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Astronomy 110

Lecture 8

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What Was Wrong With the Geocentric Universe?There were many subtle details like fluctuations in brightness and speed of solar system objects and it was hard to come up with a real physical model that behaved the right way but a major argument was the phases of Venus:

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From the Little Commentary (1514):There is no one centre in the universe.

The Earth's centre is not the centre of the universe.

The centre of the universe is near the sun.

The distance from the Earth to the sun is imperceptible compared with the distance to the stars.

The rotation of the Earth accounts for the apparent daily rotation of the stars.

The apparent annual cycle of movements of the sun is caused by the Earth revolving round it.

The apparent retrograde motion of the planets is caused by the motion of the Earth from which one observes.

Copernicus (1473-1543):

At the middle of all things lies the sun. As the location of this luminary in the cosmos, that most beautiful temple, would there be any other place or any better place than the centre, from which it can light up everything at the same time? Hence the sun is not inappropriately called by some the lamp of the universe, by others its mind, and by others its ruler.

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…but still used perfect, concentric circles.

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Thomas Digges (c. 1545-c.1595), A Perfit Description of the Coelestiall Orbes (1576)

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• Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions.

• Still could not detect stellar parallax, and thus still thoughtEarth must be at center of solar system (but recognized that other planets go around Sun)

• Hired Kepler, who used his observations to discover the truth about planetary motion.

Tycho Brahe(1546-1601)

Cassipeia,

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"There is no absolute up or down, as Aristotle taught; no absolute position in space; but the position of a body is relative to that of other bodies. Everywhere there is incessant relative change in position throughout the universe, and the observer is always at the center of things."

Giordano Bruno (1548-1600)

"Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds."On the Infinite Universe and Worlds (1584)

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Johannes Kepler(1571-1630)

• Kepler first tried to match Tycho’sobservations with circular orbits

• But an 8 arcminute discrepancy led him eventually to ellipses…

If I had believed that we could ignore these eight minutes [of arc], I wouldhave 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.

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"Henceforth it is no longer a harmony made for the benefit of our planet, but the song which the cosmos sings to its lord and centre, the Solar Logos".

Kepler called astrology 'foolish daughter' of the 'wise mother' But noted:"the mother would starve if the daughter did not earn anything"

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So what is a circle?So what is a circle?⊙⊙

What is an Ellipse?

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Eccentricity of an Ellipse

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Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

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Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times.

⇒ means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

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More distant planets orbit the Sun at slower average speeds, obeying the relationship

p2 = a3

p = orbital period in yearsa = avg. distance from Sun in AU

Kepler’s Third Law

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Graphical version of Kepler’s Third Law

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Example: An asteroid orbits the Sun at an average distance a = 4 AU. How long does it take to orbit the Sun?

We need to find p so that p2 = a3

Since a = 4, a3 = 43 = 64Therefore p2 =64, p = 8

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Galileo(1564-1642)• Solidified the Copernican revolution• Paved the way for Newton and the birth of physics

1633 - Galileo is ordered to recant his claim that Earth orbits the Sun

1824 - His book on the subject was removed from the index of banned books.

1992 - Galileo formally vindicated by the Church in 1992

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Galileo showed the heavens were not perfect

Using the telescope, Galileo saw:

•spots on Sun (“imperfections”)

• mountains and valleys on the Moon (proving it is not a perfect sphere)

• The Milky Way was made up of many distant stars – so stars must be much farther than was thought

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Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit the Earth…

Aristotle thought that all objects naturally come to rest. Galileo showed that objects will stay in motion unless a force acts to slow them down (Newton’s first law of motion).