2. 1B1B
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?
4. 1B1B
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
5. 1B1B
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
6. 1B1B
• In the heliocentric model, apparent
retrograde motion of the planets is a direct
consequence of the Earth’s motion
7. 1B1B
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?
9. 1B1B
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
10. 1B1B
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
11. 1B1B
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.
12. 1B1B
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
13. 1B1B
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
14. 1B1B
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
15. 1B1B
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.”
16. 1B1B
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
17. 1B1B
Kepler’s first Law
• The orbital paths
of the planets
are elliptical (not
circular), with
the Sun at one
focus.
18. 1B1B
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.
19. 1B1B
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/kepler.html
20. 1B1B
Planetary Properties
Planet Orbital
eccentricity,
e
Orbital semi-major
axis, a
(Astronomical units)
Orbital
period,P
(Earth years)
Mercury 0.206 0.387 0.241
Venus 0.007 0.723 0.615
Earth 0.017 1.000 1.000
Mars 0.093 1.524 1.881
Jupiter 0.048 5.203 11.86
Saturn 0.054 9.537 29.42
Uranus 0.047 19.19 83.75
Neptune 0.009 30.07 163.7
Pluto 0.249 39.48 248.0
21. 1B1B
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.)
22. 1B1B
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
