Download Lecture 6 Recall: Geocentric Model of Solar System

Lecture 6
Kepler Surveys the Solar System
Heliocentric model
how it explains retrograde motion
verifying it
Jan 30, 2006
Astro 100 Lecture 6
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Recall: Geocentric Model of Solar
System
• (most elaborate: Ptolemy, 125 AD)
– Moon and Sun motion consistent with real (almost
uniform) circular motion around stationary Earth.
– So associate Sun, Moon, and planets with spheres in
uniform rotation with Earth at center.
– Nonuniform apparent motion is allowed by attaching
planets to little uniformly rotating spheres (epicycles)
whose centers are attached to object's main sphere.
Spheres do not overlap. Except for having Moon closer than
Sun (to get solar eclipses), the size of each sphere is
arbitrary. Can be made as exact as you like by adding
epicycles to epicycles. Basically, Real = Apparent
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Heliocentric Model
• (Copernicus, 1500 AD)
– Noticed that most of nonuniformity (the retrograde
motion) in apparent motion of each planet was due to
similar epicycle with one year period.
– Could get rid of these by assuming Sun at center, with
Earth and planets circling fairly uniformly (but Moon
still needs to go around Earth).
– The one-year epicycles are not “real”,only due to the
motion, or “parallax”, of the viewer (us on Earth)
– Retrograde apparent motion due to period of planet
around sun with respect to stars (sidereal period) being
different from Earth's (one year).
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Heliocentric fixes the orbits
• To get the right amount of retrograde motion, must
fix sidereal period and orbit size for each planet.
– Time between lineups with sun (= synodic period)
– Period relative to stars = "sidereal period" = 0.24 yr
(Mercury) to 248 (Pluto) yrs:
Planet synodic
Mercury 116 days
Venus 584 days
Mars
780 days
Jupiter 399 days
sidereal
88 days
224 days
687 days
11.9 yrs
• Largest orbits have longest sidereal periods - nice.
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Argument against heliocentric
• Tycho Brahe (1570)
– pointed out that if Earth moves, and the stars are not
infinitely far away, their angular arrangement should
change slightly as Earth goes from side to side of Sun.
– He found no such effect (to < 10 arcmin), so made an
alternate model in which Earth is fixed, Sun goes
around Earth, and planets go around Sun.
– This objection was removed when this effect, stellar
heliocentric parallax, was finally actually measured by
Bessel (1800's) for the star 61 Cygni. It was 1/3
arcsecond, >1000x smaller than Tycho could measure.
– The parallax is so small because the stars are farther
away than Tycho could imagine!
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More Arguments against heliocentric
• Copernicus still needed epicycles, since he assumed
exactly uniform motion in circles around the Sun, which
still did not agree that well with the observations.
– This problem was fixed by Kepler, who removed the
assumption of uniform motion in circles (see below)
• Heliocentric model has multiple centers: Moon goes
around Earth, Earth and other planets go around Sun. This
was seen as philosophically awkward.
– This problem was resolved by Galileo (see below)
• "But it doesn't feel like I'm moving"
– Actually, body is not sensitive to linear motion
– There should be a slight apparent force from curving
motion - observed with modern instruments
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Arguments for heliocentric
• "Simpler", and motions required are more uniform.
• Has more testable (“falsifiable”) features. For
instance, the sidereal periods ("P") and sizes of
orbits ("A") are now fixed:
Planet P(yr)
Mercury 0.24
Venus 0.61
Earth 1
Jan 30, 2006
A(AU)
0.39
0.72
1
Planet
Mars
Jupiter
Saturn
P(yr)
1.88
11.86
29.46
A(AU)
1.52
5.20
9.54
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Galileo Verifies Heliocentric Model
• Using one of first telescopes, Galileo provided the
first firm verification of the heliocentric model and
falsification of the geocentric model. Can predict the
phases of Venus
– Geocentric: since the sphere of Venus does not cross
that of the Sun, Venus should either remain on this side
of the sun, in which case it should always show a
narrow crescent, or should always be on the other, and
would always be nearly full
– Heliocentric: Venus spends about half of its time on
either side of the sun, so it should show both phases
Galileo: Venus does show both new and full phases
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Geocentric Model
Figure 1.23, p45, Arny
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Geocentric Epicycles
Figure 1.24, p45, Arny
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Heliocentric - Retrograde
Sun
Figure 1.25, p47, Arny
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Heliocentric parallax
Figure 1.22, p44, Arny
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Venus Phase Prediction
Figure 1.29, p52, Arny
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Venus Phase Observation
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