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The Copernican The Copernican RevolutionRevolutionThe Birth of Modern Science

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What do we see in the What do we see in the sky?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

motionWhat does all this mean?How can we explain these

movements?What does the universe

look like?

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TimelineTimeline

Copernicus

1473-1543

Tycho

1546-1601Kepler

1571-1630

Galileo

1564-1642

Newton

1642-1727

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Geocentric Geocentric (Ptolemaic) (Ptolemaic) SystemSystem

The accepted model for 1400 years

The earth is at the centerThe 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) Heliocentric (Copernican) SystemSystem

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. Geocentric vs. HeliocentricHeliocentric

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 Phases of VenusVenusHeliocentric

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. HeliocentricGeocentric vs. HeliocentricAgainst 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 ParallaxStellar 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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MisconceptionsMisconceptions

1. 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 GalileiGalileo GalileiTurned a telescope toward the

heavensMade 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 BraheTycho BraheHad 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 changeThe 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 KeplerJohannes KeplerKepler 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 novaAstronomia novaPublished in 1609, The New Astronomy

was just that, it revolutionized the fieldIt predicted planetary positions as much

as ten times better than previous modelsIt included physical causes for the

movement of the planetsThe 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 LawKepler’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 lawKepler’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 LawKepler’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 PropertiesPlanetary 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 BodiesOther Solar System BodiesKepler 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 A force for planetary motionmotionNewton 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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GravityGravity