Transcript Lecture 1

Lecture 4
ASTR 111 – Section 002
Note
• I’ll post all slides after class
Terms
While you are waiting for class to start, try to define these terms
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Apogee/Perigee
Subtend
Parsec, light-year, AU
Parallax
Solar and Sidereal time
Small angle formula
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
Tuesday September 15th
• Class is canceled.
• Quiz is still due at 9 am on the 15th.
• I will be available via email.
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
Outline
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2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – review generally
The Moon in its orbit
Math review
Quiz (“homework”) Discussion
Bias
Many types. Two common ones are:
• Measurement bias or just “bias”
• Selection bias
Measurement Bias
True value (measured using good instrument)
Bias – measurements are not centered on true
value. (Usually due to mis-calibration of an
instrument.)
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.)
Questions
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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?
Questions
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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.
• “All of the students said
something was not clear.
Therefore the lecture was not
clear to the average student.”
• “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”.
Selection bias
Bias – measurements are not centered on true value
Everything clear responses
Something not clear responses
Average response
Selection Bias –
Average of selected measurements
are not centered on true value
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – review generally
The Moon in its orbit
Math Review – converting units and
scientific notation
View of
classroom from
above
Someone in back of
room (distant object)
Stage
Student
Instructor
Sidereal Time =
star time
Solar Time =
sun time
At 1,
line
points
atLine
sun1
goes
and
through
distant
sun and
star
distant
star
• Sidereal
Time = star
time
• Solar Time
= sun time
Line
At 1,1
goes
line
through
points
sun
and1
atLine
sun
distant
goes
and
star
through
distant
sun and
star
distant
star
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?
1. Sidereal day
2. Solar day
At 1,
line
points
at sun
and
distant
star
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?
1. Sidereal day
2. Solar day
by ~ 4 min.
At 1,
line
points
at sun
and
distant
star
At 2, 24
sidereal
hours
since 1,
line is
now
pointing at
distant
star only
Where is Cygnus 24 solar hours later?
1. West
2. East
3. Vertical
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.
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
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
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.
After 24 solar
hours, pole has
already passed
Cygnus
Draw these lines
and Earth after
24 solar hours
have elapsed
Cygnus
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – review generally
The Moon in its orbit
Math Review – converting units and
scientific notation
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.
That’s a Lie!
What causes the seasons?
2. Tilt of Earth with respect to the
ecliptic which causes
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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!)
• From http://www.dslreports.com/forum/remark,16822681
• Uses color saturation
http://en.wikipedia.org/wiki/Saturation_(color_theory)
The Moon in its orbit
Eventually we
want to be able to
explain …
A simple model
• Moon executes circular orbit
• Moon orbit is in Earth’s ecliptic plane
What is wrong with this picture?
Looking down on North Pole
Can you “see”
white ball if you
are at Equator?
Looking down on North Pole
NO! You
would need to
see through
Earth!
Can you “see” white ball
if you are at Equator?
Looking down on North Pole
If you walk around
along the equator,
where will you be able
to see the white ball?
Looking down on North Pole
NO!
Can you “see” white ball
if you are at Equator?
NO! You would need to
see through Earth!
Looking down on North Pole
Can you “see” white ball
if you are at Equator?
NO! You would need to
see through Earth!
NO!
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!
Looking down on North Pole
Closer to scale
• 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?
Sun is to the right.
1st quarter moon is first visible at noon.
B
Earth
C
View of Moon from Earth at one of the
positions (A-E) above.
Sun’s rays
A
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
E
lower-left-hand corner?
3. In the blank boxes below,
sketch how the Moon
would appear from Earth
from the four Moon
D
positions that you did not
choose for Question 2.
Label each box with a
letter.
B
Earth
C
View of Moon from Earth at one of the
positions (A-E) above.
Sun’s rays
A
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
E
lower-left-hand corner?
3. In the blank boxes below,
sketch how the Moon
would appear from Earth
from the four Moon
D
positions that you did not
choose for Question 2.
Label each box with a
letter.
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
E
lower-left-hand corner?
3. In the blank boxes below,
sketch how the Moon
would appear from Earth
from the four Moon
D
positions that you did not
choose for Question 2.
Label each box with a
letter.
A
B
Earth
C
View of Moon from Earth at one of the
positions (A-E) above.
A
C
B
E
Sun’s rays
D
F
H
Earth
I
View of Moon from Earth from one of the positions (F-I) above.
Sun’s rays
G
4. Shade in the part of the
Moon that is not
illuminated by the sun
when it is at positions F-I.
5. Which Moon position (FI) best corresponds with
the Moon phase shown in
the lower-left corner?
6. How much of the Moon’s
surface is illuminated by
the sun during this
phase?
7. How much of the Moon’s
illuminated surface is
visible from Earth for this
phase of the Moon?
F
F
H
Earth
50 %
0%
I
View of Moon from Earth from one of the positions (F-I) above.
Sun’s rays
G
4. Shade in the part of the
Moon that is not
illuminated by the sun
when it is at positions F-I.
5. Which Moon position (FI) best corresponds with
the Moon phase shown in
the lower-left corner?
6. How much of the Moon’s
surface is illuminated by
the sun during this
phase?
7. How much of the Moon’s
illuminated surface is
visible from Earth for this
phase of the Moon?
A simple model
• Moon executes circular orbit
• Moon orbit is in Earth’s ecliptic plane
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.
What does the Earth look
like from the Moon at
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Full Moon
New Moon
First Quarter
Third Quarter
What are 2 observations simple
model does not predict?
1.
2.
Eventually we
want to be able to
explain …
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
Eclipses occur only when the Sun and Moon
are both on the line of nodes
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
Solar eclipses can be
either total, partial, or
annular, depending
on the alignment of
the Sun,
Earth, and Moon
Eventually we
want to be able to
explain …
Lunar eclipses can be either total, partial, or
penumbral, depending on the alignment of
the Sun, Earth, and Moon
http://centralcoastseniors.files.wordpress.com/2008/04/lunar-eclipse-photo.jpg
Is this really the path of the moon in the sky?
http://zuserver2.star.ucl.ac.uk/~idh/apod/image/0405/tle_may2004_ayiomamitis.jpg
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
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. Can’t 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.
Lunar eclipses can be either total, partial, or
penumbral, depending on the alignment of
the Sun, Earth, and Moon
Solar eclipses can be
either total, partial, or
annular, depending
on the alignment of
the Sun,
Earth, and Moon
The Moon’s rotation always keeps the same face
toward the Earth due to synchronous rotation
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
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?
1. One year later?
2. 366.2425 days later?
3. One sidereal month later?
4. One synodic month later?
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?
1. One year later
2. 366.2425 days later
3. One sidereal month later
4. One synodic month later
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – review generally
The Moon in its orbit
Math review
Math Review
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
Review of Math that is used in
Astronomy
• Powers of 10 notation (1E8 =10^8 =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
Powers-of-ten notation is a useful shorthand
system for writing numbers
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/corporate/history.html]
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
Common prefixes you must know
Factor
Name
Symbol
(tera)
(billion)
1012
109
TeraGiga-
T
G
(million)
106
Mega-
M
(thousand)
103
kilo-
k
(hundredth) 10-2
centi-
c
(thousandth) 10-3
milli-
m
(millionth)
10-6
micro-

(billionth)
10-9
nano-
n
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
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 = 102+1
– 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.