extralunar contra Aristotle; comets pass through planetary spheres His research may have cost 5-10% of the total GNP of Denmark at that time! JOHANNES KEPLER (German) reduces Tycho's data and by triangulation determines the orbits of the planets, including Earth's. The "baseline" is given by the Earth moving in its orbit. Not a simple problem, since the orbit of the Earth was not known beforehand, and the other planets don't sit still while the Earth is moving around! Tycho Brahe (1546–1601)

Tycho Brahe Tycho Brahe observing collects detailed and accurate (1-2’ accuracy) observations of stellar and planetary positions over a period of 20 years His research costed 5-10% of Danish GNP shows that comets and novas are extralunar contrary to Aristotle Shows that stars can change (Supernova of 1572) Proves that comets are superlunar TYCHO BRAHE (Danish) collects detailed and accurate (1-2 arcmin accuracy) observations of stellar and planetary positions over a period of 20 years shows that comets and novas are extralunar contra Aristotle; comets pass through planetary spheres His research may have cost 5-10% of the total GNP of Denmark at that time! JOHANNES KEPLER (German) reduces Tycho's data and by triangulation determines the orbits of the planets, including Earth's. The "baseline" is given by the Earth moving in its orbit. Not a simple problem, since the orbit of the Earth was not known beforehand, and the other planets don't sit still while the Earth is moving around! Tycho Brahe observing

Measuring distances with the Parallax The closer an object is, the more relocated it appears with respect to the fixed stars from different points on Earth

Johannes Kepler–The Phenomenologist Key question: How are things happening? Major Works: Harmonices Mundi (1619) Rudolphian Tables (1612) Astronomia Nova Dioptrice Johannes Kepler (1571–1630)

Kepler’s Beginnings Astrologer and Mystic Tried to find “music in the skies” Tried to explain distances of the 6 known planets by spheres resting on the 5 mathematical bodies  pre-scientific

Kepler’s First Law: Orbit Shape The orbits of the planets are ellipses, with the Sun at one focus Orbits turn out not to be circles nor eccentric circles but ellipses (which can be made with string and thumbtacks as shown) The sun is at one focus (not the center). A foreshortened circle 11

a = “semimajor axis”; e = “eccentricity” Ellipses a = “semimajor axis”; e = “eccentricity” Orbits of most planets are nearly circular and have small e (Mercury and Pluto most notable exceptions) 12

Conic Sections From Halley’s book (1710)

Kepler’s Second Law: Motion in Time An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal times conservation of angular momentum: same effect makes skaters speed up when they draw in their arms 14

Kepler’s Third Law: Relating Orbits The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis: P 2  a3 Jupiter: 53 / 122 = 125/144 ~ 1 a P Planet Semi-Major Axis Orbital Period Eccentricity ____ P2/a3 Mercury 0.387 0.241 0.206 1.002 Venus 0.723 0.615 0.007 1.001 Earth 1.000 1.000 0.017 1.000 Mars 1.524 1.881 0.093 1.000 Jupiter 5.203 11.86 0.048 0.999 Saturn 9.539 29.46 0.056 1.000 Uranus 19.19 84.01 0.046 0.999 Neptune 30.06 164.8 0.010 1.000 Pluto 39.53 248.6 0.248 1.001 (A.U.) (Earth years) more distant planets move more slowly and have longer "years". Kepler can determine ratio of sizes of the planets' orbits but not the actual sizes; this is because he uses orbit of Earth as baseline for triangulation. If we know the size of one planet's orbit, we can find the rest. Earth's orbit (1 AU)=93 million mi=150 million km=8 light minutes. Nowadays determined by radar ("radio detection and ranging") bounced off Venus. 15