Download Explaining Apparent Retrograde Motion

Homework #2
 Due Monday, February 1, 11:59 PM
 Covers Chapters 1, 2, and 3
 Estimated time to complete: 1 hour 10 minutes (so don’t
wait until the last minute!) – can stop and start as you wish
 Read chapters, review notes before starting
 Some questions have multiple parts – do not skip them
 For some of the drag-and-drop ordering questions, two or
more of the answers might be in the same location (i.e., two
objects might have the exact same age if you are sorting by
age). In this case, place the two answers on top of each
other.
 Note: Incorrect guesses will count against you from now on.
We see apparent retrograde motion
when we pass by a planet in its orbit.
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 (Greeks) considered
but rejected the correct (Sun-centered)
explanation for our Solar System –
more on this in Chapter 3.
Why did the ancient Greeks reject the
real explanation for retrograde motion?
Their inability to observe stellar parallax was a major factor.
Parallax:
apparent
shifting of
position of a
foreground
object relative
to background
objects (think:
finger in front
of clock)
Highly exaggerated,
but you get the point
With the naked eye,
stars would have to
be at a distance of
~0.05 light years or
closer for parallax to
be detectable (almost
100 times closer than
the closest star)
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.  correct
OR
2. Earth does not orbit the Sun; it is the center of the
universe.  incorrect
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.
Ultimately, why didn’t the ancient
Greeks accept that the Earth went
around the Sun?
A) It violated their religious beliefs.
B) If they did, they would no longer have an
explanation for planetary retrograde motion.
C) They were unaware of the concept of stellar
parallax.
D) They were aware of stellar parallax but were
unable to measure it.
Ultimately, why didn’t the ancient
Greeks accept that the Earth went
around the Sun?
A) It violated their religious beliefs.
B) If they did, they would no longer have an
explanation for planetary retrograde motion.
C) They were unaware of the concept of stellar
parallax.
D) They were aware of stellar parallax but were
unable to measure it.
Chapter 2 Study Guide
1)
88 constellations have no real physical significance
(just used to divide up the sky)
2)
The celestial sphere is the projection of the Earth’s
surface onto the sky – poles and equator
3)
Ecliptic – the path the Sun takes eastward through
the sky relative to the background stars (@1 degree
per day) – caused by Earth’s motion around Sun
4)
Altitude of Polaris gives your latitude on Earth
5)
Earth’s 23.5 degree tilt causes seasons and different
lengths of daylight throughout the year
Chapter 2 Study Guide
6) Know meaning of solstice, equinox and when they
occur
7) Earth’s spin precesses (wobbles) over 26,000 year
period  Polaris will not be the Pole Star in a few
thousand years
8) Know lunar phases, and understand geometry of
Sun-Earth-Moon system (picture in your mind,
don’t memorize) – Earth shadow does not cause
Moon phases!
9) The Moon DOES rotate (once every 29.5 days) so
that we never see the back side of the Moon
Chapter 2 Study Guide
10) Know geometry of solar, lunar eclipses, and why they do
not happen at every new/full Moon
11) Go see the August 2017 total solar eclipse!
12) Planets undergo retrograde motion, where they move
backwards (westward) in their path among the stars 
natural consequence of Earth lapping them/being lapped
13) Retrograde motion easy to explain in Sun-centered
systems, difficult in Earth-centered systems
14) Greeks considered this, but rejected Sun-centered solar
system because they could not measure the parallax of
any of the stars  thought stars could not be that distant
Chapter 3
The Science (and History) of Astronomy
How did astronomical observations
benefit ancient societies?
Keeping track of time and seasons
• for practical purposes, including
agriculture
• for religious and ceremonial purposes
• aid to navigation
However, few cultures used the scientific method to learn
about the nature of the Universe (Greeks were an
exception), thus they were not truly studying astronomy.
Ancient people of central Africa (6500 BC)
could predict seasons from the orientation
of the crescent Moon.
England: Stonehenge (completed around 1550 B.C.)
England: Stonehenge (1550 B.C.)
Southwest United States: “Sun Dagger” marks summer solstice
Scotland: 4,000-year-old stone circle; Moon rises as
shown here every 18.6 years.
Macchu Pichu, Peru: Structures aligned with solstices.
South Pacific: Polynesians were very skilled in art of celestial
navigation.
France: Cave paintings from 18,000 B.C. may suggest
knowledge of lunar phases (29 dots)
"On the Jisi day,
the 7th day of
the month, a big
new star
appeared in the
company of the
Ho star."
"On the Xinwei day the new star dwindled."
Bone or tortoiseshell inscription from the 14th century B.C.
China: Earliest known records of supernova
explosions (1400 B.C.)
Days of week were named for the Sun, Moon, and visible planets.
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.)
Eratosthenes Measures Earth (c. 240 B.C.)
First day of summer at noon: Sun
shone directly into a well in Syene, but
missed the well in Alexandria by 7°.
Measurements:
Syene (modern day Aswan) to Alexandria
distance ≈ 5000 stadia
angle = 7°
Calculate circumference of Earth:
7/360 = (Alexandria-Syene distance)/(circum. Earth)
 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
Greeks were quite well aware that the Earth was round.
How did the Greeks explain planetary motion?
Underpinnings of the Greek geocentric model:
• Earth at the center of the universe (since no detected
parallax)
• Heavens must be “perfect”: Objects move on perfect
spheres or in perfect circles.
Plato
Aristotle
The most sophisticated
geocentric (Earth-centered)
model was that of Ptolemy
(A.D. 100-170) — the
Ptolemaic model:
• Sufficiently accurate to
remain in use for 1,500 years.
• Arabic translation of
Ptolemy’s work named
Almagest (“the greatest
compilation”)
Ptolemy
Extremely contrived…..
But this model made it difficult to explain
apparent retrograde motion of planets…
Review: Over a period of 10 weeks, Mars appears to stop,
back up, then go forward again.
So how does the Ptolemaic model explain retrograde motion?
Planets really do go backward in this (wrong) model…
Epicycles (circles
upon circles)
Needed to mimic
retrograde motion
This system predicts the orbits
reasonably well if you add
enough epicycles to the
system….
Mercury eventually required 11
epicycles in Ptolemaic model to
remain sufficiently accurate!
Extremely contrived!
Ptolemy’s Geocentric Model
• Earth is at center
• Sun orbits Earth
• Planets orbit on
small circles
(epicycles) whose
centers orbit the
Earth on larger
circles
• This view of the
Solar System held
for 1500 years….
Which of the following was not a
feature of the Ptolemaic model?
A) Epicycles were used to explain planetary
retrograde motion.
B) The Earth was at the center of the Solar
System.
C) The Earth orbited the Sun.
D) The orbits of planets were perfect circles.
Which of the following was not a
feature of the Ptolemaic model?
A) Epicycles were used to explain planetary
retrograde motion.
B) The Earth was at the center of the Solar
System.
C) The Earth orbited the Sun.
D) The orbits of planets were perfect circles.
Greeks thought the Earth did not move because
they could not measure stellar parallax.
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.
How did Copernicus, Tycho, and Kepler
challenge the Earth-centered model?
Nicolas Copernicus proposed a Suncentered model (published 1543)
•
• Used model to determine layout of
solar system (planetary distances
in AU)
But . . .
• The model was no more accurate and not
any simpler than the Ptolemaic model in
predicting planetary positions, because it still
Copernicus (1473-1543)
perfectly circular orbits
(and therefore still had to use epicycles).
assumed
Tycho Brahe
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)
• Hired Johannes Kepler, who used
Tycho’s observations to discover
the truth about planetary motion.
Johannes Kepler
Kepler first tried to match Tycho’s
observations with circular orbits -- no
success
•
• An 8-arcminute discrepancy led him
eventually to use ellipses rather
than circles
Johannes Kepler
(1571-1630)
“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.”
Good scientist!