1 Lecture 3 ASTR 111 – Section 002 Eventually we want to be able to explain things like this Observing Sessions • 16" Dobsonian • 2 Meade 12" SCTs • 2 telescopes from Mason's original observatories http://physics.gmu.edu/~hgeller/observing.html Fall schedule to be posted … Research I Building 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
Transcript
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Lecture 3ASTR 111 – Section 002
Eventually we want to be able to explain things like this
Observing Sessions
• 16" Dobsonian• 2 Meade 12"
SCTs• 2 telescopes
from Mason's original observatories
http://physics.gmu.edu/~hgeller/observing.htmlFall schedule to be posted … Research I Building
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. 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.
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. The Seasons
Quiz 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.
Quiz Question
degrees mins-arc 60
degree 1
mins-arc 29.87 498.01=
Apogee – farthest distance
Perigee – nearest distance
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Where does the “hand rule” come from?
)(2RCnceCircumfere π==)R(SSegment α==
RSα
)(2RCnceCircumfere π==)R(SSegment α==
RSα D
α is always in radians!
R
Sα D
)R(SSegment α==
αRSD =≅
Close enough!
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R
Sα D
αRS D =≅
Close enough!
When will this approximation break down?
D
Your finger
Two points on screenseparated by distance D
α
α is angular size. D is linear size.
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.
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. The Seasons
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• 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 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?
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. The Seasons
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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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
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
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?
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. 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.
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
B
George B looking straight to the left(at a distant object)
Table
B
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.
Table
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B
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
Table
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)
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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
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
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.”
Or
Sidereal Time = star timeSidereal Day = the length of time it
takes for a star to repeat its position in the sky.
Solar Time = sun timeSolar Day = the length of time it takes
the sun to repeat its position in the sky.
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Someone in back of room (distant object)
StageStudent
Instructor
Top view of classroom
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
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
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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
1. West2. East3. Vertical
Where is Cygnus 24 sidereal hours later?
Where is Cygnus 24 solar hours later?
1. West2. East3. Vertical
1. West2. East3. Vertical
Outline
1. Suggested Reading Note2. Quiz Discussion3. Angular Measurements Review4. Precision, Accuracy, and Bias Review5. Another Parallax Problem6. Rotation7. 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.
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.
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
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.
