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The Copernican The Copernican RevolutionRevolution

The Birth of Modern Science

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What do we see in the sky?

• The stars move in the sky but not with respect to each other

• The planets (or “wanderers”) move differently from stars– They move with respect to the

stars– They exhibit strange retrograde

motion

• What does all this mean?• How can we explain these

movements?• What does the universe

look like?

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Timeline

Copernicus

1473-1543

Tycho

1546-1601Kepler

1571-1630

Galileo

1564-1642

Newton

1642-1727

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Geocentric (Ptolemaic)

System• The accepted model for

1400 years• The earth is at the center• The Sun, stars, and

planets on their spheres revolve around the earth: explains daily movement

• To account for unusual planetary motion epicycles were introduced

• Fit the Greek model of heavenly perfection – spheres are the perfect shape, circular the perfect motion

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Heliocentric (Copernican) System

• Sun at center (heliocentric)• Uniform, circular motion

– No epicycles (almost)

• Moon orbited the earth, the earth orbited the sun as another planet

• Planets and stars still on fixed spheres, stars don’t move

• The daily motion of the stars results from the Earth’s spin

• The annual motion of the stars results from the Earth’s orbit

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• In the heliocentric model, apparent retrograde motion of the planets is a direct consequence of the Earth’s motion

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Geocentric vs. Heliocentric

• How do we decide between two theories?

• Use the Scientific method:– These are both explanations

based on the observation of retrograde motion

– What predictions do the models make?

– How can these predictions be tested?

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Phases of Venus

• Heliocentric predicts that Venus should show a full phase, geocentric does not

• Unfortunately, the phases of Venus cannot be observed with the naked eye

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Geocentric vs. Heliocentric

• Against heliocentric– It predicted planetary motions and events no

better than the Geocentric system– The earth does not move (things do not fly off)– The earth is different from the heavens (from

Aristotle – the heavens are perfect and unchanging) and cannot be part of the heavens

• For heliocentric– Simplified retrograde motion, but epicycles were

necessary to account for the planets’ changing speed

– The distances to the planets could be measured. These distances were ordered, and therefore aesthetically pleasing to the philosophy of the day

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Stellar Parallax

• Parallax caused by the motion of the earth orbiting the Sun

• Not observed with the naked eye

• The heliocentric model predicts stellar parallax, but Copernicus hypothesizes that the stars are too far away (much farther than the earth from the Sun) for the parallax to be measurablewith the naked eye

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Misconceptions1. The Copernican model has a force between the

sun and the planets. Actually, the natural motion of the celestial spheres drove the planetary motions.

2. The Copernican model was simpler than the Ptolemaic one. In fact, though Copernicus eliminated circles to explain retrograde motion, he added more smaller ones to account for nonuniformities of planetary motions.

3. The Copernican model predicted the planetary motions better. Because both models demanded uniform motion around the centers of circles, both worked just about as well – with errors as large as a few degrees at times.

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Galileo Galilei

• Turned a telescope toward the heavens• Made observations that:

– contradicted the perfection of the heavens• Mountains, valleys, and craters on the Moon• Imperfections on the Sun (sunspots)

– Supported the heliocentric universe• Moons of Jupiter• Phases of Venus – shows a full phase

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Tycho Brahe• Had two sets of astronomical

tables: one based on Ptolemy’s theory and one based on Copernicus’.

• He found that both tables’ predictions were off by days to a month.

• He believed that much better tables could be constructed just by more accurate observations.

• Tycho’s homemade instruments improved measurement precision from ten minutes of arc (which had held since Ptolemy) to less than one

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The skies change

• Tycho observed 2 phenomena that showed the heavens DO change:– In November 1572, Tycho noticed

a new star in the constellation Cassiopeia

– Comet of 1577• Prior to this sighting,

comets were thought to be atmospheric phenomena because of the immutability of the heavens

• But neither the star nor the comet changed position as the observer moved, as expected for atmospheric phenomena

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Johannes Kepler• Kepler succeeded Tycho as the Imperial

mathematician (but at only 1/3 the salary of the nobleman)

• Kepler worked for four years trying to derive the motions of Mars from Brahe’s observations

• In the process, he discovered that the plane of the earth’s orbit and the plane of Mars’ (and eventually the other planets) passed through the sun

• Suspecting the sun had a force over the planets, he investigated magnetism

• While this is not true, it did lead him to the idea of elliptical orbits

• “With reasoning derived from physical principles agreeing with experience, there is no figure left for the orbit of the planet except a perfect ellipse.”

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Astronomia nova• Published in 1609, The New Astronomy was

just that, it revolutionized the field• It predicted planetary positions as much as

ten times better than previous models• It included physical causes for the

movement of the planets• The ideas of the Greeks were gone – the

heavens no longer were perfect, immutable, or different from the earth

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Kepler’s first Law

• The orbital paths of the planets are elliptical (not circular), with the Sun at one focus.

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Kepler’s second law

• An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

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Kepler’s Third Law

• The square of a planet’s orbital period is proportional to the cube of its semi-major axis.

• Kepler orbit demonstration: http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html

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Planetary PropertiesPlanet Orbital

eccentricity, e

Orbital semi-major axis, a(Astronomical units)

Orbital period,P(Earth years)

Mercury 0.206 0.387 0.241

Venus 0.007 0.723 0.615

Earth 0.017 1.000 1.000

Mars 0.093 1.524 1.881

Jupiter 0.048 5.203 11.86

Saturn 0.054 9.537 29.42

Uranus 0.047 19.19 83.75

Neptune 0.009 30.07 163.7

Pluto 0.249 39.48 248.0

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Other Solar System Bodies

• Kepler derived his laws for the 6 planets known to him. The laws also apply to the 3 discovered planets and any other body orbiting the Sun (asteroids, comets, etc.)

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A force for planetary motion

• Newton proposes a force which controls the motion of the planets – GRAVITY

• The larger the mass, the larger the force of gravity

• The further the distance, the smaller the force of gravity

• Kepler’s third law can be derived from Newton’s law of gravity

• F = GMm/r2 = mg

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Gravity