ASTR 111

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Lecture 4

• ASTR 111 Section 002

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Note

• Ill post all slides after class

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Terms
While you are waiting for class to start, try to
define these terms

• Apogee/Perigee
• Subtend
• Parsec, light-year, AU
• Parallax
• Solar and Sidereal time
• Small angle formula

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Terms
While you are waiting for class to start, try to
define these terms

• Ecliptic
• Zenith
• Tropic of Cancer, Capricorn, Artic and Antarctic
  Circle
• Equinox, Solstice
• Zodiac
• Accuracy, Precision, and Bias

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Tuesday September 15th

• Class is canceled.
• Quiz is still due at 9 am on the 15th.
• I will be available via email.

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First Exam

• On 9/29
• Based on lecture notes, problems worked in
  lecture, and quizzes.
• Approximately 50 questions
• In the Testing and Tutoring Center (using
  Blackboard system)
• Typically 25 minutes to complete

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Outline

1. Quiz Discussion
2. Rotation review generally
3. The Seasons review generally
4. The Moon in its orbit
5. Math review

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Quiz (homework) Discussion
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Bias

• Many types. Two common ones are
• Measurement bias or just bias
• Selection bias

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Measurement Bias
True value (measured using good instrument)
Bias measurements are not centered on true
value. (Usually due to mis-calibration of an
instrument.)
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Measurement Bias
True value (measured using tape measure)
9 ft
10 ft
11 ft
Bias measurements are not centered on true
value. (Usually due to mis-calibration of an
instrument.)
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Questions

• Most of the lectures were very clear but the
  quarter exercise on thursday was a little unclear
  and confusing to me.
• I was a little confused on Thursday's about
  Accuracy Vs. Precision. I understand what they
  mean, but when we were in groups and answering
  the questions I was a little confused. When we
  had to draw low precision and high bias I got
  confused.
• Astronomical distance. The concept is a little
  hard to grasp and the numbers are so large which
  only aides confusion.
• The most unclear pat of the lecture on Thursday
  was the concept of angular seperation.
• Apogee and Perigee in means of degrees
• Occasionally you misunderstand a question that a
  student asks and answer with a completely
  unrelated explanation. I can usually identify
  what you thought the question was and what you're
  explaining but I feel like most students are
  often confused.
• When we discussed bias in terms of practical
  examples as opposed to the bullseye.
• Accuracy Bias and Precision
• I felt that the most unclear part of Lecture 2
  was the measurement of Parallax. I understand the
  overall concept but not how to measure it.
• I would say that the most confusing part was the
  group question, where we had to measure our
  distance from the board using the "hand rule."
• The most unclear part of the lecture was what we
  as students are required to do outside of class.
  As in are the tests and quizzes based mostly off
  the lectures, or research we do in the textbook
  outside of class?  

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Questions

• The few slides having to do with measurement
  (e.g., car hours, etc.) --- what was a little
  unclear was how it related back to astronomy.
• explanation of angular measurement
• The most unclear part was the difference between
  bias and accuracy.
• Parsec's and the bias portion of the lecture on
  thrusday.
• Some of the questions on the group projects
• how to solve the apogee vs perigee problems
• The only hazy part of the lectures was on
  Thursday. You gave an example about parallax
  using a before and after picture, I wasn't sure
  if the second picture was taken further left or
  right.
• The most unclear part of the lecture was the
  group exercise involving the lines being drawn. I
  understand the counterclockwise movement of the
  earth but I was unsure on whether both stars
  moved to the left or if only one of the stars
  did.
• Learning how to calculate angular measurements.
• Learning about angular distances and their
  equations, went a little to fast.
• Some of the stuff about arc minutes and seconds
  maybe?
• some of the vocabulary was not clearly defined
  (or defined too quickly), and it made some things
  confusing
• For me, the most unclear part was the angles and
  arcminutes. I know how to calculate arcminutes,
  it's just that I don't really understand what
  it's purpose is.
• Using your hand as a way to measure angles was a
  little bit unclear.
• The most unclear part of the lectue on Thursday
  was the small angle formula
• The most unclear part of the lecture on Tuesday
  was the instructors view on attendence.
• I was unclear about parallax and on question 6 of
  the group work at the end of thursday's lecture.
• Nearby stars and distant stars from earth in
  January and earth in July.
• The explanation on how the hands were used to
  measure degrees was a bit fuzzy. 

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• All of the students said something was not
  clear. Therefore the lecture was not clear to
  the average student.

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• All of the students said something was not
  clear. Therefore the lecture was not clear to
  the average student.

Wrong the sample of responses he showed was
bias he did not show the responses That said
everything was clear.
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Selection bias
Bias measurements are not centered on true value
Something not clear responses
Everything clear responses
Average response
Selection Bias Average of selected
measurements are not centered on true value
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Outline

1. Quiz Discussion
2. Rotation review generally
3. The Seasons review generally
4. The Moon in its orbit
5. Math Review converting units and scientific
   notation

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View of classroom from above
Someone in back of room (distant object)
Stage
Student
Instructor
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• Sidereal Time star time
• Solar Time sun time

At 1, line points at sun and distant star
Line 1 goes through sun and distant star
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At 2, 24 sidereal hours since 1, line is now
pointing at distant star only

• Sidereal Time star time
• Solar Time sun time

Line 1 goes through sun and distant star
At 1, line points at sun and distant star
Line 1 goes through sun and distant star
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At 2, 24 sidereal hours since 1, line is now
pointing at distant star only

• Sidereal Time star time
• Solar Time sun time
• Which is longer?
• Sidereal day
• Solar day

At 1, line points at sun and distant star
At 3, 24 solar hours since 1, line points at sun
only
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At 2, 24 sidereal hours since 1, line is now
pointing at distant star only

• Sidereal Time star time
• Solar Time sun time
• Which is longer?
• Sidereal day
• Solar day by 4 min.

At 1, line points at sun and distant star
At 3, 24 solar hours since 1, line points at sun
only
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Where is Cygnus 24 solar hours later?

1. West
2. East
3. Vertical

1. West
2. East
3. Vertical

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Where is Cygnus 24 solar hours later?

1. West
2. East
3. Vertical

(Over the Pacific Ocean)
A solar day is longer than a sidereal day. After
sidereal day Cygnus is overhead. To get to a
solar day, continue rotating for 4 minutes.
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The two black lines represent poles stuck into
the ground vertically (or along zenith) that
extend out into space.
Draw these lines and Earth after 24 solar hours
have elapsed
Cygnus
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After 24 sidereal hours, pole is not quite
aligned with sun
The two black lines represent poles stuck into
the ground vertically (or along zenith) that
extend out into space.
After 24 sidereal hours, pole is aligned with
Cygnus again
Cygnus
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After 24 solar hours, pole is aligned with sun
again
The two black lines represent poles stuck into
the ground vertically (or along zenith) that
extend out into space.
Draw these lines and Earth after 24 solar hours
have elapsed
After 24 solar hours, pole has already passed
Cygnus
Cygnus
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Outline

1. Quiz Discussion
2. Rotation review generally
3. The Seasons review generally
4. The Moon in its orbit
5. Math Review converting units and scientific
   notation

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What causes the seasons?

1. Distance of the sun from earth
2. Tilt of Earth with respect to the ecliptic
3. Both 1. 2.
4. None of the above
5. Primarily 2., but with a small contribution from
   1.

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Thats a Lie!
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What causes the seasons?

• Tilt of Earth with respect to the ecliptic which
  causes
• Change in length of time sun is visible
• Change in height of sun in sky
• Change in distance to sun from observer in
  northern and southern hemispheres (true, but does
  not cause seasons!)

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• From http//www.dslreports.com/forum/remark,168226
  81
• Uses color saturation http//en.wikipedia.org/wiki
  /Saturation_(color_theory)

The Moon in its orbit
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Eventually we want to be able to explain
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A simple model

• Moon executes circular orbit
• Moon orbit is in Earths ecliptic plane

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What is wrong with this picture?
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Looking down on North Pole
Can you see white ball if you are at Equator?
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Looking down on North Pole
NO! You would need to see through Earth!
Can you see white ball if you are at Equator?
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Looking down on North Pole
If you walk around along the equator, where will
you be able to see the white ball?
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Looking down on North Pole
NO!
Can you see white ball if you are at Equator?
NO! You would need to see through Earth!
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Looking down on North Pole
Can you see white ball if you are at Equator?
NO! You would need to see through Earth!
NO!
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Looking down on North Pole
Yes!
Can you see white ball if you are at Equator?
NO! You would need to see through Earth!
Yes!
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Looking down on North Pole
Closer to scale
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• Draw a diagram that explains when you will first
  be able to see the first quarter moon if you live
  on the equator.
• Stated another way, at what time will you see the
  1st quarter moon rise from Earth?

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Sun is to the right. 1st quarter moon is first
visible at noon.
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1. Fill in the dark and light parts of the Moon for
   A-D (from this perspective)
2. From the perspective of someone on Earth what
   position of A-E best fits the Moon view in the
   lower-left-hand corner?
3. In the blank boxes below, sketch how the Moon
   would appear from Earth from the four Moon
   positions that you did not choose for Question 2.
   Label each box with a letter.

A
E
Suns rays
Earth
D
B
C
View of Moon from Earth at one of the positions
(A-E) above.
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1. Fill in the dark and light parts of the Moon for
   A-D (from this perspective)
2. From the perspective of someone on Earth what
   position of A-E best fits the Moon view in the
   lower-left-hand corner?
3. In the blank boxes below, sketch how the Moon
   would appear from Earth from the four Moon
   positions that you did not choose for Question 2.
   Label each box with a letter.

A
E
Suns rays
Earth
D
B
C
View of Moon from Earth at one of the positions
(A-E) above.
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1. Fill in the dark and light parts of the Moon for
   A-D (from this perspective)
2. From the perspective of someone on Earth what
   position of A-E best fits the Moon view in the
   lower-left-hand corner?
3. In the blank boxes below, sketch how the Moon
   would appear from Earth from the four Moon
   positions that you did not choose for Question 2.
   Label each box with a letter.

D
A
E
Suns rays
Earth
D
B
A
B
C
C
E
View of Moon from Earth at one of the positions
(A-E) above.
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1. Shade in the part of the Moon that is not
   illuminated by the sun when it is at positions
   F-I.
2. Which Moon position (F-I) best corresponds with
   the Moon phase shown in the lower-left corner?
3. How much of the Moons surface is illuminated by
   the sun during this phase?
4. How much of the Moons illuminated surface is
   visible from Earth for this phase of the Moon?

G
Suns rays
F
H
Earth
I
View of Moon from Earth from one of the positions
(F-I) above.
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1. Shade in the part of the Moon that is not
   illuminated by the sun when it is at positions
   F-I.
2. Which Moon position (F-I) best corresponds with
   the Moon phase shown in the lower-left corner?
3. How much of the Moons surface is illuminated by
   the sun during this phase?
4. How much of the Moons illuminated surface is
   visible from Earth for this phase of the Moon?

G
F
Suns rays
F
50
H
Earth
0
I
View of Moon from Earth from one of the positions
(F-I) above.
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A simple model

• Moon executes circular orbit
• Moon orbit is in Earths ecliptic plane

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Model can explain the phases of the Moon

• The phases of the Moon occur because light from
  the Moon is actually reflected sunlight
• As the relative positions of the Earth, the Moon,
  and the Sun change, we see more or less of the
  illuminated half of the Moon.

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What does the Earth look like from the Moon at

• Full Moon
• New Moon
• First Quarter
• Third Quarter

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What are 2 observations simple model does not
predict?

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Eventually we want to be able to explain
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What are 2 observations simple model does not
predict?

1. Why there are not eclipses every month
2. Why there are annular and total eclipses

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Eclipses occur only when the Sun and Moonare
both on the line of nodes
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What are 2 observations simple model does not
predict?

1. Why there are not eclipses every month
2. Why there are annular and total eclipses of
   the sun

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Solar eclipses can be either total, partial,
orannular, depending on the alignment of the
Sun,Earth, and Moon
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Eventually we want to be able to explain
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Lunar eclipses can be either total, partial,
orpenumbral, depending on the alignment of the
Sun, Earth, and Moon
70
http//centralcoastseniors.files.wordpress.com/200
8/04/lunar-eclipse-photo.jpg Is this really the
path of the moon in the sky?
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http//zuserver2.star.ucl.ac.uk/idh/apod/image/04
05/tle_may2004_ayiomamitis.jpg
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Question

• If you were looking at Earth from the side of the
  Moon that faces Earth, what would you see when
  someone on Earth sees
• A total lunar eclipse
• A total solar eclipse

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Question

• If you were looking at Earth from the side of the
  Moon that faces Earth, what would you see when
  someone on Earth sees
• A total lunar eclipse The part of Earth that
  you can see is dark. Cant see the sun.
• A total solar eclipse Part of Earth is sunlit,
  part is a little dimmer, and there is a very
  small dark patch.

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Lunar eclipses can be either total, partial,
orpenumbral, depending on the alignment of the
Sun, Earth, and Moon
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Solar eclipses can be either total, partial,
orannular, depending on the alignment of the
Sun,Earth, and Moon
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The Moons rotation always keeps the same face
toward the Earth due to synchronous rotation
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Time and the Moon

• Two types of months are used in describing the
  motion of the Moon.
• With respect to the stars, the Moon completes one
  orbit around the Earth in a sidereal month,
  averaging 27.32 days.
• The Moon completes one cycle of phases (one orbit
  around the Earth with respect to the Sun) in a
  synodic month, averaging 29.53 days.

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• sidereal month, averaging 27.32 days.
• sidereal day 23 hr 56 min
• synodic (lunar) month, averaging 29.53 days.
• solar day 24 hr

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Question

• On a certain date the Moon is in the direction of
  the constellation Gemini as seen from Earth.
  When will the Moon next be in the direction of
  Gemini?
• One year later?
• 366.2425 days later?
• One sidereal month later?
• One synodic month later?

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Question

• On a certain date the Moon is in the direction of
  the constellation Gemini as seen from Earth.
  When will the Moon next be in the direction of
  Gemini?
• One year later
• 366.2425 days later
• One sidereal month later
• One synodic month later

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Outline

1. Quiz Discussion
2. Rotation review generally
3. The Seasons review generally
4. The Moon in its orbit
5. Math review

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Math Review
84
Astronomical distances are often measured in
astronomical units, parsecs, or light-years

• Light Year (ly)
• One ly is the distance light can travel in one
  year at a speed of about 3 x 105 km/s or 186,000
  miles/s
• Parsec (pc)
• the distance at which 1 AU subtends an angle of 1
  arcsec or the distance from which Earth would
  appear to be one arcsecond from the Sun
• Astronomical Unit (AU)
• One AU is the average distance between Earth and
  the Sun
• 1.496 X 108 km or 92.96 million miles

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Review of Math that is used in Astronomy

• Powers of 10 notation (1E8 108 108)
• Powers of 10 words (from nano to peta)
• How to "derive" rules for manipulating numbers in
  scientific notation
• How to make an educated guess about a formula
  given only units

87
Powers-of-ten notation is a useful shorthand
system for writing numbers
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Google is a play on the word googol, which was
coined by Milton Sirotta, nephew of American
mathematician Edward Kasner, and was popularized
in the book, Mathematics and the Imagination by
Kasner and James Newman. It refers to the number
represented by the numeral 1 followed by 100
zeros. Google's use of the term reflects the
company's mission to organize the immense,
seemingly infinite amount of information
available on the web. http//www.google.com/corpo
rate/history.html
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Review of Math that is used in Astronomy

• Powers of 10 notation
• Powers of 10 prefixes (from nano to peta)
• How to "derive" rules for manipulating numbers in
  scientific notation
• How to make an educated guess about a formula
  given only units

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Common prefixes you must know
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Review of Math that is used in Astronomy

• Powers of 10 notation
• Powers of 10 words (from nano to peta)
• How to "derive" rules for manipulating numbers in
  scientific notation

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How to "derive" rules for manipulating numbers in
scientific notation

• You should know that when you multiply numbers in
  powers of ten notation you need to do something
  with the exponents. So make up problems you know
  how to answer
• 102 x 101 100x10 1000 103 1021
• 102 x 10-1 100x0.1 10 102(-1)
• Looks like adding the exponents should work.
• You should always remember that if you forget
  something, you may still know enough to reason
  things out.