Giants of Science Part Two
Tycho 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 Brahe’s 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.
Brahe’s 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 Brahe’s
observations.
Brahe and assistants making observations
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Kepler’s 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).
Johannes Kepler (1571-1630)
“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
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Kepler’s Breakthrough
• Kepler’s 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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Kepler’s 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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Kepler’s 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 Ptolemy’s
perfect circular orbits.
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Kepler’s 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
Ptolemy’s uniform
motion
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Kepler’s 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
Earth’s orbit. Earth’s
average distance from the
Sun.
– It doesn’t matter how
elliptical the orbit as long
as the average distance is
the same
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