Lecture 4

ASTR 111 – Section 002

Note

• I’ll post all slides after class

Terms

• Apogee/Perigee

• Subtend

• Parsec, light-year, AU

• Parallax

• Solar and Sidereal time

• Small angle formula

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

Terms

• Ecliptic

• Zenith

• Tropic of Cancer, Capricorn, Artic and Antarctic Circle

• Equinox, Solstice

• Zodiac

• Accuracy, Precision, and Bias

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

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

1. Quiz Discussion

2. Rotation – review generally

3. The Seasons – review generally

4. The Moon in its orbit

5. Math review

Quiz (“homework”) Discussion

Bias

Many types. Two common ones are:

• Measurement bias or just “bias”

• Selection bias

Measurement BiasTrue value (measured using good instrument)

Bias – measurements are not centered on true value. (Usually due to mis-calibration of an instrument.)

Measurement BiasTrue value (measured using tape measure)

Bias – measurements are not centered on true value. (Usually due to mis-calibration of an instrument.)

9 ft 10 ft 11 ft

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?

 

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. 

• “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

Average response

Something not clear responsesEverything clear responses

Selection Bias – Average of selected measurementsare not centered on true value

Bias – measurements are not centered on true value

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

Someone in back of room (distant object)

StageStudent

Instructor

View of classroom from above

Line 1 goes through sun and distant star

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

• Sidereal Time = star time

• Solar Time = sun time

Line 1 goes through sun and distant star

At 2, 24 sidereal hours since 1, line is now pointing at distant star only

At 1, line points at sun and distant star

At 3, 24

solar

hours

since 1,

line

points at

sun only

• Sidereal Time = star time

• Solar Time = sun time

• Which is longer?

1. Sidereal day

2. Solar day

At 2, 24 sidereal hours since 1, line is now pointing at distant star only

At 1, line points at sun and distant star

At 3, 24

solar

hours

since 1,

line

points at

sun 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

1. West

2. East

3. Vertical

1. West

2. East

3. Vertical(Over the Pacific Ocean)

Where is Cygnus 24 solar hours later?

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.

Cygnus

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

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 not quite aligned with sun

After 24 sidereal hours, pole is aligned with Cygnus again

Cygnus

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 is aligned with sun again

After 24 solar hours, pole has already passed Cygnus

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

What causes the seasons?

1. Distance of the sun from earth2. Tilt of Earth with respect to the

ecliptic3. Both 1. & 2.4. None of the above5. 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

• 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

Can you “see” white ball if you are at Equator?

NO! You would need to see through Earth!

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

Can you “see” white ball if you are at Equator? NO! You would need to see through Earth!

NO!

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

Can you “see” white ball if you are at Equator? NO! You would need to see through Earth!

Yes!

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.

A

B

C

D

E

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.

Earth

View of Moon from Earth at one of thepositions (A-E) above.

Sun

’s r

ays

A

B

C

D

E

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.

Earth

View of Moon from Earth at one of thepositions (A-E) above.

Sun

’s r

ays

A

B

C

D

E

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.

Earth

View of Moon from Earth at one of thepositions (A-E) above.

Sun

’s r

ays

D

A

C

B

E

G

H

I

F

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 (F-I) 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?

Earth

View of Moon from Earth from one of the positions (F-I) above.

Sun

’s r

ays

G

H

I

F

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 (F-I) 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?

Earth

View of Moon from Earth from one of the positions (F-I) above.

Sun

’s r

aysF

50 %

0 %

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

• 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 Moonare 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, orannular, 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, orpenumbral, depending on the alignment of

the Sun, Earth, and Moon

http://centralcoastseniors.files.wordpress.com/2008/04/lunar-eclipse-photo.jpgIs 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, orpenumbral, depending on the alignment of

the Sun, Earth, and Moon

Solar eclipses can be either total, partial, orannular, 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

• 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.

Time and the Moon

• 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. Quiz Discussion

2. Rotation – review generally

3. The Seasons – review generally

4. The Moon in its orbit

5. 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) 1012

(billion) 109

Tera-Giga-

TG

(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.