Kepler’s Laws
Why you can get there from here.
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Goals
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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
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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. Presidents
Aries - 2 Presidents
Taurus - 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.
2.
3.
4.
5.
It takes power out of the hands of scientists.
It can’t be tested.
It has failed when tested.
It proposes forces that are non-physical.
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)
-- Chief of Staff, Donald] Regan and
“[Former
White
House
others
make
a compelling
case that as
in far
1986 and 1987
“The First
Lady
dabbled in astrology
astrological
dramatically
reduced the
back as 1967.influence
In 1981 [Joan]
Quigley made
Nancy [Reagan]
a believer ….
thenby keeping
presidency's
effectiveness,
atAnd
leastfrom
partly,
on, no presidential
public
appearance
was
Ronald
Reagan under
wraps
for much
of the time.
slated without the Friend's say-so. To this
Nancy's
intrusions in the scheduling process, Regan said
day, Nancy's Friend continues to influence
inthe
anPresident's
interviewschedule.
with TIME
week, ‘began to interfere
For last
the Reaganwith
the normal
conductsummit,
of the presidency.’”
Gorbachev
Washington
she cast the
charts ofMay
both16,
men1988)
and determined
(TIME,
that 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).”
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Astrology to Astronomy
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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 Laws
1. Orbits are always
ellipses.
2. Sweep out equal
areas in equal times.
3. The period of orbit is
related to average
separation.
Period  const.  Separation
2
3
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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.
2.
3.
4.
5.
Planets move fastest when they are moving toward the Sun.
Planets move equal distances throughout their orbit of the
Sun.
Planets move slowest when they are moving away from the
Sun.
Planets move farther in a given time when they are closer to
the Sun.
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:
Mm
F G 2
r
Period  const.  Separation
2
3
• Becomes:
Separation
( AU
42 Separation
3 )
Period
 const
Period
Period
( years
)  .  Separation
GMassTotalMass
Mass
( M Sun )
TotalTotal
2
3
3
22
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Concept Test
Separation( AU )
Period ( years ) 
MassTotal ( M Sun )
3
2
• You discover a new comet around our Sun:
– Average distance from Sun = 4 AU.
– What is the period?
1.
2.
3.
4.
5.
1 year
4 years
8 years
64 years
Don’t have all the necessary information.
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Concept Test
Separation( AU )
Period ( years ) 
MassTotal ( M Sun )
3
2
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Saturn takes about 30 years to go once around the
Sun? About how are away from the Sun is it?
1.
2.
3.
4.
5.
1 AU
5 AU
10 AU
20 AU
30 AU
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Concept Test
Separation( AU )
Period ( years ) 
MassTotal ( M Sun )
3
2
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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.
2.
3.
4.
5.
1 year
5 years
11 years
15 years
125 years
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Orbital Mechanics
Courtesy David Crisp and WFPC2 Science Team
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Mars
Courtesy NASA/JPL
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Homework #2
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For Thursday/Friday Lab:
Read Cosmos Chapter 3 article on my faculty website
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Do HW2 on MasteringAstronomy.com
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