Johannes Kepler 1571 1630

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Johannes Kepler(1571 - 1630)
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Keplers Life

• Johannes Kepler was born in Weil der Stadt in
  Swabia, in southwest Germany in 1571.
• In 1584 he entered the Protestant seminary at
  Adelberg, and in 1589 he began his university
  education at the Protestant university of
  Tübingen.
• Here he studied theology and read widely. He
  passed the M.A. examination in 1591 and continued
  his studies as a graduate student.

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Keplers Life

• Kepler's teacher in the mathematical subjects was
  Michael Maestlin (1580-1635). Maestlin was one of
  the earliest astronomers to subscribe to
  Copernicus's heliocentric theory, although in his
  university lectures he taught only the Ptolemaic
  system.
• Only in what would be called today graduate
  seminars did he acquaint his students, among whom
  was Kepler, with the technical details of the
  Copernican System. Kepler stated later that at
  this time he became a Copernican for "physical
  or, if you prefer, metaphysical reasons."

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Kepler and Brahe

• Because of his talent as a mathematician,
  displayed in this volume, Kepler was invited by
  Tycho Brahe to Prague to become his assistant and
  calculate new orbits for the planets from Brahe's
  observations.
• Kepler moved to Prague in 1600.
• Brahe wanted Kepler to mathematically verify his
  (Brahes) own system, and, because Kepler
  believed in the Copernican system, they clashed.

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Kepler and Brahe

• Kepler served as Tycho Brahe's assistant until
  the latter's death in 1601.
• When Brahe died, his family tried to take his
  data. Kepler sued in court and won.
• Before he died, Brahe urged Kepler to declare war
  on Mars, probably because he had the most data on
  Mars.

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Kepler and Brahe

• This is fortunate because Mars has the most
  elliptical orbit of the inner planets and it is
  doubtful that Kepler would have detected
  elliptical orbits of any of the others.

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Astronomia Nova

• In 1609 his Astronomia Nova ("New Astronomy")
  appeared, which contained his first two laws
  (planets move in elliptical orbits with the sun
  as one of the foci, and a planet sweeps out equal
  areas in equal times).
• In this book, Kepler detailed his attempts to
  devise models that fit the data for Mars, based
  on the Ptolomaic, the Copernican, and the
  Tychonic Systems.

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Astronomia Nova

• Finally, Kepler decided that none of the systems
  worked. He could get the data to very nearly fit
  the models to an accuracy of /- 8' of arc, which
  would have been more than adequate to fit any
  previously known data.
• But Kepler had Brahe's data, accurate to /- 4' .
  Therefore he rejected orbits based on any
  previous systems and devised his own model based
  on elliptical orbits.

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Keplers Work

• In 1619 he published Harmonice Mundi ("Harmony of
  the World"), in which he derived the heliocentric
  distances of the planets and their periods from
  considerations of musical harmony.
• This work presents Keplers third law, relating
  the periods of the planets to their mean orbital
  radii.

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Keplers Laws

• Law I Each planet revolves around the Sun in an
  elliptical path, with the Sun occupying one of
  the foci of the ellipse.
• Law II The straight line joining the Sun and a
  planet sweeps out equal areas in equal intervals
  of time.
• Law III The squares of the planets' orbital
  periods are proportional to the cubes of the
  semimajor axes of their orbits.

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First Law
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The Ellipse
MARS

r
1
r
SEMIMAJOR
2
SUN
AXIS
a


c
EMPTY
FOCUS
FOCUS
b
SEMIMINOR
AXIS
2
2
2
a b c
r r 2a constant
1
2
FOR A CIRCLE, a b, r r , c 0
1
2
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Drawing an Ellipse
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Keplers Laws

• Law I Each planet revolves around the Sun in an
  elliptical path, with the Sun occupying one of
  the foci of the ellipse.
• Law II The straight line joining the Sun and a
  planet sweeps out equal areas in equal intervals
  of time.
• Law III The squares of the planets' orbital
  periods are proportional to the cubes of the
  semimajor axes of their orbits.

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Keplers Laws

• Law I Each planet revolves around the Sun in an
  elliptical path, with the Sun occupying one of
  the foci of the ellipse.
• Law II The straight line joining the Sun and a
  planet sweeps out equal areas in equal intervals
  of time.
• Law III The squares of the planets' orbital
  periods are proportional to the cubes of the
  semi-major axes of their orbits.
• Mathematical statement P ka3/2 , where P
  sidereal period, and a semi-major axis.

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Example Third Law
P ka3/2 , where P sidereal period, and a
semi-major axis

• Planet P (yr.) a (AU) P2 a3
• Mercury 0.24 0.39 0.06 0.06
• Venus 0.62 0.72 0.39 0.37
• Mars 1.88 1.52 3.53 3.51
• Jupiter 11.9 5.20 142 141
• Saturn 29.5 9.54 870 868

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Keplers Laws

• Kepler's laws apply not just to planets orbiting
  the Sun, but to all cases in which one celestial
  body orbits another under the influence of
  gravitation moons orbiting planets, artificial
  satellites orbiting the Earth, other solar system
  bodies, and stars orbiting each other.

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Kepler vs. Aristotle

• First Law
• Orbits are not circles.
• Sun is at the center.
• Aristotle's cosmology required circular orbits
  with Earth at the center.
• Second Law
• Orbits are not at constant speed.
• Aristotle's cosmology required constant speed.

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Kepler vs. Aristotle

• Third Law
• Planets further from the sun move slower.
• Aristotle's and Ptolomys cosmology required all
  planets to move at the same speed.