The Copernican Revolution The Birth of Modern Science

What do we see in the sky? The stars move in the sky but not with respect to each other The planets (or “wanderers”) move differently from stars They move with respect to the stars They exhibit strange retrograde motion What does all this mean? How can we explain these movements? What does the universe look like?

Timeline Galileo 1564-1642 Newton 1642-1727 Tycho 1546-1601 Copernicus 1473-1543 Kepler 1571-1630

Geocentric (Ptolemaic) System The accepted model for 1400 years The earth is at the center The Sun, stars, and planets on their spheres revolve around the earth: explains daily movement To account for unusual planetary motion epicycles were introduced Fit the Greek model of heavenly perfection – spheres are the perfect shape, circular the perfect motion

Heliocentric (Copernican) System Sun at center (heliocentric) Uniform, circular motion No epicycles (almost) Moon orbited the earth, the earth orbited the sun as another planet Planets and stars still on fixed spheres, stars don’t move The daily motion of the stars results from the Earth’s spin The annual motion of the stars results from the Earth’s orbit

In the heliocentric model, apparent retrograde motion of the planets is a direct consequence of the Earth’s motion

Geocentric vs. Heliocentric How do we decide between two theories? Use the Scientific method: These are both explanations based on the observation of retrograde motion What predictions do the models make? How can these predictions be tested?

Phases of Venus Heliocentric predicts that Venus should show a full phase, geocentric does not Unfortunately, the phases of Venus cannot be observed with the naked eye

Geocentric vs. Heliocentric Against heliocentric It predicted planetary motions and events no better than the Geocentric system The earth does not move (things do not fly off) The earth is different from the heavens (from Aristotle – the heavens are perfect and unchanging) and cannot be part of the heavens For heliocentric Simplified retrograde motion, but epicycles were necessary to account for the planets’ changing speed The distances to the planets could be measured. These distances were ordered, and therefore aesthetically pleasing to the philosophy of the day

Stellar Parallax Parallax caused by the motion of the earth orbiting the Sun Not observed with the naked eye The heliocentric model predicts stellar parallax, but Copernicus hypothesizes that the stars are too far away (much farther than the earth from the Sun) for the parallax to be measurable with the naked eye

Misconceptions The Copernican model has a force between the sun and the planets. Actually, the natural motion of the celestial spheres drove the planetary motions. The Copernican model was simpler than the Ptolemaic one. In fact, though Copernicus eliminated circles to explain retrograde motion, he added more smaller ones to account for nonuniformities of planetary motions. The Copernican model predicted the planetary motions better. Because both models demanded uniform motion around the centers of circles, both worked just about as well – with errors as large as a few degrees at times.

Galileo Galilei Turned a telescope toward the heavens Made observations that: contradicted the perfection of the heavens Mountains, valleys, and craters on the Moon Imperfections on the Sun (sunspots) Supported the heliocentric universe Moons of Jupiter Phases of Venus – shows a full phase

Tycho Brahe Had two sets of astronomical tables: one based on Ptolemy’s theory and one based on Copernicus’. He found that both tables’ predictions were off by days to a month. He believed that much better tables could be constructed just by more accurate observations. Tycho’s homemade instruments improved measurement precision from ten minutes of arc (which had held since Ptolemy) to less than one

The skies change Tycho observed 2 phenomena that showed the heavens DO change: In November 1572, Tycho noticed a new star in the constellation Cassiopeia Comet of 1577 Prior to this sighting, comets were thought to be atmospheric phenomena because of the immutability of the heavens But neither the star nor the comet changed position as the observer moved, as expected for atmospheric phenomena

Johannes Kepler Kepler succeeded Tycho as the Imperial mathematician (but at only 1/3 the salary of the nobleman) Kepler worked for four years trying to derive the motions of Mars from Brahe’s observations In the process, he discovered that the plane of the earth’s orbit and the plane of Mars’ (and eventually the other planets) passed through the sun Suspecting the sun had a force over the planets, he investigated magnetism While this is not true, it did lead him to the idea of elliptical orbits “With reasoning derived from physical principles agreeing with experience, there is no figure left for the orbit of the planet except a perfect ellipse.”

Astronomia nova Published in 1609, The New Astronomy was just that, it revolutionized the field It predicted planetary positions as much as ten times better than previous models It included physical causes for the movement of the planets The ideas of the Greeks were gone – the heavens no longer were perfect, immutable, or different from the earth

Kepler’s first Law The orbital paths of the planets are elliptical (not circular), with the Sun at one focus.

Kepler’s second law An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

Kepler’s Third Law The square of a planet’s orbital period is proportional to the cube of its semi-major axis. Kepler orbit demonstration: http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html

Planetary Properties Planet Orbital eccentricity, e Orbital semi-major axis, a (Astronomical units) Orbital period,P (Earth years) Mercury 0.206 0.387 0.241 Venus 0.007 0.723 0.615 Earth 0.017 1.000 Mars 0.093 1.524 1.881 Jupiter 0.048 5.203 11.86 Saturn 0.054 9.537 29.42 Uranus 0.047 19.19 83.75 Neptune 0.009 30.07 163.7 Pluto 0.249 39.48 248.0

Other Solar System Bodies Kepler derived his laws for the 6 planets known to him. The laws also apply to the 3 discovered planets and any other body orbiting the Sun (asteroids, comets, etc.)

A force for planetary motion Newton proposes a force which controls the motion of the planets – GRAVITY The larger the mass, the larger the force of gravity The further the distance, the smaller the force of gravity Kepler’s third law can be derived from Newton’s law of gravity F = GMm/r2 = mg

Gravity