Lecture 5 Galileo and Brahe September 21, 2015

Transcription

1 Lecture 5 Galileo and Brahe September 21,

2 2 Galileo Galilei ( ) Supported Copernican model. Used telescope to observe sky (1610). Mountains on the moon Rings of Saturn Sunspots Milky Way is made of stars

3 3 Geocentric Model of Venus

4 4 Observations of Venus Venus has phases similar to the moon. The apparent size of Venus changes with the phase.

5 5 If Venus was orbiting the Earth, its distance would not change and its size would stay the same. Phases of Venus

6 6 Basic Geocentric View Order of planets somewhat arbitrary. Mercury and Venus always orbit at velocity to keep them near the Sun. Celestial Sphere Mars Saturn Jupiter Venus E Sun Mercury Moon

7 7 Observations of Jupiter Observations of Jupiter Observed the 4 largest moons of Jupiter (Galilean Moons). The fact that bodies could orbit other planets supported heliocentric view.

8 8 What would you expect to see if Venus orbited the Earth in the manner Ptolemy described? A. You would not observe all of the phases, but the size would change. B. You would observe all of the phases and the size would change. C. You would observe all of the phases but the size would not change. D. You would not observe all of the phases and the size would not change. 12% 17% 41% 29% A. B. C. D.

9 9 Tycho Brahe ( ) Supported geocentric model Pre-dates invention of telescope

10 11 Tycho s Observations Designed state of the art instruments to observe sky (all naked eye observations). Made detailed observations of planetary and stellar positions. Positions accurate up to 1 arcminute (1/60 of a degree)

11 12 Tycho s observations Used many instruments to confirm results. Same method used by modern astronomers.

12 13 Tycho s Supernova (1592) Believed stars unchanging New star must be near Earth Tried to measure distance to object using parallax. No parallax observed Object much more distant that originally thought. Heavens are not unchanging

13 14 A key contribution that Tycho Brahe made to astronomy is A. his accurate predictions of planetary positions B. his observation that a supernova was very distant. C. his observations of the phases of Venus. D. his invention of the telescope. 58% 41% 1% 0% A. B. C. D.

14 15 Johannes Kepler ( ) Assistant to Brahe ( ) Believed in heliocentric model (Copernicus). Wanted mathematical model of orbits Used observations by Brahe Used trial and error to test models

15 17 Kepler s First Law The orbit of a planet about the Sun is an ellipse with the Sun at one focus. Animation of how to draw

16 18 Elliptical Orbit There is nothing physically at the second focus of the ellipse. Focus b Focus Aphelion: furthest distance from the Sun erihelion: closest istance to the un Semi-major axis Animation applet For the Sun and the planets the orbits are are almost circular. a

17 19 Eccentricity = Shape of Orbit Values range from 0 to 1 0 = circle 0.5 = ellipse 1 = straight line 2 1 b a 2

18 20 Kepler s Second Law The Law of Equal Areas -- A line joining a planet and the Sun always sweeps out equal areas in equal intervals of time. Animation applet

19 21 What does Kepler s Second Law imply about the speed of the planet? A. It moves fastest when it is midway between the nearest and farthest points from the Sun. B. It moves faster when it is far from the Sun. C. It moves faster when it is near the Sun. D. Its speed is constant. 99% 0% 1% 0% A. B. C. D.

20 22 Speed of planets in elliptical Planet moves fastest at perihelion orbits Animation Planet moves slowest at aphelion

21 23 P 2 = a 3 Kepler s Third Law P = sidereal period in years a = semi-major axis in AU The closer a planet is to the Sun, the less time it takes to go around the Sun. Example: If P 8.0 years then P a 3 a AU

22 24 What is the semi-major axis of an asteroid that orbits the Sun with a period of 11 years? A. 3 AU 86% B. 5 AU C. 7 AU D. 11 AU 8% 4% 1% A. B. C. D.

23 25 What is the semi-major axis of an asteroid that orbits the Sun with a period of 11 years? A. 3 AU B. 5 AU C. 7 AU D. 11 AU a a 3 2 P AU 5 AU

24 26 If this asteroid has a perihelion distance of 1.5 AU, what is its aphelion distance? A. 1.5 AU 79% B. 3.5 AU C. 5.0 AU D. 8.5 AU 4% 9% 8% A. B. C. D.

25 27 If this asteroid has a perihelion distance of 1.5 AU, what is its aphelion distance? A. 1.5 AU B. 3.5 AU C. 5.0 AU PD AD 2a AD 2a PD 2 5 AU 1.5 AU D. 8.5 AU AD 8.5 AU

26 28 General Comments on Kepler s Laws Can apply to all orbiting bodies (moons, planets, stars, galaxies..) in slightly modified form. Best model that fit data -- not derived from physical principles Simpler than Copernican model Fits data more accurately