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Kepler’s Laws

Why you can get there from here.

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Goals

• Is astrology a science?• Why should we care?• Kepler: Astrologer turned Astronomer.• Kepler’s Laws.• Proof of Kepler’s Laws.

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Theories

• So: a theory is a highly successful hypothesis.

• All theories make predictions.• All theories can be tested.• Result: Any scientific theory is subject

to change as our ability to make tests, or make observations of a test’s results, improves with time.

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Non-scientific Theories• Make no predictions• Un-testable• Can’t be falsified

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Non-scientific Theories

• Cholesterol too high? Aliens are clogging your arteries with invisible probes.

• Spaghetti is bland? You were meant to eat bland food.

• Cholesterol too high? Gods must be angry.

• Spaghetti is bland? At the instant of tasting, tongue is transported to alternate dimension where all flavors are rendered nullified. Happens instantaneously.

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Non-scientific Theories

Viking Orbiter (1976) Mars Global Surveyor (1998)

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Falsification

• A real Scientific Theory tells you what observations are necessary to falsify it.– Not so proponents of:

• Face on Mars• Moon Hoax• Astrologers

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Astrology

• The date, time, (and place) of birth affect:– Your personality– Your actions– Events that will affect your life

• Horoscopes appear in most papers.• Millions of people read them daily.

http://www.azcentral.com/ent/horoscopes/astrology101.html

http://astrology.about.com/od/basicsofastrology/

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Astrology

• Like other “-ologies”, is it a science?– Explain what is seen?– Make predictions?

• Does it work?• What test would falsify astrology?

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Astrology Tests

• Come up with a test of astrology that could, theoretically, be carried out in this room or on campus.

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Signs for U.S. PresidentsAries - 2 PresidentsTaurus - 4 Gemini - 2 Cancer - 4 Leo - 3 Virgo - 2 Libra - 4 Scorpio - 5 Sagittarius - 3 Capricorn - 4 Aquarius - 5 Pisces - 4

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Does Astrology Work?

• Does it pass the test?• Does it work better than chance?• Does it matter?

“One of the other prime uses of astrology is in connection with the basic psychology of children and recognizing in children, at an early age, a basis for later psychological difficulties. The horoscope is perhaps the best method to reveal these tendencies while the child is still in infancy. When parents know from the beginning where the seeds of difficulties lie in the child's life, early care and training might mitigate much later unhappiness.”

- The Cosmic Palette: Astrology 101 by Haizen Paige

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Science vs. Astrology

• Scientists are skeptical of astrology because:1. It takes power out of the hands of

scientists.2. It can’t be tested.3. It has failed when tested.4. It proposes forces that are non-physical.5. It threatens our belief in a knowable

universe.• But no one believes astrology so who

cares?

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Astrology and the President

(TIME, May 16, 1988) -- “The First Lady dabbled in astrology as far back as 1967. In 1981 [Joan] Quigley made Nancy [Reagan] a believer …. And from then on, no presidential public appearance was slated without the Friend's say-so. To this day, Nancy's Friend continues to influence the President's schedule. For the Reagan-Gorbachev Washington summit, she cast the charts of both men and determinedthat 2 p.m. on Dec. 8, 1987, was the most propitious moment for them to sign the intermediate-range nuclear forces treaty. At Nancy's behest, the entire summit was built around that hour. For the upcoming Moscow summit, Gorbachev's chart (he is a Pisces) has been recast alongside Reagan's (Aquarius).”

“[Former White House Chief of Staff, Donald] Regan and others make a compelling case that in 1986 and 1987 astrological influence dramatically reduced the presidency's effectiveness, at least partly, by keeping Ronald Reagan under wraps for much of the time. Nancy's intrusions in the scheduling process, Regan said in an interview with TIME last week, ‘began to interfere with the normal conduct of the presidency.’”(TIME, May 16, 1988)

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Astrology to Astronomy

• Kepler was an astrologer.• Looked for Perfect Solids• Wants did not match with Observations

(tests).• Followed the facts where they led.• The result works.

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Kepler’s Laws1. Orbits are always

ellipses.2. Sweep out equal

areas in equal times.

3. The period of orbit is related to average separation. 32 . SeparationconstPeriod

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Concept Test

• Kepler’s second law says “a line joining a planet and the Sun sweeps out equal areas in equal amounts of time.” Which of the following statements means nearly the same thing?1. Planets move fastest when they are moving toward

the Sun.2. Planets move equal distances throughout their orbit

of the Sun.3. Planets move slowest when they are moving away

from the Sun.4. Planets move farther in a given time when they are

closer to the Sun.5. Planets move the same speed at all points during

their orbit of the Sun.

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Gravity is the Force

• Newton’s Law of Gravity:

• So:

• Becomes:

32 . SeparationconstPeriod

32

2 4 SeparationGMass

PeriodTotal

2rMmGF

TotalMassSeparationconstPeriod

32 .

)()()(

32

SunTotal MMassAUSeparationyearsPeriod

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Concept Test

• You discover a new comet around our Sun:– Average distance from Sun = 4 AU.– What is the period?

1. 1 year2. 4 years3. 8 years4. 64 years5. Don’t have all the necessary information.

)()()(

32

SunTotal MMassAUSeparationyearsPeriod

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Concept Test

• Saturn takes about 30 years to go once around the Sun? About how are away from the Sun is it?

1. 1 AU2. 5 AU3. 10 AU4. 20 AU5. 30 AU

)()()(

32

SunTotal MMassAUSeparationyearsPeriod

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Concept Test

• In a few billion years the sun will expand. In order to avoid the destruction of the Earth, humanity moves the Earth 5 times farther away from the Sun than it is now. How long will it take the Earth to go around the Sun at this new distance?

1. 1 year2. 5 years3. 11 years4. 15 years5. 125 years

)()()(

32

SunTotal MMassAUSeparationyearsPeriod

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Orbital Mechanics

Courtesy David Crisp and WFPC2 Science Team

4Courtesy NASA/JPL

Mars

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Homework #2

• For Thursday/Friday Lab:• Read Cosmos Chapter 3 article on my faculty

website• Do HW2 on MasteringAstronomy.com