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Phys 181-701

Astronomy

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“The danger to which the success of revolutions is most exposed, is that of attempting them before the principles on which they proceed, and the advantages to result from them,

are sufficiently seen and understood.” Thomas Paine - American Revolutionary

“Anyone in a free society where the laws are unjust has an obligation to break the law.”

Henry David Thoreau - American Philosopher

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(rěv΄ə-lōō’shən))1. n A drastic and far-reaching

change in ways of thinking and behaving.

2. n Orbital motion about a point, the planetary revolution about the sun.

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The Copernican Revolution

1473 - 1542

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Problems with Ptolemy

There are problems with the Ptolemaic Model

The solar system according to the Ptolemaic Model from 100 A.D. to 1500

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Features

Features…•Deferent Circles•Epicycles on the Deferents•Inferior planets are never more than 47º from the sun•Retrograde motion of mars is explained

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• As the precision of astronomical measurements grew the need for adjustments to the model called for additional epicycles.

• In 1252 King Alfonso X of Castile funded a 10 year project by Arab and Jewish astronomers to calculate extensive tables.

• Calculations became horrendously complicated and even Alfonso suggested that the model should by simpler if it was to have any truth in it.

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“Multiplicity ought not be posited without necessity.”

William Occam – English Scholar - 1340

“Keep it simple, stupid.”Anonymous 20th Century Philosopher

This principle is known as Occam’s Razor…

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Copernican Theory…

The motions of the planets would be more easily explained if the sun were at the center.

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DeRevolutionibus, 1543…

“Venus and Mercury revolve around the sun and cannot go nearer or further from it than the circles of their orbits permit…If, acting upon this supposition, we connect Saturn, Jupiter and Mars with the same center, keeping in mind the greater extent of their orbits…we cannot fail to see the explanation of the regular order of their motions.

This proves sufficiently that their center belongs to the sun…”

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Going Further…

“The extent of the universe…is so great that…[the earth] disappears when compared to the sphere of the fixed stars.”

“Although this may appear incomprehensible and contrary to the opinion of many, I shall, if God wills, make it clearer than the sun, at least to those who are not ignorant of mathematics.”

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“…that fool who would reverse the entire art of astronomy…Joshua bade the SUN and not the earth to stand still.”

Martin Luther - 1539

Under very real threat of persecution, Copernicus changed the title of his book and its publication was finished only in the final days of his life.

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Tycho Brahe•Royal Astronomer of Denmark

•Uraniborg

•Observations with the naked eye

•Measured parallax of planets

•Observed a supernova (1572)

•Realized that Ptolemy was not right but denied Copernicus

•Proposed a model with the earth at the center and the sun revolving around it, but all of the other planets revolved around the sun

•Collected the best data available

1546-1601

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KEPLER!

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KeplerJohannes Kepler – 1571-1630

Deeply religious believer in astrology

Mathematics was evidence of God

Subscriber to the Copernican theory

Hired by Tycho to prove the earth centered model

Convinced that a mathematical “harmony” existed for the planets

Inherited Tycho’s fine data

Analyzed data regarding mars

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Kepler’s laws

Kepler’s Laws

1. Each planet moves in an ellipse, with the sun at one focus.

2. The line between the sun and the planet sweeps out equal areas in equal times.

3. The ratio of the cube of the average radius of a planets orbit to the square of its orbital period of revolution is the same for each planet. (Harmonic Law)

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Ellipses and AreasThis orbit is in the shape of an ellipse….

The area AAB= The Area ACD

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Law of Conservation ofAngular Momentum

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Harmonic Law

The Harmonic Law:

kP

a

2

3

ka

P

3

2

a = Average radius of planet’s orbitP = The orbital period of the planetk = A constant for all objects orbiting the sun

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Harmonic ConstantConsider the earth…

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1

1

12

3

2

3

yr

AU

P

a

This is true for all planets no matter what the radius of their orbit.

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Retrograde MotionRetrograde motion explained at long last…

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How does Kepler know times?

How does Kepler know the time periods of planets other than the earth?

Consider…

•You can’t go to mars

•You can’t watch mars ‘go round’

•Every so often, mars exhibits retrograde motion

•Retrograde motion is caused by the passing of mars by the earth at various points in their orbits.

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Working late on this lecture, the clock strikes midnight…And the hands line up.

A little while later… And they aren’t lined up at all.

I notice that they line up again sometime around1:05 am. Is there some sort of a math rule that can predict when the hands will align?

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A little scratch work and some calculations…

Big deal…

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Time period of marsIf I use the hands of the clock as an analogy for the motion of the planets…

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Radius of mars’ orbit

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Measurement

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IMPORTANT

• Occam’s Razor• Copernicus• Law of Ellipses • Law of Areas• Harmonic Law

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EndNEXT TIME:NEXT TIME:

Newton’s Law of

Universal Gravitation