Lecture 4: Kepler and Galileo

Astronomy 111

ASTR111 Lecture 4

Was Tycho’s assistant

Used Tycho’s data to discover

Three Laws of Planetary Motion

Johannes Kepler (1571-1630): German

ASTR111 Lecture 4

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.!

Kepler

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Kepler’s First Law of planetary motion

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

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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.

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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.

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Circle: !

"eccentricity=0!

Ellipse: !

"eccentricity 0<e<1!

Eccentricity

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Example

Mars

Semimajor axis = 1.524 A.U.

Eccentricity = 0.093 (much smaller than one)

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Kepler’s Second Law of planetary motion

A line from the Sun to a planet sweeps out equal areas in equal time

intervals.

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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

ASTR111 Lecture 4

ASTR111 Lecture 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.

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

Example: The orbit of Mars

Kepler’s Third Law of planetary motion

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Kepler solved problems of heliocentric models

•  Kepler’s Third Law means no more epicycles!

ASTR111 Lecture 4

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.!

Kepler

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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 106 miles

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Answer

•  4 a.u. = 3.7 x 107 miles

•  Note that it is highly unlikely to find a comet with such a short period—someone would have found it by now!

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Galileo

Galileo Galilei (1564-1642): Italian

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

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Galileo

“Galileo, perhaps more than any other single person, was responsible for the birth of modern science.”

–Stephen Hawking

Galileo made telescopic observations supporting the heliocentric model

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What is Science?

The SYSTEMATIC study of the Universe

Gather facts

Modify hypothesis Guess an explanation

(Guess=hypothesis)

Test hypothesis

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Galileo’s telescope

•  1st 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

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Sidereus Nuncius: “The Starry Messenger” (1610)

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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.

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ASTR111 Lecture 4

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?

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ASTR111 Lecture 4

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.

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Two pages from the Sidereal

Messenger (1610)

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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.

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Phases of Venus in the geocentric model of Ptolemy

Only new and

crescent phases.

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Phases of Venus in the heliocentric model

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

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More observations

•  “Cloud” of Milky Way is actually composed of stars

•  Planets were disks, not points of light like other stars

•  Saturn had “ears”

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“Dialogue Concerning the Two Chief World Systems” (1632)

•  Another bestseller •  Favored

Copernican universe

•  Written in Italian! •  Church placed on

the “Index Forbidden Books” until 1835

aka “Dialogue on the Ebb and Flow of the Sea”

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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…

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