The Heliocentric Universe

1. The Heliocentric Universe Scientific reasoning began again in earnest in Europe in the 1400’s. Francis Bacon and other philosophers embarked on experiments to test hypotheses and challenged Aristotle’s claims. The Renaissance in art, literature and engineering (e.g. Leonardo da Vinci) flowed from Italy northward.

2. The Copernican Revolution • Nicholas COPERNICUS (1473-1543), a Polish cleric, argued in favor of a • HELIOCENTRIC COSMOLOGY: THE EARTH IS NOT THE CENTER OF THE UNIVERSE. • The center of the Earth is the center of gravity for objects near it and for the MOON. • The other PLANETS REVOLVE around the SUN. • The STARS are MUCH FARTHER from the EARTH than is the SUN. • STELLAR (SOLAR) ``MOTIONS'' ARE APPARENT: ALL ARE DUE TO MOTION OF THE EARTH. • PLANETARY ``MOTIONS'' are also substantially DUE TO THE EARTH'S MOTIONS.

3. Copernicus’ Model Explains Retrograde Motions of Planets

4. Copernicus vs. Ptolemy • Copernicus' model still assumed circular orbits and still had epicycles --- but now the main orbits went around the Sun and the epicycles could be smaller. • While this model fit the data available then, it was only slightly better and certainly not proven. • SO WHY IS IT ``BETTER''? • THE HELIOCENTRIC MODEL is BOTH SIMPLER and more BEAUTIFUL than the geocentric model. • "Occam's razor”: if two hypotheses both describe the same data equally well, choose the simpler one. • Back then each gave nearly equal explanations of the data; Heliocentric model was a little simpler. • Still, it gained few adherents: it went against "common sense" and was written in Latin.

5. Better Observations Mean Better Models • TYCHO Brahe (1546--1601), a Danish noble, designed and had built HUGE instruments at Uraniborg on Hveen, including: • sextants (for measuring angles) • astrolabes (for locating positions on the sky) • These allowed for PRECISION MEASUREMENTS, particularly of planetary positions. • Accuracies of about 1 arc minute in planetary and stellar positions were achieved. • Tycho was the first to quote errors along with his measurements. • After the peasants protested that his taxes were too high, he lost favor with the new Danish king and moved to Prague in 1597.

6. Tycho in Uraniborg: a naked eye observatory, with large instruments that worked like protractors to measure angles to high accuracy. He discovered and tracked the brightness of a supernova in 1572 and showed a comet in 1577 had to be outside the earth’s atmosphere But he still thought earth was at rest, w/ Sun orbiting it, while other planets went around the Sun.

7. A Key Empirical Discovery • Johannes KEPLER (1571-1630) an Austrian, a great amateur observer, worked under Tycho from 1600 and inherited his data. • He had already accepted the Copernican picture and tried to use this superior data to see if it could fit better than the Ptolemaic theory. • Tycho assigned Kepler to examine the data on Mars first, since it required the biggest epicycles. • Finally, he could understand the relative positions of Mars and Earth if • MARS MOVED IN AN ELLIPSE, WITH THE SUN AT ONE FOCUS. • This broke with the longstanding assumption that combinations of circles were the only way to explain things. But after all, a circle is just a special ellipse, • with ECCENTRICITY = 0. • By 1609 he had also realized that Mars' orbit swept out equal areas in equaltimes.

8. Kepler’s Laws of Planetary Motion • Ten more years of work led to the THREE EMPIRICAL LAWS: • 1. All planets follow elliptical orbits, with the Sun located at one focus. (Nothing is at the other focus.) • 2. Every planet sweeps out equal areas in equal times as it orbits the Sun. • In other words, planets move fastest when closest to the Sun (near PERIHELION) and slowest when furthest away (APHELION).

9. Kepler’s Second Law: Equal Areas Swept out in Equal Times

10. Kepler and Ellipses

11. Sidebar on Ellipses: 1 • To draw one, loop a string around two tacks, holding it taught with a pencil point. • Definition: the locus of points the sum of whose distances from two other points (the foci) is constant. • The longest axis through an ellipse is the MAJOR AXIS One half of that is the SEMI-MAJOR AXIS, a • One half of the shortest axis ( perpendicular to the major axis) is the SEMI-MINOR AXIS, b • Distance from the Center to each Focus is semi-major axis times the ECCENTRICITY or FC = ae • e = [1 - (b/a)2]1/2 OR: b2 = a2(1 - e2) • If e = 0 we have a circle (b=a; foci and center coincide); • if e = 1 we have a line-segment

12. Sidebar on Ellipses: 2 • An ellipse is a conic section: slice a cone with a plane not parallel to its base but not as steep as its side. • The other conic sections are: circle (slice parallel to base), parabola (as steep as side) & hyperbola (steeper)

13. Ellipses and Planetary Orbits

14. Kepler’s Third Law of Planetary Motion • 3. The cube of the semi-major axis of a planet's orbit is proportional to the square of its period. • a3 = P2 if a is in units of AU and P is in years (in OUR solar system). • Examples: • aMars = 1.524 AU so PMars = (1.524)3/2 = 1.881 years; aJupiter= 5.20 AU so PJupiter = (5.20)3/2 = 11.86 years. • More generally, a  P2/3 or P  a3/2 • Later Newton showed that these general proportionalities (but not equality) was always true for systems with a single dominating mass, not just our solar system.

15. New Technology & New Evidence • GALILEO Galilei (1564--1642) taught mathematics and astronomy at Padua. • He performed EXPERIMENTS: e.g., balls rolling down inclined planes and learned about INERTIA. • Galileo Built a TELESCOPE in 1609. Instead of commercial or military use (since 1608) • GALILEO POINTED IT AT THE SKY and DISCOVERED: • The LUNAR TERMINATOR WAS IRREGULAR; it had MOUNTAINS and WASN'T A PERFECT SPHERE. • PLANETS LOOKED LIKE DISKS, STARS STILL LOOKED LIKE POINTS. • MILKY WAY IS COMPRISED OF MANY STARS --- many fainter stars could be seen between those visible to the naked eye.

16. Galileo and the Moon

17. More of Galileo’s Discoveries • VENUS WENT THROUGH PHASES (including a Full phase, not possible in Ptolemaic model) --- reflecting light from the Sun. Phases of Venus applet • THE SUN HAD SPOTS --- the most perfect of all heavenly bodies had blemishes. • JUPITER HAD FOUR MOONS --- something other than Earth had things going around it. • All of these discoveries, published in 1610 Sidereus nuncius, challenged the Aristotlean / Catholic picture of the Universe --- perfect spheres shining by themselves, perfect circular orbits, only the Earth at the center of everything. • While he had already thought Copernicus' model was best Galileo felt this DATA had PROVEN it.

19. Galileo & the Vatican • While others in Germany, England, etc., confirmed these discoveries and accepted the HELIOCENTRIC PICTURE, the response in Rome wasn't very good: • Although Vatican astronomers confirmed his observations, they didn't accept his logic and demanded that Copernicus' model not be taught. • Galileo was ordered to stop supporting this view, and he became more circumspect, finally publishing a Dialog Concerning the Two Chief World Systems in Italian in 1632. • After facing the Inquisition and nominally renouncing his ideas, he was placed under house arrest in 1633. • Catholic church stopped banning heliocentric books in 1757 but formally vindicated Galileo only in 1992!

20. When was the Earth known to be circular and its circumference measured? • From the earliest times • By the Greeks • At the start of the Renaissance • By Galileo, in the early 17th century • Around 1800

21. When was the Earth known to be circular and its circumference measured? • From the earliest times • By the Greeks • At the start of the Renaissance • By Galileo, in the early 17th century • Around 1800

22. Whose suggestion that the Sun is the center of the solar system was first taken seriously by many people? • Copernicus • Tycho • Kepler • Galileo

23. Whose suggestion that the Sun is the center of the solar system was first taken seriously by many people? • Copernicus • Tycho • Kepler • Galileo