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Heliocentric Models
Copernicus and Kepler
Intro to Solar System
Kepler
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Copernicus - 1500 A.D.
helio-centric: Sun-centered
Zeilik - 6/e
• Sun at the center of the Cosmos
• Earth revolves around the Sun on a yearly
basis (period = one year)
• Earth rotates on its axis daily
Intro to Solar System
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assumptions: uniform circular motion
aesthetics:
pleasing, harmonious
predictions: no better than Ptolemy’s
• distance from Earth to celestial sphere is MUCH
greater than Earth-Sun distance
– explains why no parallax observed
• daily motion of heavens becomes the rotation of
the Earth on its axis
• motion of many spheres becomes the motion of
only one
Intro to Solar System
Kepler
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BUT !
no explanation of why things
don’t fly off
• apparent motion of Sun relative to stars results
from annual revolution of Earth around the Sun
• planets’ retrograde motions occur from the motion
of the Earth relative to the planets
– passing of planets
• based the sequence of planets on their sidereal
periods (periods of revolution wrt the stars)
• calculated the distance of planets from the Sun
Intro to Solar System
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Using the unit of distance
1 AU = Earth-Sun distance
PLANETS COPERNICUS
MODERN
Mercury
Venus
Earth
Mars
Jupiter
Saturn
0.387
0.723
1.00
1.52
5.20
9.54
Intro to Solar System
0.38
0.72
1.00
1.52
5.22
9.17
Kepler
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Problems with the Copernican model
• predictions are, in the end, no better
• no physical explanations (still natural
motion)
• enthralled with sphere
– > circular orbits, constant speeds
Intro to Solar System
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Johannes Kepler - 1600 A.D.
foundation for modern cosmological concepts
• built on successes and failures
• demanded that his model’s predictions be
at least as accurate as the observations (1
arcmin error)
“I have discovered among the celestial movements
the full nature of harmony.”
Intro to Solar System
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Kepler - the Ellipse
two focal points foci
minor axis
focal distance
semi-minor axis - half the minor axis
Intro to Solar System
Kepler
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Kepler - the Ellipse
major axis
minor axis
semi-major axis - half the major axis (a)
semi-minor axis - half the minor axis
Intro to Solar System
Kepler
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Kepler - the Ellipse
two focal points foci
major axis
minor axis
focal distance
semi-major axis - half the major axis (a)
semi-minor axis - half the minor axis
eccentricity = focal distance
major axis
Intro to Solar System
Kepler
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Kepler - the Ellipse
major axis
focal distance
eccentricity = focal distance
major axis
Intro to Solar System
Kepler
e = 0 means ????
e = 1 means ????
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Kepler’s Three Laws
I. Law of Ellipses
Each planet’s orbit is an ellipse with
the Sun at one of the foci.
implication: distance of the planet to
the Sun varies
Intro to Solar System
Kepler
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Kepler’s Three Laws
II. Law of Equal Areas
A line drawn from a planet to the Sun
sweeps out equal areas in equal times.
implication: orbital speeds are non-uniform
yet vary in a regular way
Closer a planet is the the Sun, the faster
it moves in its orbit
(force ????)
Intro to Solar System
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Kepler’s Three Laws
III. Harmonic Law
Planet
p (Earth years)
a (AU)
============================
Mercury
0.24
0.39
Venus
0.62
0.72
Earth
1.0
1.0
Mars
1.9
1.5
Jupiter
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5.2
Saturn
29
9.5
Intro to Solar System
Kepler
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Kepler’s Three Laws
III. Harmonic Law
Square of the orbital period is proportional
to the cube of the average distance.
p2 = k a3
implication: planets with large orbits
move slowly
Proportion holds for all planets =>
A PHYSICAL CAUSE !!
Intro to Solar System
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Kepler’s Third Law
p2 = k a3
k = proportionality constant
p (years)
a (AU’s)
=> k = 1
True for any body orbiting the Sun, even spacecraft!
“I contemplate its beauty with incredible
and ravishing delight.
Intro to Solar System
Kepler
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Kepler
made perhaps the greatest leap in scientific thinking
predictions were 10 times more accurate than either
Ptolemaic model (geocentric)
Copernican model (heliocentric)
gave birth to astronomy as a physical science
Intro to Solar System
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Orbital Eccentricities
Planet
Orbital Eccentricity
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Intro to Solar System
0.206
0.007
0.017
0.094
0.048
0.054
0.048
0.007
0.253
Kepler
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