Lecture 2ASTR 111 – Section 002

Introductory Astronomy:Solar System

Dr. Weigel

http://www.astro.ljmu.ac.uk/courses/phys134/magcol.html

Reading for this week

– The reading for this week is Chapter 1 (all) and Chapter 2 (sections 2.1-2.2 only)

– The quiz will cover this reading and the topics covered in this week’s lectures

– The quiz will be available on BlackBoard at 10:15 am … noon today.

A note on lecture notes

Outline

• Angular Measurements Review• Accuracy, Precision, and Bias• The Scientific Method• Astronomical Distances• Ancient Astronomy

Angular Measurements Result

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

3. Do you think there will be a relationship between a person’s 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!) Based on this, the answer is that we don’t expect them to have different angular measurements.

A B

4. 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 the angular distance you measured to increase (skinnier hand and finger).

• If you used the distance between your knuckles on your finger, you would not expect a change in your measurement (if you lose weight, the distance between your knuckles is not expected to change because your bone size should not change).

A B

http://antwrp.gsfc.nasa.gov/apod/ap071025.html

Outline

1. Angular Measurements2. Accuracy, Precision, and Bias3. The Scientific Method4. Astronomical Distances5. Ancient Astronomy

Precision, Accuracy, and Bias

• Whenever you take measurements, you should account for them

• Fundamental terms that you must understand when interpreting measurements

• Not covered in your book

Accuracy vs. PrecisionTarget is redShots are black

Accuracy vs. PrecisionTarget is redShots are black

High precisionLow accuracy

High precisionHigh accuracy

Accuracy vs Precision

Mnemonic: You’ll get an A for Accuracy

BiasTarget is redShots are black

• The left target shows bias – the measurements were made with high precision, but the were consistently “off” in the same direction.

Summary• Accuracy – all measurements or

values are clustered around the true value (you’ll get an A for accuracy, because you are on the true value)

• Precision – all measurements are clustered but are not centered on true value

• Bias – measurements are not centered on true value

No bias

Center of red dot is true value

Group work (~ 4 minutes)

1. Draw a diagram like the ones on the previous slide that show

1. Low precision and high bias2. High accuracy and very low precision

2. On a piece of paper, write down • Possible causes of low accuracy – be

specific! (Don’t say “human error”)• Possible causes of bias – be specific!associated with your angular measurements

Question 1.

Question 1.Impossible to have both High accuracy and very low precision.

But you can have moderate accuracy and moderate precision

Question 2.

• Low accuracy because of moving hand and difficulty in lining up dots exactly

• Low precision because you are using scale that increments in degrees

• Bias could happen if your hand (or everyone’s hand in group) was exceptionally large. Then everyone would measure angle to be smaller than it really is.

• Which diagram best represents the statement: “Preliminary polling results indicated that Obama won Virginia by a landslide because the preliminary poll results were all from Northern Virginia”.

Group work (~ 3 minutes)

A B C D

• Which diagram best represents the statement: “Preliminary polling results indicated that Obama won Virginia by a landslide because the preliminary poll results were all from Northern Virginia”.

Group work (~ 3 minutes)

A B C D

Outline

1. Angular Measurements2. Accuracy, Precision, and Bias3. The Scientific Method4. Astronomical Distances5. Ancient Astronomy

The Scientific Method

What is Science?

1) A set of facts2) Something that professional scientists

do3) The underlying Truth about the

Universe4) The collection of data and formation of

a hypothesis5) None of the above

What is Science?1) A set of facts?

• We are constantly making new discoveries and collecting new data

• Technology and experiments are changing

• Old Theories are replaced by new Theories

• Scientific ``Facts''

What is Science?2) A thing that professional scientists do?

• What is a scientist?• Do you need a PhD?• Amateur Scientists play an important role

in discovery• Being scientific DOES NOT required a

Union Card

What is Science?3) The underlying Truth about the Universe?

Capitalization, too much? Suspect a Scientist should be.

What is Science?4) The collection of data and formation of a hypothesis

• No, but getting closer

What is Science?5) The collection of data and formation of a hypothesis

• None of the above

What is Science?

• A system of knowledge covering general truths or the operation of general laws especially as obtained and tested through the scientific method

http://www.merriam-webster.com/dictionary/science

The Scientific Methodthe process

• characterization of existing data • formulation of a hypothesis• formulation of a predictive test• experimental testing, (important: error

elimination and characterization)• report and peer review• validate or revise hypothesis

Cat Scientist

http://shakespearessister.blogspot.com/2009/08/cat-experiments.html

Comment on reddit.com• Ask a Question -Is what i'm seeing my reflection

or another cat? • Do Background Research - Go to other mirror to

determine what true reflection looks like• Construct a Hypothesis - The other cat is my

reflection. • Test Your Hypothesis by Doing an Experiment -

move myself. see if reflection duplicates my motions as in the mirror.

• Analyze Your Data and Draw a Conclusion - I am seeing another cat

• Communicate Your Results - have my master post on reddit

http://www.reddit.com/r/science/comments/9e1vh/olivia_the_cat_doublechecks_if_similar_cat_beyond/

Important

• Science is a process

• Humans have concluded that this is the best process by which to explain observations

Outline

1. Angular Measurements2. Accuracy, Precision, and Bias3. The Scientific Method4. Astronomical Distances5. Ancient Astronomy

Parallax

Parallax

Parallax

10 20 30 40 50 60 70 80 90

Parallax

• When the apparent position of an object (numbers on speedometer) changes because of the change in position of the observer (driver’s seat to passenger’s seat).

http://www.astro.ljmu.ac.uk/courses/phys134/magcol.html

Another example

The Parsec

Astronomical distances are never measured in Car hours, dotsecs, and Moon Units

• Car Hour (ch)– the distance a car can travel in one hour at a speed of

about 60 miles/hour. How far is Baltimore? About an hour.

• Car Year (cy)– the distance a car can travel in one year at a speed of

about 60 miles/hour• dotsec (ds)

– the distance at which the two dots on the screen subtend an angle of 1 arcsec

• Moon Unit (MU)– One Moon Unit is the average distance between

Earth and the Moon

A distanceA time

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

Observer’s view of Sun and Earth from outer planet

SunEarth

“Observer’s view

Gods-eye view -Looking down onSun and Earth

Observer’s view

Gods-eye view

Group Problem• Form groups of exactly 4• Optimal configuration is two

students in one row and two students in another row

No

Yes

1. Imagine that you are looking at the stars from Earth in January. Use a straightedge to draw a line from Earth in January, through the nearby star (Star A), out to the Distant Stars. Which of the distant stars would appear closest to Star A in your night sky in January. Circle this distant star and label it Jan.

2. Repeat Question 1 for July and label the distant star “July”.

3. In the box below, the same distant stars are shown as you would see them in the night sky. Draw a small x to indicate the position of Star A as seen in January and label it “Star A Jan.”

4. In the same box, draw another x to indicate the position of Star A as seen in July and label it “Star A July”.

5. Describe how Star A would appear to move among the distant stars as Earth orbits the Sun counterclockwise from January of one year, through July, to January of the following year.

6. Consider two stars (C and D) that both exhibit parallax. If Star C appears to move back and forth by a greater amount than Star D, which star do you think is actually closer to you? If you’re not sure, just make a guess. We’ll return to this question later in this activity. Earth

(January)Earth(July)

Nearby Star(Star A)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

Distant Stars

1 AU

1. and 2.

Earth(January)

Earth(July)

Nearby Star(Star A)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

Distant Stars

1 AU

Star A JanStar A July

Earth(January)

Earth(July)

Nearby Star(Star A)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

1 AU

July

Jan

Star A July Star A January

3. And 4.

Earth(January)

Earth(July)

Nearby Star(Star A)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

1 AU

July

Jan

5. From January till July, star A appears to move to the left relative to the distant stars. From July till January, star A appears to move to the right.

Star A July Star A January

Earth(January)

Earth(July)

Nearby Star(Star A)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

1 AU

July

Jan

Star C is closer

6.Consider two stars (C and D) that both exhibit parallax. If Star C appears to move back and forth by a greater amount than Star D, which star do you think is actually closer to you? If you’re not sure, just make a guess.

Earth(January)

Earth(July)

Star C

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

1 AU

July

Jan

Star C is closer

6.Consider two stars (C and D) that both exhibit parallax. If Star C appears to move back and forth by a greater amount than Star D, which star do you think is actually closer to you? If you’re not sure, just make a guess.

Earth(January)

Earth(July)

(Star D)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

1 AU

Star C is closer.

6.Consider two stars (C and D) that both exhibit parallax. If Star C appears to move back and forth by a greater amount than Star D, which star do you think is actually closer to you? If you’re not sure, just make a guess.

Group Question

1. 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.

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

Finger

Left eye Right eye

1. 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. See right

2. How does what you observe change with the distance of your arm from your face? As you move finger closer, distance object seems to “jump”.

Top of head

Group question

1. How many light-years are in 10 parsecs?2. How many light-years could a human

travel in a space craft?3. Which is larger, a parsec or an AU?4. 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)

Group question

1. How many light-years are in 10 parsecs?

years-light parsec 1

year-light x1

parsec 6.3226.310

Group question

2. How many light-years could a human travel in a space craft?

• Somewhere between 0 and 100 light-years, if the were traveling at the speed of light. (Human lifetime)

• A light-year is the distance light travels in one year.

Group question

3. Which is larger, a parsec or an AU?• A parsec is much larger

Group question

4. 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)

• Light-year is useful for expressing distances when we want to know how long light will take to move across that distance

• Parsec is useful when we are looking at angular sizes – An object that subtends 1 arc-second in the sky will be a distance of 1 parsec.

To describe the distances to stars, astronomers use a unit of length called the parsec. One parsec is defined as the distance to a star that has a parallax angle of exactly 1 arcsecond.

Earth(January)

Earth(July)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

Distant Stars

PA

• If the parallax angle for Star A (PA) is 1 arcsecond, what is the distance from the Sun to Star A? (Hint use parsec as your unit of distance.) Label this distance on the diagram.

• Is a parsec a unit of length or a unit of angle? (It can’t be both.)

• As Star A moves outward, what happens to its parallax angle?

To describe the distances to stars, astronomers use a unit of length called the parsec.

One parsec is defined as the distance to a star that has a parallax angle of exactly 1 arcsecond.

Earth(January)

Earth(July)

Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35

Distant Stars

PA

1 pa

rsec

• If the parallax angle for Star A (PA) is 1 arcsecond, what is the distance from the Sun to Star A? (Hint us parsec as your unit of distance.) Label this distance on the diagram.

• Is a parsec a unit of length or a unit of angle? (It can’t be both.)

• As Star A moves outward, what happens to its parallax angle?

1 parsec

Length

Decreases

Outline

1. Angular Measurements2. Accuracy, Precision, and Bias3. The Scientific Method4. Astronomical Distances5. Ancient Astronomy

Ancient Astronomy

http://www.google.com/sky/

Naked-eye astronomy had an important place in ancient civilizations

• Positional astronomy– the study of the positions of objects in the sky

and how these positions change• Naked-eye astronomy

– the sort that requires no equipment but human vision

• Extends far back in time– British Isles Stonehenge– Native American Medicine Wheel– Aztec, Mayan and Incan temples– Egyptian pyramids

Stonehenge

http://archaeoastronomy.wordpress.com/2005/06/15/stonehenge-astronomy-ii-solar-alignments/See also http://news.bbc.co.uk/2/hi/uk_news/england/wiltshire/7465235.stm

Aztec, Mayan and Incan temples

Eighty-eight constellations cover the entire sky

• Ancient peoples looked at the stars and imagined groupings made pictures in the sky

• We still refer to many of these groupings

• Astronomers call them constellations (from the Latin for “group of stars”)

Modern Constellations• On modern star charts,

the entire sky is divided into 88 regions

• Each is a constellation• Most stars in a

constellation are nowhere near one another

• They only appear to be close together because they are in nearly the same direction as seen from Earth