2. 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 1B
look like?
4. 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
1B
5. 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 1B
6. In the heliocentric model, apparent
retrograde motion of the planets is a direct
consequence of the Earth’s motion
1B
7. 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?
1B
8. 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 1B
9. 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
1B
aesthetically pleasing to the philosophy of the day
10. 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 1B
with the naked eye
11. 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.
1B
12. Galileo Galilei
Turneda 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
1B
13. 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 1B
14. 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 1B
15. 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.”
1B
16. 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
1B
17. Kepler’s first Law
The orbital
paths of the
planets are
elliptical (not
circular), with
the Sun at one
focus.
1B
18. 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.
1B
19. 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/kep
1B
20. Planetary Properties
Planet Orbital Orbital semi-major Orbital
eccentricity, axis, a period,P
e (Astronomical units) (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 1B
21. 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.)
1B
22. 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
1B