ASTR 111

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Lecture 3

• ASTR 111 Section 002

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Eventually we want to be able to explain things
like this
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Observing Sessions
http//physics.gmu.edu/hgeller/observing.html Fal
l schedule to be posted
Research I Building

• 16" Dobsonian
• 2 Meade 12" SCTs
• 2 telescopes from Mason's original observatories

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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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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.
• 
  

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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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Quiz (aka Homework) Discussion

• The quiz counts as 10 of your Lecture grade
• Your lecture and lab are independent. You will
  receive a separate grade for lab and for lecture
  on your report card
• I will post the quiz within a few hours of the
  end of lecture, typically on Thursday.

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Quiz Question
Apogee farthest distance
Perigee nearest distance
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Where does the hand rule come from?
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R
S
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a is always in radians!
R
D
S
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Close enough!
S
D
R
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Close enough!
S
D
R
When will this approximation break down?
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Two points on screen separated by distance D
D
Your finger
a is angular size. D is linear size.
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Group question

• What is the ratio of the width of your index
  finger to the distance of your finger from your
  arm? Answer in degrees.

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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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• Accuracy all measurements or values are
  clustered around the true value (youll 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

Center of red dot is true value
No bias
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Group question

1. Can you have high accuracy and high bias?
2. Can you have low precision and high accuracy?
3. Suppose many people used the small angle formula
   to estimate the linear distance between two dots
   on the screen. They all sat in the same seat
   while making the measurements. Will there be a
   bias in their measurements?

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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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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)

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Distant Stars

• 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.

PA
Earth (July)
Earth (January)
Based on Lecture Tutorials for Introductory
Astronomy, Prather et al., pg 35
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Distant Stars

• 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.

1 parsec
PA
Earth (July)
Earth (January)
Based on Lecture Tutorials for Introductory
Astronomy, Prather et al., pg 35
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Group Question

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

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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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Thinking about rotation

• With parallax, we learned that the position of
  a near object relative to a distant object can
  change if the observer moves.
• With rotation, the time it takes for the
  position of a near object to change relative to a
  distant object can be different if the observer
  moves.

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Slippage Meaning

• When you skid a tire, there is slippage same
  part of tire always touches ground
• When you roll a tire, there is no slippage
  different parts of tire touch ground

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George B looking straight to the left (at a
distant object)
B
Table
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I can get him across the table by skidding or
slipping the 9 always touches the table. In
this case he always is looking to the left at the
distant object.
B
Table
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Instead of skidding or slipping, he can
roll. On a flat table, he will look at same
place in distance after 1 revolution or after
he has rolled the distance of his circumference
B
Table
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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.

B
A
(A is glued to the table)
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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.

One time
B
A
Two times
(A is glued to the table)
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With slippage
The nine on B always touches A
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Without slippage
Note George B only looks directly at George As
center one time right about here
B rolls on A, in the same way a tire rolls on
the ground.
B
B
A
B
B
George B is looking to the left again here!
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Question

• Rotate B around A without slippage (like a gear).
  How many times does B rotate?
• Same as when B was a quarter
• More than when B was a quarter
• Less than when B was a quarter

A
B
(A is glued to the table)
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Question

• Rotate B around A without slippage (like a gear).
  How many times does B rotate?
• Same as when B was a quarter
• More than when B was a quarter
• Less than when B was a quarter

A
B
(A is glued to the table)
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Sidereal Time Definition

• From text A sidereal day is the time between
  two successive upper meridian passages of the
  vernal equinox. By contrast, an apparent solar
  day is the time between two successive upper
  meridian crossings of the Sun.

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Or

• Sidereal Time star time
• Sidereal Day the length of time it takes for a
  star to repeat its position in the sky.
• Solar Time sun time
• Solar Day the length of time it takes the sun
  to repeat its position in the sky.

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Top view of classroom
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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Key

• A solar day is longer than a sidereal day
• This means it takes longer for the sun to repeat
  its position in the sky than a distant star

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Where is Cygnus 24 sidereal hours later?

1. West
2. East
3. Vertical

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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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Outline

1. Suggested Reading Note
2. Quiz Discussion
3. Angular Measurements Review
4. Precision, Accuracy, and Bias Review
5. Another Parallax Problem
6. Rotation
7. The Seasons

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Seasonal Stars

• Where do the names of the zodiac come from?
  During certain months, a constellation is
  (approximately) behind the sun
• Approximately, because precession has caused
  things to shift a bit.

http//historyday.crf-usa.org/1708/images/zodiac.j
pg
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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
4. None of the above
5. Primarily 2., but with a small contribution from
   1.

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Group question

• At summer solstice, when the sun is highest in
  the sky, who is closer to the sun
• A person on Tropic of Capricorn
• A person on Tropic of Cancer?

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Group question

• At summer solstice, when the sun is highest in
  the sky, who is closer to the sun
• A person on Tropic of Capricorn
• A person on Tropic of Cancer?

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Sun-Earth Distance

• December 147 million km
• June 152 million km
• September 150 million km
• March 149 million km

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Sun in afternoon.
Sun at noon.
Where do these rays end up for the sun in the
afternoon?
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Sun in afternoon.
Sun at noon.
Where do these rays end up for the sun in the
afternoon?
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The ecliptic is the imaginary plane that the
Earth moves on as it rotates around the sun
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The Celestial Sphere

• Sometimes it is useful to think of the stars and
  planets as moving along a sphere centered on Earth

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The two circled yellow arrows point to the same
line of latitude. The right arrow is
perpendicular to surface. The left arrow is less
than perpendicular to surface.