ASTRONOMY 161Introduction to Solar System Astronomy

Class 6

Tycho, Kepler, & GalileoWednesday, January 17

“E pur si muove!” [It still moves!]

- Galileo

Astronomical movies:

The Phases of Venushttp://antwrp.gsfc.nasa.gov/apod/ap060110.html

When Moons and Shadows Dance (Jupiter)http://antwrp.gsfc.nasa.gov/apod/ap030227.html

Large Sunspot Group (Sun)http://antwrp.gsfc.nasa.gov/apod/ap010411.html

Tycho, Kepler, & Galileo: Key Concepts

(1) Tycho Brahe made accurate measurements of planetary motion.

(2) Planetary orbits are ellipses with the Sun at one focus.

(3) A line between planet & Sun sweeps out equal areas in equal times.

(4) The square of a planet’s orbital period is proportional to the cube of its average distance from the Sun.

(5) Galileo made telescopic observations supporting the heliocentric model.

(1) Tycho Brahe made accurate measurements of planetary motion.

Tycho Brahe (1546-1601): Danish astronomer

Tycho discovered ‘new star’, or ‘nova’, upsetting ancient notion of perfect, unchanging heavens.

Made very accurate measurements of planetary positions.

Tycho’s contributions to astronomy

Copernican system

Tycho’s system

Was Tycho’s assistant.Used Tycho’s data to

discover

Three Laws of Planetary Motion.

Johannes Kepler (1571-1630): German

(2) Kepler’s First Law of planetary motion

The orbits of planets around the Sun are ellipses with the Sun at one focus.

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.

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.

Example: Mars

Semimajor axis = 1.524 A.U.

Eccentricity = 0.093 (much smaller than one)

Ellipse comes from the family of Conic Sections

(3) Kepler’s Second Law of planetary motion

A line from the Sun to a planet sweeps out equal

areas in equal time intervals.

Consequences of Kepler’s Second Law:

Planets move fastest when closest to the Sun.

Example: MarsPerihelion: 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

(4) 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*:

*A planet’s average distance from the Sun is equal to the semimajor axis of its orbit.

32 aP =

Kepler’s Third Law in mathematical form:

P = orbital period (in years)a = semimajor axis (in A.U.)

Example: The orbit of Mars

54.3 A.U. 524.1

54.3 yr 881.13

2

==

==

aa

PP

32 aP =

(5) Galileo made telescopic observations supporting the heliocentric model.

Galileo Galilei (1564-1642): Italian

Galileo was among the first to observe the sky with a telescope (1609).

Flashback to Class 1: What is Science?The SYSTEMATIC study of the Universe

Gather facts

Modify hypothesis Guess an explanation(Guess=hypothesis)

Test hypothesis

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.

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?

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.

4) Venus shows phases like those of the Moon.

Venus goes through all phases: looks big when nearly new, looks small when full.

Results consistent with Copernicus, inconsistent with Ptolemy.

Phases of Venus in the geocentric model of Ptolemy.

Only new and crescent phases.

Phases of Venus in the heliocentric model.

All phases; smaller angular size when full than when new.

Few closing questions:

1) Do the inner planets show retrograde motions? (again)

2) See picture on the right. What is it?

3) Does Mercury show phases? Mars? Jupiter?

Few closing questions continued:

4) If the Sun is at one focus of the ellipse, what is at the other focus?

5) See picture on the right. What is it? Is it real?