Download MAPPING THE SOLAR SYSTEM

MAPPING THE SOLAR
SYSTEM
The Tycho Brahe, Johanes Kepler
Connection
MAPPING THE SOLAR SYSTEM
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Tycho Brahe
Johannes Kepler
Keplers Laws
Sample Problems
Tycho Brahe
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Born 1546 in Denmark
At age 15 went to Leipzig at to study law,
secretly studied astronomy.
Spent several years at European universities
studying astronomy
Tycho Brahe
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The king of Denmark and Norway gave Tycho a
prodigious quantity of cash ($5 billion in today's
money, by one estimate) and his own island.
Tycho Brahe Accomplishments
observed one of the first
supernovae to be seen with the
naked eye (new star)
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He proved that comets are not
objects in the atmosphere.
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He showed irregularities in the
moons orbit.
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He made an instrument out of
brass and wood that could measure
the altitude of the sun and planets
to 1/6 of a minute of arc.
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Tycho believed that the earth was
fixed in the center of the world.
Around the earth circulated the
moon and the sun.
Around the sun orbited the rest of
the planets
Tycho Brahe other “ Accomplishments ”
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At age 20-year-old Tycho was studying at the University of Rostock in
Germany. Attending a dance at a professor's house.
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He got into a quarrel with one Manderup Parsbjerg, like himself a member of
the Danish gentry.
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Over a woman? No!, the two were fighting over some fine point of
mathematics. (Fermat's Next-to-Last Theorem, which posits that 2 + 2 = 5
for very large values of 2.)
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They got into it again at a Christmas party a couple weeks later and decided to
take it outside in the form of a duel.
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The duel was conducted in pitch darkness with swords. Parsbjerg, a little
quicker off the dime, succeeded in slicing off the bridge of Tycho's nose.
Tycho Brahe other “Accomplishments ”
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Had an artificial nose made, not from wax, but from an alloy of gold and silver
Carried a small box with a paste or glue, with which he often would put on the nose.
Never married the mother of his eight children,
Employed a dwarf as a jester,
Kept a pet elk (which died after breaking a leg while going downstairs drunk),
Tyrannized the local peasantry.
Managed to tick off everyone in Denmark,
Eventually found it wise to leave the country.
Relocated to Prague
Rumor: died after drinking heavily at a dinner.
Johannes Kepler
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Born Dec. 27 1571.
He studied astronomy at the University of
Tubingen.
Died Nov. 15 1630.
Johannes Kepler
Accomplishments
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First to investigate the
formation of pictures with a
pin hole camera;
First to explain the process
of vision by refraction within
the eye;
First to formulate eyeglass
designing for nearsightedness
and farsightedness;
First to explain the use of
both eyes for depth
perception.
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First to describe: real, virtual,
upright and inverted images
and magnification;
First to explain the principles
of how a telescope works;
First to discover and describe
the properties of total
internal reflection
Johannes Kepler
Tycho Brahe’s Assistant
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1600. Johannes Kepler is employed as an assistant.
Kepler and Brahe did not get along well.
Unlike Brahe, Kepler believed firmly in the Copernican
system. (Sun at Center of Universe)
Brahe feared that his bright young assistant might eclipse
him as the premiere astonomer of his day.
He let Kepler see only part of his voluminous data.
Two days after Tycho's death, Kepler was appointed his
successor as imperial mathematician.
He inherited Tycho's observations as well as the
responsibility to complete his unfinished work.
Keplers Solar System
Keplers Laws of Planetary
Motion
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1st Law: Planets move in ellipses with the
Sun at one focus.
Keplers Laws of Planetary
Motion
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2nd Law: The radius vector describes equal areas
in equal times
Keplers Laws of Planetary
Motion
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3rd Law: The ratio of the squares of the
revolutionary periods for two planets is
equal to the ratio of the cubes of their
semimajor axes.
2
2
T /T
3
3
=r /r
Or
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The Period of the Planet are proportional to the
3/2 power of the major axis length of the orbit.
 T=2πr3/2/(√Gm)
 T=2
πr√(r/Gm)
 r=length of semi major axis
=length of major axis divided by 2
Sample Problems
Planet
Mercury
Period of Orbit Average
Orbital Radius
88 days
Earth
1 year
Mars
Saturn
1 A.U.
2.125 A.U.
29 years
Sample Problems
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The average radius of the moons orbit around
the earth is 384 748 km and has a period of 27.3
days. A Direct TV satellite has a period of
exactly one day.
What is the radius of the satellites orbit?
How far is the satellite above the Earths surface?