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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)
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
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
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
Brahe and assistants making observations
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
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
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.
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
• 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
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.
Kepler’s First Law of Planetary Motion
The orbit of each planet
around the Sun is an
ellipse with the Sun at one
– There is nothing at the other
– The average distance of the
planet from the Sun is the
semimajor axis.
– Throws out Ptolemy’s
perfect circular orbits.
Kepler’s Second Law of Planetary Motion
As a planet moves
around its orbit, it
sweeps out equal
areas in equal
– A planet travels
faster when it is
nearer the Sun and
slower farther away
– Throws out
Ptolemy’s uniform
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
– It doesn’t matter how
elliptical the orbit as long
as the average distance is
the same