Transcript PowerPoint Presentation - Copernicus

Announcements
1. Lunar Eclipse Feb 20 (Next Wednesday)!!!!
Next Tuesday’s class will be devoted to
the moon and the eclipse. We’ll watch from
the mall on Wednesday evening. No class
next Thursday - but there will be homework
related to our lunar observations.
2. Homework 2 is due now. Homework 3 will
be posted today, due Feb 21 (Thursday).
2. Astrobiology Lecture Tonight
3. Essay Topics due Today.
Date:
Tuesday February 12, 2008
Time:
Lecture (7pm) followed by book signing (8pm)
Place: Center for Creative Photography (UA Main Campus).
Gregory Benford, Author and Astrophysicist at UC Irvine
"Seeking Ozymandias: Building and Searching for Beacons”
What would transmitters be like if built by civilizations with a variety of
motivations, but who cared about cost? We have considered the physical
limitations a beacon builder would face in constructing extremely high power
radiators. Beacons built by distant advanced, wealthy societies may have very
different characteristics from what SETI researchers now seek.Very high power
systems have driving factors set by fundamental properties of materials, such
as cooling of such high powers. The Principle of Parsimony suggests that
beacon will compete with other social goods, for altruistic reasons. Such
Beacons will have narrow beam widths, be pulsed and broadband, to minimize
costs. Therefore, the transmission strategy for a distant beacon may be a rapid
scan of the galactic plane, to cover the angular space. Searches for such
intermittent, broadband signals could find signals we have neglected, because
we believed earlier that the Beacon builders will be spendthrifts. Yet stable
societies do not sacrifice their societies for distant others. Perhaps we should
consider long-term stability from a moral point of view.
“Finally we shall place the Sun himself at the center
of the Universe. All this is suggested by the
systematic procession of events and the harmony
of the whole Universe, if only we face the facts, as
they say, ‘with both eyes open’ ”
- Nicolaus Copernicus
De Revolutionibus
orbium
coelestium
“There was music in the cafes at night and
revolution in the air. ” - Bob Dylan
Copernicus (1473-1543) was
the sun of a successful
merchant in central Poland.
Copernicus studied to be a
physician, which, at the time
included the study of
astronomy, because doctors
used astrology to decide on
treatments. Copernicus worked
as a deacon in the Church and
spent his time studying
Astronomy. He wrote the first draft of De Revoluitonibus in
1513, but, because of worries about how it would be
received, he delayed publication until 1543, when he was on
his death bed.
What else was going on at the Beginning of the
16th Century?
• Europe was coming out of the
dark ages, rediscovering Greek
and Roman learning and
exploring the world.
• Explorers were sailing to Africa and Asia. Columbus
discovered America while Copernicus was studying at the
University. Malgalhães (Magellan) circumnavigated the
globe. All this relied heavily on Astronomy.
• Printing was becoming common. A man of modest
means, like Copernicus, could own books. He had 2
copies of the Almagest.
• There was an explosion in artistic activity.
Michelangelo’s “David”
1501-1504
da Vinci’s “Mona Lisa”
1503-1506
Copernicus’ Solar System
•The Sun is in the center
•Simpler than Ptolemy’s Model
(No need for epicycles)
• Circular Orbits are assumed.
This will be proved wrong.
• More accurate? No, it had
about the same accuracy.
• Why would we prefer this model
to Ptolemy’s?
From De Revolutionibus
Ptolemy’s Geocentric System, codified
in the Almagest
Figures from Astronomy Today by Chaisson and McMillan
This is getting complicated.
Link to movie
Occam’s Razor
William of Ockham (1285-1349) was a
Franciscan monk and philosopher who
espoused the virtues of simplicity and
poverty in science and in life.
Suggesting that the Pope conform to
the latter got him excommunicated.
“One
should not increase, beyond what is necessary, the
number of entities required to explain anything.”
If you have two theories that are equally successful in
explaining a phenomenon, the simpler one is better.
The conviction of simplicity persists.
Tycho Brahe (1546 – 1601)
The discovery of a new star
Stellar Parallax
• Tycho argued that the
new star must be in the
celestial sphere because it
exhibited no parallax.
• This discovery showed
that the heavens were not
perfect and unchanging.
25 Years of Planetary Observations
Tycho caught the attention
of King Frederick II of
Denmark
With royal funds, he built the
ultimate observatory.
He designed, & tested
instruments, compiling the
most comprehensive
planetary observations ever,
with accuracy of 1°, about
5x better than before.
Uraniborg, Hven
complete with wine cellar and prison
Johannes Kepler
(1571-1630)
Kepler joined Tycho a year
before Tycho’s death (1600).
Assuming Tycho’s position,
Kepler inherited the records of
Tycho’s observations.
From this Kepler knew that
planets did not travel on circles
and devised a new way to
describe planetary motion.
Kepler searched for a single physical explanation to
planetary motion – a force between planets and the Sun.
Kepler aimed to explain
Tycho’s observations which
showed that planets do not
move in circles
He noted that planets closer to
the Sun in Copernicus’ model
moved faster than those
further out.
A force must therefore act.
Kepler thought it was
magnetic*
Thus he believed that a simple
set of laws existed by which all
planets move.
*Influenced by William Gilbert’s De Magnete
Kepler’s Three Laws
1. Planets move about the Sun in elliptical orbits
with the Sun at one focus.
2. The line joining a planet to the Sun sweeps
over equal areas in equal intervals of time.
3. The square of the time of one revolution of a
planet about the Sun is proportional to the
cube of the orbit’s semimajor axis.
1. Planets move in
elliptical orbits with
the Sun at one
focus.
2. The line joining the Sun to the planet
sweeps equal areas in equal intervals of
time.
Link to movie
3. The square of a planet’s period
equals the cube of its semi-major axis
2
P
= k·
3
a
P is the period, a is the semi-major axis, k is a
constant which depends on the units of P & a.
(For P in years and a in Astronomical Units, k=1.)
The farther a planet is from the Sun, the longer it’s
year
Simple Example of P2=a3
• Consider a hypothetical planet orbiting the
sun with a semi-major axis of 4 A.U.
• Let a = 4 A.U. (Astronomical Units)
• Then a3 = 43 A.U.3 = 64 A.U.3
• P2 = 64 years2
• P = SQRT(P2)=SQRT(64) years = 8 years
• The period of the planet is 8 years.
Kepler’s Third Law
a
P2
a3
Mercury
0.24
0.39
0.058
0.058
Venus
0.61
0.72
0.378
0.378
Earth
1.00
1.00
1.00
1.00
Mars
1.88
1.52
3.53
3.53
Jupiter
11.86
5.20
140.6
140.8
Saturn
29.42
9.54
865.8
867.4
Uranus
83.75
19.19
7014.
7067.
Neptune
163.7
30.07
26804.
27186.
Pluto
248.0
39.48
61514.
61540.
80000
60000
a^3
P
40000
20000
0
0
20000
40000
P^2
60000
80000
Summary
In the 16th century Europeans began exploring
the planet, navigating by the stars, and renewed
their interest in science and the arts. In
Astronomy this led to the first new theory
describing celestial motions in 1400 years. The
Copernican revolution was a tentative, first step
towards the establishment of the modern
scientific method.