Download Motion of stars, planets

The Copernican
Revolution
The Birth of Modern Science
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What do we see in the sky?
• The stars move in the sky but not
with respect to each other
• The planets (or “wanderers”) move
differently from stars
– They move with respect to the stars
– They exhibit strange retrograde motion
• What does all this mean?
• How can we explain these
movements?
• What does the universe
look like?
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Timeline
Galileo
Newton
1564-1642
1642-1727
Tycho
Copernicus
1473-1543
1546-1601
Kepler
1571-1630
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Geocentric
(Ptolemaic) System
• The accepted model for
1400 years
• The earth is at the center
• The Sun, stars, and
planets on their spheres
revolve around the earth: explains daily movement
• To account for unusual planetary motion epicycles were
introduced
• Fit the Greek model of heavenly perfection – spheres are the
perfect shape, circular the perfect motion
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Heliocentric (Copernican) System
• Sun at center (heliocentric)
• Uniform, circular motion
– No epicycles (almost)
• Moon orbited the earth, the earth
orbited the sun as another planet
• Planets and stars still on fixed
spheres, stars don’t move
• The daily motion of the stars results
from the Earth’s spin
• The annual motion of the stars
results from the Earth’s orbit
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• In the heliocentric model, apparent retrograde
motion of the planets is a direct consequence of
the Earth’s motion
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Geocentric vs. Heliocentric
• How do we decide between two
theories?
• Use the Scientific method:
– These are both explanations based
on the observation of retrograde
motion
– What predictions do the models
make?
– How can these predictions be
tested?
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Phases of
Venus
• Heliocentric predicts
that Venus should
show a full phase,
geocentric does not
• Unfortunately, the
phases of Venus
cannot be observed
with the
naked eye
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Geocentric vs. Heliocentric
• Against heliocentric
– It predicted planetary motions and events no better than the
Geocentric system
– The earth does not move (things do not fly off)
– The earth is different from the heavens (from Aristotle – the
heavens are perfect and unchanging) and cannot be part of the
heavens
• For heliocentric
– Simplified retrograde motion, but epicycles were necessary to
account for the planets’ changing speed
– The distances to the planets could be measured. These
distances were ordered, and therefore aesthetically pleasing to
the philosophy of the day
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Stellar Parallax
• Parallax caused by the motion of the
earth orbiting the Sun
• Not observed with the naked eye
• The heliocentric model predicts
stellar parallax, but Copernicus
hypothesizes that the stars are too far
away (much farther than the earth
from the Sun) for the parallax to be
measurable
with the naked eye
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Misconceptions
1. The Copernican model has a force between the sun and
the planets. Actually, the natural motion of the celestial
spheres drove the planetary motions.
2. The Copernican model was simpler than the Ptolemaic
one. In fact, though Copernicus eliminated circles to
explain retrograde motion, he added more smaller ones to
account for nonuniformities of planetary motions.
3. The Copernican model predicted the planetary motions
better. Because both models demanded uniform motion
around the centers of circles, both worked just about as
well – with errors as large
as a few degrees at times.
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Galileo Galilei
• Turned a telescope toward the heavens
• Made observations that:
– contradicted the perfection of the heavens
• Mountains, valleys, and craters on the Moon
• Imperfections on the Sun (sunspots)
– Supported the heliocentric universe
• Moons of Jupiter
• Phases of Venus – shows a full phase
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Tycho Brahe
• Had two sets of astronomical
tables: one based on Ptolemy’s
theory and one based on
Copernicus’.
• He found that both tables’
predictions were off by days
to a month.
• He believed that much better
tables could be constructed
just by more accurate observations.
• Tycho’s homemade instruments improved measurement
precision from ten minutes of arc (which had held since
Ptolemy) to less than one
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The skies change
• Tycho observed 2 phenomena that
showed the heavens DO change:
– In November 1572, Tycho noticed
a new star in the constellation
Cassiopeia
– Comet of 1577
• Prior to this sighting,
comets were thought to be atmospheric
phenomena because of the immutability
of the heavens
• But neither the star nor the comet changed position as the
observer moved, as expected for atmospheric phenomena
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Johannes Kepler
• Kepler succeeded Tycho as the Imperial mathematician (but at
only 1/3 the salary of the nobleman)
• Kepler worked for four years trying to derive the motions of
Mars from Brahe’s observations
• In the process, he discovered that the plane of the earth’s orbit
and the plane of Mars’ (and eventually the other planets) passed
through the sun
• Suspecting the sun had a force over the planets, he investigated
magnetism
• While this is not true, it did lead him to the idea of elliptical
orbits
• “With reasoning derived from physical principles agreeing with
experience, there is no figure left for
the orbit of the planet except a perfect ellipse.”
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Astronomia nova
• Published in 1609, The New Astronomy was just that, it
revolutionized the field
• It predicted planetary positions as much as ten times
better than previous models
• It included physical causes for the movement of the
planets
• The ideas of the Greeks were gone – the heavens no
longer were perfect, immutable, or different from the
earth
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Kepler’s first Law
• The orbital paths
of the planets are
elliptical (not
circular), with the
Sun at one focus.
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Kepler’s second law
• An imaginary line
connecting the
Sun to any planet
sweeps out equal
areas of the ellipse
in equal intervals
of time.
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Kepler’s Third Law
• The square of a
planet’s orbital
period is
proportional to
the cube of its
semi-major axis.
• Kepler orbit demonstration:
http://csep10.phys.utk.edu/guidry/java/kepler/kepl
er.html
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Planetary Properties
Planet
Orbital
eccentricity,
e
Orbital semi-major
axis, a
(Astronomical units)
Orbital
period,P
(Earth years)
Mercury
Venus
Earth
0.206
0.007
0.017
0.387
0.723
1.000
0.241
0.615
1.000
Mars
Jupiter
Saturn
0.093
0.048
0.054
1.524
5.203
9.537
1.881
11.86
29.42
Uranus
Neptune
Pluto
0.047
0.009
0.249
19.19
30.07
39.48
83.75
163.7
248.0
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Other Solar System Bodies
• Kepler derived his
laws for the 6
planets known to
him. The laws also
apply to the 3
discovered planets
and any other body
orbiting the Sun
(asteroids, comets,
etc.)
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A force for planetary motion
• Newton proposes a force which controls the
motion of the planets – GRAVITY
• The larger the mass, the larger the force of gravity
• The further the distance, the smaller the force of
gravity
• Kepler’s third law can be derived from Newton’s
law of gravity
• F = GMm/r2 = mg
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Gravity
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