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Lecture 2ASTR 111 – Section 002

Introductory Astronomy:Solar System

Dr. Weigel

Outline1. Suggested Reading2. Quiz Discussion3. Precision, Accuracy, and Bias4. Angular Measurements Review5. Finish Parallax Problem6. Ancient Astronomy7. Rotation8. The Seasons9. Math Review

Suggested Reading

• In general, the quiz and exams will be based on material that I cover in class. Almost all of this material is also covered in the book.

• Ideally you should review notes and read suggested sections in book and then take quiz.

• Suggested Reading for this quiz: Chapter 2.

Quiz Discussion

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Quiz question 5

• The question about how your angular measurements would change has caused some confusion.

• I will drop this question.

Quiz question 9

degrees mins-arc 60

degree 1

mins-arc 29.87 498.01=

Precision, Accuracy, and Bias Angular Measurements Result

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1. What is the angular distance between points A and B on this slide (In degrees and arcminutes). Answer depends on where you are sitting. To get arcminutes, take angle in degrees and multiply by 60.

2. Predict what will happen if you made your measurement in two different parts of the room. Relative to the middle of the room: (1) as you move to the front of the room, angular distance should increase (2) as you move to the walls, angular distance should decrease.

A B

• This symbol means that this is not something I will put on the exam.

3. Next week you sit in the same chair but weigh 30 pounds less. Will your (angular) measurements change? If you used the width of your hand or the width of your finger to measure, you would expect your angular distance to increase (skinnier hand and finger). If you used the distance between your knuckles on your finger, you would not expect a change (if you lose weight, the distance between your knuckles is not expected to change because your bone size should not change).

4. Do you think there will be a relationship between a persons height and the angle they measure? A shorter person will have smaller fingers -> larger angular measurements. A shorter person will have shorter arms -> smaller angular measurements. (Try to simulate this with your hand and arm!) So the answer is that they should not have different angular measurements.

A B Where does the “hand rule” come from?

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D

R

αR D ≅

)π(2 R nceCircumfere =

S

αR S =

RSα

Small Angle Formula

D

R

αR D ≅

inches) 30inches)/ (0.5D/R (=≅α

degrees radians degress

1radians 0.0167 95.0180

==π

α

Width of finger Length of arm

See also Box 1-1 of text

Parallax

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Group Question

• If you close one eye and hold out your index finger, your finger appears to cover an object. If you switch eyes, your finger no longer covers that object. With a diagram, explain why.

• How does what you observe change with the distance of your arm from your face?

Group question

• How many light-years are in 10 parsecs?• How many light-years could a human

travel in a space craft?• Which is larger, a parsec or an AU?• Why do you think we have two units, the

parsec and the light year, when they are so close to each other? (1 parsec = 3.26 light-years)

Ancient Astronomy

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Group Question

• List ways in which knowledge of astronomical observations could be of use to the ancient people.

Rotation

Group Question• Rotate B around A with

slippage. How many times does George B look straight to the left?

– With slippage, the 9 on the top quarter always touches the bottom quarter

• Rotate B around A without slippage (like a gear). How many times does George B look straight to the left?

– Without slippage, first the 9 in the 1993 on the top quarter touches the bottom quarter, then 1 then the “In God We Trust”.

A

B

(A is glued to the table)

Answer

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Conclusion

• Break the rotation of B into two parts:– rotation about A (the central object)– rotation about its own axis

Question• Rotate B around A without

slippage (like a gear). How many times does B rotate?

1. Same as when B was a quarter

2. More than when B was a quarter

3. Less than when B was a quarter

(A is glued to the table)

A

B

B

• Rotate E every 24 hours. E looks straight to the left every 24 hours.

E

B

• Rotate E every 24 hours. E looks straight to the left every 24 hours.

• Now rotate E around S every 365 days. E now looks to the left 366 times by the time it gets back to where it started.

E

S

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Or

Sidereal Time = star time = the length of time it takes for a star to repeat its position. Sidereal Day =

Solar Time = sun time = the length of time it takes the sun to repeat its position. Solar Day =

Important

• Distant objects vs near objects– When you move, distant objects appear to

stay in the same place• Break rotation into two parts

– Rotation about a central object– Rotation about its own axis

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 siderealhours since 1, line is now pointing at distant star only

At 1, line points at sun and distant star

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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 day2. 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

Verify with software

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Where is Cygnus 24 solar hours later?

1. West2. East3. Vertical

Seasonal Stars

• Where do the names of the zodiac come from?

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The Seasons What causes the seasons?

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

ecliptic3. Both4. None of the above5. Primarily 2., but with a small

contribution from 1.

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The Celestial Sphere

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• See Seasons Lecture Tutorial at end

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Math Review 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]

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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

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- μ

(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.

Part I: Earth-Sun Distance

Seasons

Drawing not to scale

91

Listed below are the distances, in kilometers(km), between the Sun and Earth for fourmonths of the year. The drawing at the rightshows four different locations of Earth duringits orbit around the Sun. Note that for each

location drawn, Earth is correctly shown withits rotational axis tilted at an angle of 23.5°.

Month Earth-Sun Distance

December

147.2 million km

June

152.0 million km

September

150.2 million km

March

149.0 million km

/////////III

\\"\\\ \ ,,,,

1) Using the information listed above, does Earth stay the same distance from the Sunthroughout the year? If not, what month(s) and during which season (for the NorthernHemisphere) is Earth closest to the Sun? Farthest from the Sun?

2) Would you say the temperature stays approximately the same every month of the year atyour location?

3) Are the seasons (summer or winter) the same in the Northern and SouthernHemispheres at the same time? When it is summer in the Northern Hemisphere, whatseason is it in the Southern Hemisphere?

4) Consider the following discussion between two students about the cause of the seasons.

Student 1: I know that it's hotter in the summer and colder in the winter, so we mustbe closer to the Sun in the summer than in the winter.

Student 2: I disagree. Although the distance between Earth and the Sun does changethroughout the year, I don't believe that the seasons and changes inEarth's surface temperature are caused by the distance between the Sunand Earth. If the seasons were due to the Sun-Earth distance, then both

hemispheres of Earth would have the same seasons at the same time.

Do you agree or disagree with either or both of the students? Explain your reasoning.

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LECTURE TUTORIALS FOR INTRODUCTORY ASTRONOMY

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92 Seasons

At different times of the year, locations in the Northern Hemisphere can be a few thousandkilometers closer to (or farther from) the Sun than locations that are at the same latitude inthe Southern Hemisphere (as shown in the drawing below). However, the distance betweenEarth and the Sun is, on average, about 150 million kilometers.

(

Southern Hemisphere Location/

Drawing not to scale

Sun

\\

Northern Hemisphere Location -------.. \

5) Do you think these differences in distance between locations at the same latitudein the Northern and Southern Hemispheres are the cause of the seasons? Explain yourreasoning.

(6) Consider the following discussion between two students about the cause of the seasons.

Student 1: I get it. So since Earth is tilted, there are times when the northern part ofEarth is closer to the Sun than the southern part. So the north has summerand the south has winter. And then later the south is tilted toward the Sun

and gets closer and has summer.Student 2: I disagree. Although the tilt does bring one hemisphere closer to the Sun,

the difference in distance between the northern half and southern half of

Earth is really small compared to how far away Earth is from the Sun.

Do you agree or disagree with either or both of the students? Explain your reasoning.

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LECTURE TUTORIALS FOR INTRODUCTORY ASTRONOMY

SECOND EDITION

Part II: Direct Light and Tilt

Seasons 93

Consider the picture above in which two spotlights (#1 and #2) are shown casting light ontoa screen. Note: Each spotlight gives off the same total amount of light.

7) Which of the two lighted areas (the one created by Spotlight #1 or #2) would appearbrighter?

8) Which of the two lighted areas is smaller?

9) Which of the two lighted areas receives more direct light (amount of energy on eachunit of area) from the spotlight?

10) If a thermometer were placed in each of the lighted areas, which one would read thehigher temperature?

11) Which of the two positions would be similar to the way the sunlight would shine on theSouthern Hemisphere of Earth during winter? Explain your reasoning.

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LECTURE TUTORIALS FOR INTRODUCTORY ASTRONOMY

SECOND EDITION

94 Seasons

Consider the picture below illustrating three different regions of Earth (the NorthernHemisphere, the Southern Hemisphere, and the equatorial region) at two different times ofthe year, six months apart.

\\\

\\\

< Sunlight

-E

?Sun

Sunlight >~

.::".,

\\\

\\\

Note: this drawing is not to scale. In fact you could fit more than 11,000 Earths between the Sun and Earth.

12) Which location( s) (A-F) correspond( s) with summer in the Northern Hemisphere?Explain your reasoning.

13) Which location(s) (A-F) correspond(s) with winter in the Southern Hemisphere? Explainyour reasoning.

(

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Publishing as Pearson Addison-Wesley.

LECTURE TUTORIALS FOR INTRODUCTORY ASTRONOMY

SECOND EDITION