ASTRONOMY 161 Introduction to Solar System Astronomy

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ASTRONOMY 161Introduction to Solar System
Astronomy
Class 6
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Tycho, Kepler, GalileoMonday, October 5

• E pur si muove! It still moves!
• - Galileo

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Astronomical movies

• The Phases of Venus
• http//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

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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 planets orbital period is
  proportional to the cube of its average distance
  from the Sun.
• (5) Galileo made telescopic observations
  supporting the heliocentric model.

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

• Tycho Brahe (1546-1601) Danish astronomer

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Tychos contributions to astronomy

• Tycho discovered new star, or nova, upsetting
  ancient notion of perfect, unchanging heavens.
• Made very accurate measurements of planetary
  positions.

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• Copernican system

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• Tychos system

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Johannes Kepler (1571-1630) German

• Was Tychos assistant.
• Used Tychos data to discover
• Three Laws of Planetary Motion.

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(2) Keplers 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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Example Mars

• Semimajor axis 1.524 A.U.
• Eccentricity 0.093 (much smaller than one)

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Ellipse comes from the family of Conic Sections
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(3) Keplers
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 Keplers 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

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(4) Keplers Third Law of
planetary motion

• The square of a planets orbital period is
  proportional to the cube of its average distance
  from the Sun
• A planets average distance from the Sun is
  equal to the semimajor axis of its orbit.

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Keplers Third Law in mathematical form

• P orbital period (in years)
• a semimajor axis (in A.U.)
• Example The orbit of Mars

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(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).

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Flashback to Class 1 What is Science?

• The SYSTEMATIC study of the Universe
• Gather facts
• Modify hypothesis Guess an
  explanation
• (Guesshypothesis)
• Test hypothesis

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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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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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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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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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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?

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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?