Download Document

Lecture 3
ASTR 111 – Section 002
Eventually we want to be
able to explain things like
this
Observing Sessions
http://physics.gmu.edu/~hgeller/observing.html
Fall schedule to be posted …
Research I Building
• 16" Dobsonian
• 2 Meade 12"
SCTs
• 2 telescopes
from Mason's
original
observatories
Outline
1.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
The Seasons
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.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
The Seasons
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.
Quiz Question
Apogee – farthest distance
Perigee – nearest distance
29.87 arc - mins 1 degree
 0.498 degrees
1
60 arc - mins
Where does the “hand rule” come
from?
R

S
Circumference  C  R (2 )
Segment  S  R( )
 is always in radians!
R

D
S
Circumference  C  R (2 )
Segment  S  R( )
Close enough!
D  S  R

D
S
R
Segment  S  R( )
Close enough!
D  S  R

D
S
R
When will this approximation
break down?
Two points on screen
separated by distance D

D
Your finger
 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.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
The Seasons
• 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
Center of
red dot is
true value
No bias
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.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
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)
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
(January)
Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35
Earth
(July)
Distant Stars
One parsec is defined as
the distance to a star that
has a parallax angle of
exactly 1 arcsecond.
PA
Earth
(January)
Based on Lecture Tutorials for Introductory Astronomy, Prather et al., pg 35
1 parsec
To describe the distances to
stars, astronomers use a
unit of length called the
parsec.
Earth
(July)
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.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
The Seasons
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
George B looking
straight to the left
(at a distant object)
B
Table
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
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
B
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)
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
One time
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”.
Two times
B
A
(A is glued
to the table)
With slippage
A
B
B
B
B
The nine on B
always touches
A
Without slippage
B
George B is
looking to the left
again here!
B
A
B
B “rolls” on A, in
the same way a
tire rolls on the
ground.
B
Note: George
B only looks
directly at
George A’s
center one time
right about
here
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 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.
Top view of
classroom
Someone in back of
room (distant object)
Stage
Student
Instructor
Sidereal Time =
star time
Solar Time =
sun time
At 1,
line
points
atLine
sun1
goes
and
through
distant
sun and
star
distant
star
• Sidereal
Time = star
time
• Solar Time
= sun time
Line
At 1,1
goes
line
through
points
sun
and1
atLine
sun
distant
goes
and
star
through
distant
sun and
star
distant
star
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?
1. Sidereal day
2. Solar day
At 1,
line
points
at sun
and
distant
star
At 2, 24
sidereal
hours
since 1,
line is
now
pointing at
distant
star only
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
Where is Cygnus 24 sidereal hours
later?
1. West
2. East
3. Vertical
Where is Cygnus 24 solar hours later?
1. West
2. East
3. Vertical
Outline
1.
2.
3.
4.
5.
6.
7.
Suggested Reading Note
Quiz Discussion
Angular Measurements Review
Precision, Accuracy, and Bias Review
Another Parallax Problem
Rotation
The Seasons
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.jpg
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.
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?
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?
Sun-Earth Distance
•
•
•
•
December: 147 million km
June: 152 million km
September: 150 million km
March: 149 million km
Sun in afternoon.
Sun at noon.
Where do these rays
end up for the sun in
the afternoon?
Sun in afternoon.
Sun at noon.
Where do these rays
end up for the sun in
the afternoon?
The ecliptic is the imaginary plane that the Earth
moves on as it rotates around the sun
The Celestial Sphere
• Sometimes it is useful to think of the stars
and planets as moving along a sphere
centered on Earth
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.