# Lecture 4: Kepler and Galileo. Astronomy 111 Wednesday September 6, 2017

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1 Lecture 4: Kepler and Galileo Astronomy 111 Wednesday September 6, 2017

2 Reminders Online homework #2 due Monday at 3pm

3 Johannes Kepler ( ): German Was Tycho s assistant Used Tycho s data to discover Three Laws of Planetary Motion

4 Kepler Formulated laws of planetary motion: 1. Each planet moves in an ellipse with the Sun at one focus. 2. The line between the Sun and the planet sweeps over equal areas in equal time intervals. 3. The ratio of the cube of the semi-major axis to the square of the period is the same for each planet.

5 Kepler s First Law of planetary motion The orbits of planets around the Sun are ellipses with the Sun at one focus.

6 Ellipse = an oval built around two points, called focuses (or foci) SIZE of ellipse: Major axis = longest diameter of ellipse. Semimajor axis = half the major axis.

7 SHAPE of ellipse: Eccentricity = distance between foci divided by major axis. Foci close together: ellipse nearly circular, eccentricity close to zero. Foci far apart: ellipse very flattened, eccentricity close to one.

8 Eccentricity Circle: Ellipse: eccentricity=0 eccentricity 0<e<1

9 Example Mars Semimajor axis = A.U. Eccentricity = (much smaller than one)

10 Kepler s Second Law of planetary motion A line from the Sun to a planet sweeps out equal areas in equal time intervals.

11 Consequences of Kepler s Second Law: Planets move fastest when closest to the Sun. Example: Mars Perihelion: 206,600,000 km (1.381 A.U.) Max. Orbital Speed: 26.5 km/s Aphelion: 249,200,000 km (1.666 A.U.) Min. Orbital Speed: 22.0 km/s

12

13 Kepler s Third Law of planetary motion The square of a planet s orbital period is proportional to the cube of its average distance from the Sun*: P 2 a 3 *A planet s average distance from the Sun is equal to the semimajor axis of its orbit.

14 Kepler s Third Law of planetary motion P 2 a 3 P = orbital period (in years) a = semimajor axis (in A.U.) Example: The orbit of Mars P yr P a A.U. a

15 Kepler solved problems of heliocentric models Kepler s Third Law means no more epicycles!

16 Kepler Formulated laws of planetary motion: 1. Each planet moves in an ellipse with the Sun at one focus. 2. The line between the Sun and the planet sweeps over equal areas in equal time intervals. 3. The ratio of the cube of the semi-major axis to the square of the period is the same for each planet.

17 In-class assignment: New Comet: A new comet is discovered and studies of its motion indicate that it orbits the Sun with a period of 8 years. Use Kepler s third law to find the comet s average distance from the Sun (i.e. find the semi-major axis of the comet s orbit). Convert your answer into miles 1 a.u. = 9.3 x 10 6 miles Show your work!

18 Answer 4 a.u. = 3.7 x 10 7 miles Note that it is highly unlikely to find a comet with such a short period someone would have found it by now!

19 Galileo Galileo Galilei ( ): Italian Galileo was among the first to observe the sky with a telescope (1609).

20 Galileo Galileo made telescopic observations supporting the heliocentric model Galileo, perhaps more than any other single person, was responsible for the birth of modern science. Stephen Hawking

21 What is Science? The SYSTEMATIC study of the Universe Gather facts Modify hypothesis Guess an explanation (Guess=hypothesis) Test hypothesis

22 Galileo s telescope 1 st telescope invented in Holland in 1609 Galileo learned of this and made his own: small 30X scope Observed the moon and began the modern age of Astronomy in which measurement was more important than philosophy

23 Sidereus Nuncius: The Starry Messenger (1610) ASTR111 Lecture 4

24 1) Mountains on the Moon Aristotle & Ptolemy said the Moon is a perfect, smooth sphere. In fact, the Moon is no more perfect than the Earth. ASTR111 Lecture 4

25

26 2) The Sun has spots on its surface The Sun is not perfect. Motion of sunspots indicates that the Sun is rotating. If the Sun rotates, why not the Earth?

27

28 3) The planet Jupiter has moons of its own Four Galilean moons of Jupiter: Io, Europa, Ganymede, & Callisto. The Earth is NOT the center of all orbits in the universe.

29 Two pages from the Sidereal Messenger (1610) ASTR111 Lecture 4

30

31 4) Venus shows phases like those of the Moon ASTR111 Lecture 4 Venus goes through all phases: looks big when nearly new, looks small when full. Results consistent with Copernicus, inconsistent with Ptolemy.

32 Phases of Venus in the geocentric model of Ptolemy Only new and crescent phases. ASTR111 Lecture 4

33 Phases of Venus in the heliocentric model All phases; smaller angular size when full than when new. ASTR111 Lecture 4

34 Compilation of actual photographs of Venus taken through a telescope by Dave Smith between July 2010 and January The images are placed on an ellipse (not shown) at their correct distance from the Sun. ASTR111 Lecture 4

35 More observations Cloud of Milky Way is actually composed of stars Planets were disks, not points of light like other stars Saturn had ears

36 Dialogue Concerning the Two Chief World Systems (1632) aka Dialogue on the Ebb and Flow of the Sea Another bestseller Favored Copernican universe Written in Italian! Church placed on the Index Forbidden Books until 1835

37 Galileo Persecuted for his work imprisoned in 1632 convicted of grave suspicion of heresy Catholic church did not accept the heliocentric model Famously muttered E pur si muove and yet it moves! In 1992 the Church apologized for its treatment of Galileo

38

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