Johannes Kepler 15711630

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Johannes Kepler (1571-1630)

• German Mathematician and Astronomer
• Passionately convinced of the rightness of the
  Copernican view.
• Set out to prove it!

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Early Life and Values

• Studied at University of Tubingen
• Intended to be Lutheran Minister.
• .But got diverted into Astronomy!
• Devout Christian, who saw God as the Great
  Geometer Pythagorian Tendencies
• In 1594 moved to University of Graz, Austria as
  mathematics and astronomer teacher.

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Details of Keplers Mysterium

• The five regular solids of Antiquity
• Shape Sides

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Keplers Mysterium1596

• Geometric Solar system of perfect solids
  nested in spheres.

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Mysterium Cosmographicum 1596

• Euclidean Geometry
• Only 5 regular solids that could be both
  circumscribed and inscribed by spheres.

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Keplers Emphasis

• Cosmical Mystery unashamedly Copernican.
• Sun was driving mechanism, as distant planets
  travel slower.
• Thats why there are only 6 planets!
• God is a mathematician!
• Pythagorean harmony and beauty.
• Seeking mechanism for the motion of planets, not
  just charting them.

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Kepler and Brahe (1600-1601)

• Tycho Brahes Assistant from 1600, while near
  Prague.
• Studied the problematical motion of Mars.
• Kepler promoted after Brahes untimely death to
  Imperial Mathematicus to Rudolph II.
• Acquired Tychos data after his death!

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Incidentally Kepler andThe Star of Bethlehem

• In 1604 Kepler observed a brilliant conjunction
  (a close apparent mutual approach) of Jupiter,
  Saturn and Mars.
• He calculated that this type of conjunction takes
  place every 805 years.
• Hence previously occurred in AD 799 and in
  (February) 6 BC.
• This is now regarded as the Star of Bethlehem.

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Keplers Nova(1604)
Also seen by Galileo
Remnant as seen today
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Keplers Astronomia Nova (1609)
Title page mentions both Tycho Brahe.and his
Patron, Emperor Rudolph.
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Keplers Astronomia Nova (1609)

• Accurate data ultimate challenge to circular
  motion.
• Eventually discovered that ellipses would
  dramatically describe the observations!

Marks the site of Keplers house while in Prague.
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Keplers First Law

• The orbital paths of planets are elliptical
• (not circular) with the Sun at one focus.

Properties of conic sections known since
Apollonius and Euclid
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Definition on an Ellipse

• Locus of points produced by this practical
  geometric construction.

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Property of an Ellipse

• Major and Minor axes
• Two Foci.
• The Sun is at one focus, the other is not
  physically significant.

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Comments on Elliptical Motion

• Elliptical motion No small achievement!
• Challenged the Authority of Aristotle.
• Except for Mercury (and Pluto) eccentricity is so
  small cannot easily distinguish it from circular
  motion.
• Hence Ptolemaic and Copernican models did so well
  for so long.
• Galileo did not like ellipses!

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Keplers Second Law(Though discovered First!)

• An imaginary line connecting the Sun to any
  planet sweeps out equal areas in equal intervals
  of time.
• Planets therefore have different speeds at
  perihelion and aphelion.
• Challenges Aristotles insistence that planets
  have a constant or uniform speed.

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Keplers Second Law Visualised

• Red arcs all take the same time
• for equal areas A, B, C.

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Keplers Harmonices Mundi 1619

• Never lost his admiration for Pythagorean
  harmony.
• Was aware of Gilberts Magnetism (1600)
• Seeking a causation for motion
• My aim is to show that the celestial machine is
  to be likened not to a divine organism, but
  rather to clockwork. Johannes Kepler

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Keplers Third Law

• Laws (1) and (2) published in 1609, based on a
  long study of the motion of Mars.
• An appeal to simplicity in mathematics.
• During next 10 years extended to all known
  planets and devised 3rd law.
• The square of the planets orbital period is
  proportional to the cube of its semi-major
  axis. or P2/a3 Constant

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Orbital Properties of the Planets
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Further Notes

• Period is Sidereal period
• Astronomical Unit semi-major axis of the
  Earths orbit
• (or average Sun-Earth distance)
• Deviations in P2/a3 for Uranus and Neptune is
  mutual gravitational effect.
• Predictive Law .applies to all planets.

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The Size of the Solar System

• Keplers 3rd Law (P2/a3 Constant) only gives
  the relative scale of the solar system
• Orbital periods known in terms of Earth years.
• Semi-major axis known in terms of that of the
  Earth.
• Need to determine the actual length of the
  Astronomical unit (A.U.)..how?
• Need reliable measure of the parallax when the
  planet is closest to us (hence biggest
  parallax)

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Keplers Rudolphine Tables (1627)

• Pillars of Astronomy Hipparchus, Ptolemy,
  Copernicus and Brahe
• Most accurate planetary tables
• Significantly better than Copernican
  Prutenic Tables

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Keplers Rudolphine Tables (1627)
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Reaction to Keplers Work

• Slow acceptance, despite certain religious
  misgivings.
• Ultimately his reliable Rudolphine Tables would
  force people to recognize his achievements
  but mainly after his death
• Welcomed in England, Galileo sceptical.
• Increased emphasis on mechanism not teleology.
• Pivotal figure in challenging Aristotle.

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Doppelmayer Celestial Atlas Frontispiece (1742)

• Ptolemy, Copernicus, Kepler and Brahe