ASTRONOMY 161

ASTRONOMY 161
Introduction to Solar System Astronomy
Class 6
Tycho, Kepler, & Galileo
Wednesday, January 17
“E pur si muove!” [It still moves!]
- Galileo
Astronomical movies:
The Phases of Venus
http://antwrp.gsfc.nasa.gov/apod/ap060110.html
When Moons and Shadows Dance (Jupiter)
http://antwrp.gsfc.nasa.gov/apod/ap030227.html
Large Sunspot Group (Sun)
http://antwrp.gsfc.nasa.gov/apod/ap010411.html
Tycho, Kepler, & Galileo: Key Concepts
(1) Tycho Brahe made accurate measurements of planetary
motion.
(2) Planetary orbits are ellipses with the Sun at one focus.
(3) A line between planet & Sun sweeps out equal areas in
equal times.
(4) The square of a planet’s orbital period is proportional to
the cube of its average distance from the Sun.
(5) Galileo made telescopic observations supporting the
heliocentric model.
(1) Tycho Brahe made accurate measurements
of planetary motion.
Tycho Brahe (1546-1601):
Danish astronomer
Tycho’s contributions to astronomy
Tycho discovered ‘new
star’, or ‘nova’,
upsetting ancient
notion of perfect,
unchanging heavens.
Made very accurate
measurements of
planetary positions.
Copernican
system
Tycho’s
system
Johannes Kepler (1571-1630): German
Was Tycho’s assistant.
Used Tycho’s data to
discover
Three Laws of
Planetary Motion.
(2) Kepler’s First Law
of planetary motion
The orbits of planets around the Sun are
ellipses with the Sun at one focus.
Ellipse = an oval built around two points,
called focuses (or foci).
SIZE of ellipse:
Major axis = longest
diameter of ellipse.
Semimajor axis = half
the major axis.
SHAPE of ellipse:
Eccentricity = distance between foci divided by major axis.
Foci close together: ellipse nearly circular, eccentricity close to zero.
Foci far apart: ellipse very flattened, eccentricity close to one.
Example: Mars
Semimajor axis =
1.524 A.U.
Eccentricity = 0.093
(much smaller
than one)
Ellipse comes from the family of Conic Sections
(3) Kepler’s
Second Law of planetary motion
A line
to a planet
from the Sun
sweeps out equal
areas in equal time intervals.
Consequences of Kepler’s Second Law:
Planets move fastest when closest to the Sun.
Example: Mars
Perihelion: 206,600,000 km (1.381 A.U.)
Max. Orbital Speed: 26.5 km/s
Aphelion: 249,200,000 km (1.666 A.U.)
Min. Orbital Speed: 22.0 km/s
(4) Kepler’s Third Law
of planetary motion
The square of a planet’s orbital period is
proportional to the cube of its average
distance from the Sun*:
P
2
=
a
3
*A planet’s average distance from the Sun is equal to the
semimajor axis of its orbit.
Kepler’s Third Law in mathematical form:
P
2
=
a
3
P = orbital period (in years)
a = semimajor axis (in A.U.)
Example: The orbit of Mars
P = 1.881 yr
a = 1.524 A.U.
2
P = 3.54
3
a = 3.54
(5) Galileo made telescopic observations supporting
the heliocentric model.
Galileo Galilei (15641642): Italian
Galileo was among the
first to observe the
sky with a telescope
(1609).
Flashback to Class 1: What is Science?
The SYSTEMATIC study of the Universe
Gather facts
Modify hypothesis
Guess an explanation
(Guess=hypothesis)
Test hypothesis
1) Mountains on the Moon
Aristotle & Ptolemy said the Moon is a perfect,
smooth sphere.
In fact, the Moon is no more “perfect” than the Earth.
2) The Sun has spots on its surface.
The Sun is not
perfect.
Motion of sunspots
indicates that the
Sun is rotating.
If the Sun rotates,
why not the
Earth?
3) The planet Jupiter has moons of its own.
Four “Galilean” moons of
Jupiter: Io, Europa,
Ganymede, & Callisto.
The Earth is NOT the center of
all orbits in the universe.
4) Venus shows phases
like those of the Moon.
Venus goes through
all phases: looks
big when nearly
new, looks small
when full.
Results consistent
with Copernicus,
inconsistent with
Ptolemy.
Phases of Venus in the
geocentric model of Ptolemy.
Only new and
crescent
phases.
Phases of Venus in the
heliocentric model.
All phases; smaller angular size
when full than when new.
Few closing questions:
1) Do the inner planets
show retrograde
motions? (again)
2) See picture on the
right. What is it?
3) Does Mercury show
phases? Mars?
Jupiter?
Few closing questions continued:
4) If the Sun is at one
focus of the ellipse,
what is at the other
focus?
5) See picture on the
right. What is it? Is
it real?