Download models

Astronomy 115
01/17/13
Video:
http://apod.nasa.gov/apod/ap130115.html
Thursday, January 17, 13
1
Seasons on Mars
http://www.msss.com/mars_images/moc/opposition_6_2001/
Thursday, January 17, 13
2
CHAPTER 3
THE SCIENCE OF ASTRONOMY
Thursday, January 17, 13
3
PLANETS KNOWN IN ANCIENT TIMES
• Mercury
–difficult to see; always close
to Sun in sky
• Venus
–very bright when visible;
morning or evening “star”
• Mars
–noticeably red
• Jupiter
–very bright
• Saturn
–moderately bright
Thursday, January 17, 13
4
Days of week were named for the Sun, Moon, and the
visible planets.
Thursday, January 17, 13
5
ANCIENT GREEK SCIENCE
Thursday, January 17, 13
6
Why does modern science trace its roots to
the Greeks?
• Greeks were the
first people known to
make models of
nature.
They tried to
explain patterns in
nature without
resorting to myth or
the supernatural.
•
Greek geocentric model (c. 400 B.C.)
Thursday, January 17, 13
7
Special Topic: Eratosthenes Measures Earth (c. 240 B.C.)
Measurements:
Syene to Alexandria
distance ≈ 5000 stadia
angle = 7°
Calculate circumference of Earth:
7/360 × (circum. Earth) = 5000 stadia
⇒ circum. Earth = 5000 × 360/7 stadia ≈
250,000 stadia
Compare to modern value (≈ 40,100 km):
Greek stadium ≈ 1/6 km ⇒ 250,000 stadia ≈
42,000 km
Thursday, January 17, 13
8
How did the Greeks explain planetary motion?
Underpinnings of the Greek geocentric model:
• Earth at the center of the universe
• Heavens must be “perfect”:
Objects moving on perfect spheres
or in perfect circles.
Plato
Aristotle
Thursday, January 17, 13
9
BUT THIS MADE IT DIFFICULT TO
EXPLAIN APPARENT RETROGRADE
MOTION OF PLANETS…
Over a period of 10 weeks, Mars appears to stop, back
up, then go forward again.
Thursday, January 17, 13
10
WHAT WAS ONCE SO MYSTERIOUS
ABOUT PLANETARY MOTION IN OUR
SKY?
• Planets
usually move slightly eastward from night to night
relative to the stars.
• But
sometimes they go westward relative to the stars for a
few weeks: apparent retrograde motion.
Thursday, January 17, 13
11
WE SEE APPARENT RETROGRADE
MOTION WHEN WE PASS BY A PLANET
IN ITS ORBIT.
Thursday, January 17, 13
12
EXPLAINING APPARENT RETROGRADE
MOTION
• Easy
for us to explain: occurs when we “lap” another planet
(or when Mercury or Venus laps us).
• But
very difficult to explain if you think that Earth is the center
of the universe!
• In fact, ancients considered but rejected the correct
explanation.
Thursday, January 17, 13
13
WHY DID THE ANCIENT GREEKS REJECT
THE REAL EXPLANATION FOR PLANETARY
MOTION?
• Their inability to observe stellar parallax was a major
factor.
Thursday, January 17, 13
14
THE GREEKS KNEW THAT THE LACK OF
OBSERVABLE PARALLAX COULD MEAN ONE
OF TWO THINGS:
1. Stars are so far away that stellar parallax is too small
to notice with the naked eye.
2. Earth does not orbit the Sun; it is the center of the
universe.
With rare exceptions such as Aristarchus, the Greeks rejected
the correct explanation (1) because they did not think the
stars could be that far away.
Thus, the stage was set for the long, historical showdown between
Earth-centered and Sun-centered systems.
Thursday, January 17, 13
15
The most sophisticated
geocentric model was
that of Ptolemy (A.D.
100-170) — the
Ptolemaic model:
• Sufficiently accurate to
remain in use for 1,500
years.
•
Ptolemy
Thursday, January 17, 13
Arabic translation of
Ptolemy’s work named
Almagest (“the greatest
compilation”)
16
So how does the Ptolemaic model explain retrograde
motion?
Planets really do go backward in this model..
Thursday, January 17, 13
17
THOUGHT QUESTION
WHICH OF THE FOLLOWING IS NOT A
FUNDAMENTAL DIFFERENCE BETWEEN THE
GEOCENTRIC AND SUN-CENTERED MODELS OF
THE SOLAR SYSTEM?
A. Earth is stationary in the geocentric model but moves around Sun in Suncentered model.
B. Retrograde motion is real (planets really go backward) in geocentric
model but only apparent (planets don’t really turn around) in Suncentered model.
C. Stellar parallax is expected in the Sun-centered model but not in the
Earth-centered model.
D. The geocentric model is useless for predicting planetary positions in the
sky, while even the earliest Sun-centered models worked almost perfectly.
Thursday, January 17, 13
18
THOUGHT QUESTION
WHICH OF THE FOLLOWING IS NOT A
FUNDAMENTAL DIFFERENCE BETWEEN THE
GEOCENTRIC AND SUN-CENTERED MODELS OF
THE SOLAR SYSTEM?
A. Earth is stationary in the geocentric model but moves around Sun in Suncentered model.
B. Retrograde motion is real (planets really go backward) in geocentric
model but only apparent (planets don’t really turn around) in Suncentered model.
C. Stellar parallax is expected in the Sun-centered model but not in the
Earth-centered model.
D. The geocentric model is useless for predicting planetary positions in
the sky, while even the earliest Sun-centered models worked almost
perfectly.
Thursday, January 17, 13
19
Artist’s reconstruction of the Library of Alexandria.
Thursday, January 17, 13
20
How was Greek knowledge preserved through
history?
• The Muslim world preserved and enhanced the
knowledge they received from the Greeks.
• Al-Mamun’s House of Wisdom in Baghdad was a
great center of learning around A.D. 800.
• With the fall of Constantinople (Istanbul) in 1453,
Eastern scholars headed west to Europe, carrying
knowledge that helped ignite the European
Renaissance.
Thursday, January 17, 13
21
Our mathematical and scientific heritage
originated with the civilizations of the Middle
East.
Thursday, January 17, 13
22
How did Copernicus, Tycho, and Kepler
challenge the Earth-centered model?
• Proposed a Sun-centered model
(published 1543)
• Used model to determine layout of
solar system (planetary distances
in AU)
But . . .
Copernicus
(1473-1543)
Thursday, January 17, 13
• The model was no more
accurate than the Ptolemaic
model in predicting planetary
positions, because it still used
perfect circles.
23
• Compiled the most accurate
(one arcminute) naked eye
measurements ever made of
planetary positions.
Still could not detect stellar
parallax, and thus still thought
Earth must be at center of solar
system (but recognized that
other planets go around Sun).
•
Tycho Brahe
(1546-1601)
Thursday, January 17, 13
• Hired Kepler, who used Tycho’s
observations to discover the
truth about planetary motion.
24
• Kepler first tried to match
Tycho’s observations with
circular orbits
• But an 8-arcminute
discrepancy led him eventually
to ellipses.
Johannes Kepler
(1571-1630)
Thursday, January 17, 13
“If I had believed that we could ignore
these eight minutes [of arc], I would have
patched up my hypothesis accordingly.
But, since it was not permissible to
ignore, those eight minutes pointed the
road to a complete reformation in
astronomy.”
25
What is an ellipse?
An ellipse looks like an elongated circle.
Thursday, January 17, 13
26
What are Kepler’s three laws of planetary motion?
Kepler’s First Law: The orbit of each planet around the
Sun is an ellipse with the Sun at one focus.
Thursday, January 17, 13
27
Kepler’s Second Law: As a planet moves around its
orbit, it sweeps out equal areas in equal times.
This means that a planet travels faster when it is nearer
to the Sun and slower when it is farther from the Sun.
Thursday, January 17, 13
28
Thursday, January 17, 13
29
Kepler’s Third Law
More distant planets orbit the Sun at slower
average speeds, obeying the relationship
2
p
=
3
a
p = orbital period in years
a = avg. distance from Sun in AU
Thursday, January 17, 13
30
Graphical version of Kepler’s Third Law
Thursday, January 17, 13
31
THOUGHT QUESTION
AN ASTEROID ORBITS THE SUN AT AN AVERAGE
DISTANCE A = 4 AU. HOW LONG DOES IT TAKE TO
ORBIT THE SUN?
A. 4 years
B. 8 years
C. 16 years
D. 64 years
Hint: Remember that p2 = a3
Thursday, January 17, 13
32
Thought Question
An asteroid orbits the Sun at an average distance
a = 4 AU. How long does it take to orbit the Sun?
A. 4 years
B. 8 years
C. 16 years
D. 64 years
We need to find p so that p2 = a3.
Since a = 4, a3 = 43 = 64.
Therefore, p = 8, p2 = 82 = 64.
Thursday, January 17, 13
33
THOUGHT QUESTION
Suppose a comet had a very eccentric orbit that brought it
quite close to the Sun at closest approach (perihelion) and
beyond Mars when furthest from the Sun (aphelion), but with
an average distance of 1 AU. How long would it take to
complete an orbit and where would it spend most of its time?
A.
B.
C.
D.
E.
one year, mostly beyond Earth’s orbit
one year, mostly within Earth’s orbit
more than one year, mostly beyond Earth’s orbit
less than one year, mostly within Earth’s orbit
It depends on the exact value of the eccentricity.
Thursday, January 17, 13
34
THOUGHT QUESTION
Suppose a comet had a very eccentric orbit that brought it
quite close to the Sun at closest approach (perihelion) and
beyond Mars when furthest from the Sun (aphelion), but with
an average distance of 1 AU. How long would it take to
complete an orbit and where would it spend most of its time?
A.
B.
C.
D.
E.
one year, mostly beyond Earth’s orbit
one year, mostly within Earth’s orbit
more than one year, mostly beyond Earth’s orbit
less than one year, mostly within Earth’s orbit
It depends on the exact value of the eccentricity.
Thursday, January 17, 13
35
HOW DID GALILEO SOLIDIFY THE COPERNICAN
REVOLUTION?
Galileo overcame major objections
to the Copernican view. Three key
objections rooted in Aristotelian
view were:
1. Earth could not be moving
because objects in air would be
left behind.
2. Non-circular orbits are not
“perfect” as heavens should be.
3. If Earth were really orbiting Sun,
we’d detect stellar parallax.
Thursday, January 17, 13
36
Overcoming the first objection (nature of motion):
Galileo’s experiments showed that objects in
air would stay with Earth as it moves.
• Aristotle thought that all objects naturally come
to rest.
• Galileo showed that objects will stay in motion
unless a force acts to slow them down (Newton’s
first law of motion).
Thursday, January 17, 13
37
Overcoming the second objection (heavenly
perfection):
• Tycho’s observations of
comet and supernova already
challenged this idea.
• Using his telescope, Galileo
saw:
• Sunspots on Sun
(“imperfections”)
• Mountains and valleys on
the Moon (proving it is not
a perfect sphere)
Thursday, January 17, 13
38
Overcoming the third objection (parallax):
• Tycho thought he had measured stellar
distances, so lack of parallax seemed to rule
out an orbiting Earth.
• Galileo showed stars must be much farther
than Tycho thought — in part by using his
telescope to see the Milky Way is countless
individual stars.
 If stars were much farther away, then lack
of detectable parallax was no longer so
troubling.
Thursday, January 17, 13
39
Galileo also saw four
moons orbiting Jupiter,
proving that not all
objects orbit Earth.
Thursday, January 17, 13
40
Galileo’s observations of phases of Venus
proved that it orbits the Sun and not Earth.
Thursday, January 17, 13
41
The Catholic Church ordered Galileo to recant his
claim that Earth orbits the Sun in 1633.
His book on the subject was removed from the
Church’s index of banned books in 1824.
Galileo was formally vindicated by the Church in
1992.
Thursday, January 17, 13
42
CHAPTER 4
MAKING SENSE OF THE UNIVERSE:
UNDERSTANDING MOTION, ENERGY, AND
GRAVITY
Thursday, January 17, 13
43
HOW DO WE DESCRIBE
MOTION?
Precise definitions to describe motion:
•
Speed: Rate at which object moves
Example: 10 m/s
Thursday, January 17, 13
•
Velocity: Speed and direction
Example: 10 m/s, due east
•
Acceleration: Any change in
velocity units of speed/time (m/
s2)
44
THE ACCELERATION OF GRAVITY
• All falling objects
accelerate at the
same rate (not
counting friction of
air resistance).
• On Earth, g ≈ 10 m/
s2: speed increases
10 m/s with each
second of falling.
Thursday, January 17, 13
45
THE ACCELERATION OF GRAVITY (G)
• Galileo showed that g is
the same for all falling
objects, regardless of
their mass.
Apollo 15 demonstration
Thursday, January 17, 13
46