1. NATS 1311 - From the Cosmos to Earth Nicholas Copernicus (1473-1543) - wanted better way to predict planetary positions - adopted Sun-centered planetary system suggested by Aristarchus - worked out simple geometric relationships that allowed calculation of planet’s true orbital period and distance from Sun in terms of Earth-Sun distance (AU) - still believed that heavenly motion must still be perfect circles - had to add circles upon circles as in the Ptolemaic model - did not make substantially better predictions and was not accepted for another 50 years Heliocentric World View - The Copernican Revolution

2. NATS 1311 - From the Cosmos to Earth Tycho Brahe (1546 - 1601) - observed alignment of Jupiter and Saturn in 1563 - occurred two days later than Copernicus prediction - decided to compile precise measurements of stellar and planetary positions - compiled best set of naked-eye observation ever made - to within 1 arcminute (thickness of a fingernail at arm’s length) - observed supernova of 1572 - proved it was farther away than the Sun - called it a nova (“new star”) - observed comet - proved was in the heavens - believed planets must orbit Sun but never succeeded in explaining planetary motion. Inability to detect stellar parallax led him to believe that Sun orbited Earth while all other planets orbited Sun

3. NATS 1311 - From the Cosmos to Earth A Complete Reformation of Astronomy Johannes Kepler (1571 - 1630) - hired by Tycho Brahe to explain observations - years of calculations trying to find circular orbit for Mars that matched Tycho’s observations - succeeded in matching Mars’ position in ecliptic - could not match position north or south of ecliptic - finally realized planetary orbits were not circular but elliptical - developed three laws of orbital motion - accurately predicted planetary motions and matched Tycho’s data

4. NATS 1311 - From the Cosmos to Earth : Law 1: Law of elliptical orbits Each planet moves in an elliptical orbit. Law 2: Law of areas The imaginary line connecting any planet to the sun sweeps over equal areas of the ellipse in equal intervals of time. Law 3: Law of periods The square of any planet's period of orbital revolution is proportional to the cube of its mean distance from the sun. Kepler’s Laws of Planetary Motion

5. NATS 1311 - From the Cosmos to Earth Kepler’s First Law The orbit of each planet around the Sun is an ellipse with the Sun at one focus

6. NATS 1311 - From the Cosmos to Earth (a)Drawing a circle. (b) Drawing an ellipse. (c) Eccentricity describes how much an ellipse deviates from a perfect circle.

7. NATS 1311 - From the Cosmos to Earth Drawing an Ellipse Animation

8. NATS 1311 - From the Cosmos to Earth Eccentricity and Semi-Major Axis Animation

9. NATS 1311 - From the Cosmos to Earth As a planet moves around its orbit, it sweeps out equal areas in equal times. Kepler’s Second Law

10. NATS 1311 - From the Cosmos to Earth Area and Time Animation

11. NATS 1311 - From the Cosmos to Earth Velocity vs Orbit Animation

12. NATS 1311 - From the Cosmos to Earth The square of any planet's period, P, of orbital revolution is proportional to the cube of its mean distance, r, from the sun. I.e., the more distant a planet, the slower it moves on average. Example: For earth, r E = 1 AU, P E = 1 year. For Mars, r M = 1.52 AU, P M = 1.88 years Kepler’s Third Law

13. NATS 1311 - From the Cosmos to Earth A plot of the cube of the average planetary distance vs the square of the orbital period is a straight line The average orbital speed is inversely proportional to the average distance from the sun

14. NATS 1311 - From the Cosmos to Earth Orbital Period vs Distance Animation

15. NATS 1311 - From the Cosmos to Earth Galileo Galilei (1564 - 1642) - demonstrated that a moving object remains in motion unless acted on by an outside force (Newton’s 1st law) - contradicted Aristotle’s claim that the natural tendency of any moving object is to come to rest. Birds, falling stones, clouds, etc.. would stay with the Earth unless knocked away by some force - used telescope that he built (invented by Hans Lippershey) - - saw sunspots on the Sun, craters and valleys on the moon - proved that the heavens were not perfect and unchanging - observed moons orbiting Jupiter - observed the phases of Venus - showed that Milky Way resolved into countless individual stars - argued stars far more numerous and distant than imagined - reason stellar parallax not observed - recanted before Church inquisition in Rome in 1633 - formerly vindicated by the Church in 1992 The Death of the Earth Centered Universe

16. NATS 1311 - From the Cosmos to Earth Major Discoveries of Galileo Moons of Jupiter (4 Galilean moons) Rings of Saturn (What he really saw)

17. NATS 1311 - From the Cosmos to Earth Surface structures on the moon - shadows; first estimates of the height of mountains on the moon

18. NATS 1311 - From the Cosmos to Earth Sun spots (proving that the sun is not perfect!)

19. NATS 1311 - From the Cosmos to Earth Phases of Venus (including “full Venus”) - In the Ptolemaic system, phases would only range from new to crescent. Proved that Venus orbits the sun, not the Earth!

20. NATS 1311 - From the Cosmos to Earth Phases of Venus Animation

21. NATS 1311 - From the Cosmos to Earth Speed, Velocity, and Acceleration Speed - rate of travel - distance per unit time Velocity - speed of travel in a certain direction - a vector - has magnitude and direction Acceleration - rate of change of velocity - change in velocity per unit time

22. NATS 1311 - From the Cosmos to Earth Acceleration of Gravity All objects in a gravitational field fall at a constant acceleration - g - regardless of mass On Earth - g=9.8 m/s 2 or 32 ft/s 2 On the Moon - g=1.63 m/s 2 or 1/6th that of Earth Calculate height of building - drop a rock and time ‘its fall - h=1/2gt 2

23. NATS 1311 - From the Cosmos to Earth Gravity and Acceleration Animation Galileo demonstrated that acceleration of gravity is independent of the mass of the falling object - supposedly dropped balls of different mass from Leaning Tower of Pisa - Newton showed why.

24. NATS 1311 - From the Cosmos to Earth

25. Feather and Hammer Animation