Giants of Science Part Two Tycho Brahe

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Giants of Science Part TwoTycho Brahe
Johannes Kepler

• These two scientists showed that the Universe was
  not some ideal perfection as Ptolemy proposed and
  worked towards acceptance of Copernicus
  heliocentric model
• Tycho Brahe
• made the most accurate observations of stars and
  planets up to that time.
• was a flamboyant Danish nobleman who wore a
  silver nose when part of his nose was cut off in
  a duel!

Tycho Brahe (1546-1601)
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Tycho Brahe and Uraniborg

• He lived in a mansion/observatory on an island
  off the coast of Denmark.
• The mansion had very sophisticated equipment (but
  no telescopes!) to help him and his assistants to
  measure the positions of stars and planets.
• He named the mansion Uraniborg (Sky Castle).

Some of the equipment used at Uraniborg
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Tycho Brahes Discoveries

• As a young man he proved that comets had to be
  farther from Earth than the Moon.
• He also proved that a star which appeared to
  brighten dramatically over a few weeks was also
  beyond the Moon.
• Both observations showed that the heavens could
  change like the Earth.
• He also came up with his own compromise model of
  the Universe.

Brahes compromise All the planets went around
the Sun while the Sun moved around a fixed Earth
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Tycho Brahe Johannes Kepler

• A few years before he died, Brahe hired Johannes
  Kepler to help in analyzing the data he had
  collected.
• Brahe started him out on his hardest problem
  determine the orbit of Mars.
• Mars has the largest observed retrograde motion
  and no circular orbit could be found to match
  Brahes observations.

Brahe and assistants making observations
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Keplers Models

• After years of work, the most accurate circle he
  could find for Mars orbit still left an error of
  8 arcminutes (about 1/4 the angular size of the
  full Moon).
• If I had believed that we could ignore these
  eight minutes of arc, I would have patched up
  my hypothesis accordingly. But since it was not
  permissible to ignore, those eight minutes
  pointed the road to a complete reformation in
  astronomy
•      - Kepler

Johannes Kepler (1571-1630)
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Keplers Breakthrough

• Keplers key discovery
• planets do not orbit in circles but rather in
  ellipses.
• the Sun was not at the center of the ellipse but
  rather at one focus.
• With this breakthrough he obtained excellent
  agreement between his model and observations.

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Properties of Ellipses

• Each point marked by a tack is called a focus.
• The farther apart one focus is from another the
  more eccentric the ellipse.
• The line cutting the ellipse in half that passes
  through each focus is called a major axis. Half
  the major axis is called a semimajor axis.
• The semimiajor axis is the average distance of
  the planet from the Sun

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Keplers 3 Laws of Planetary Motion

• These laws describe the observed planetary
  motions but do not describe why these motions
  occur as they do.

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Keplers First Law of Planetary Motion

• The orbit of each planet around the Sun is an
  ellipse with the Sun at one focus.
• There is nothing at the other focus.
• The average distance of the planet from the Sun
  is the semimajor axis.
• Throws out Ptolemys perfect circular orbits.

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Keplers Second Law of Planetary Motion

• As a planet moves around its orbit, it sweeps out
  equal areas in equal times.
• A planet travels faster when it is nearer the Sun
  and slower farther away
• Throws out Ptolemys uniform motion

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Keplers Third Law of Planetary Motion

• The amount of time it takes a planet to orbit the
  Sun is related to the size of its orbit by
  P2(years) a3(AU)
• 1 AU (astronomical unit) is the semimajor axis of
  the Earths orbit. Earths average distance from
  the Sun.
• It doesnt matter how elliptical the orbit as
  long as the average distance is the same