giants of science part two tycho brahe & johannes kepler

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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 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 Sunwhile 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).

“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”

     - KeplerJohannes Kepler (1571-1630)

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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 MotionAs 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