Transcript Document

Lecture 3
ASTR 111 – Section 002
Terms
•
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•
•
•
•
•
•
•
•
Apogee/Perigee
Subtend
Parsec, light-year, AU
Parallax
Solar and Sidereal time
Small angle formula
Ecliptic
Zenith
Tropic of Cancer, Capricorn, Artic and Antarctic Circle
Equinox, Solstice
Zodiac
Notes on Lecture Notes
• Sent out Tuesday afternoon/evening
• I suggest that you print them out and bring
them to class
• I will also post PowerPoints
• If you have problems with the file, email
me!
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – finish lecture tutorial
The Moon in its orbit
Math Review – converting units and
scientific notation
#3
• In class, we estimated the angular
separation of two points on the screen that
were separated by 10 feet. Suppose that
these two points were separated by 1 AU.
How far away from the screen would you
need to walk so that the dots appeared to
subtend 1 arc-second?
A
B
Gods-eye view
Observer’s view
“
#4
• How many light-years are in 10 parsecs?
10 parsec 3.26 light - year
x
 32.6 light - years
1
1parsec
• How many parsecs are in 5 light-years?
5 light - year
1 parsec
x
 1.3 parsec
1
3.26 light - year
Units conversion
• Start with a relationship like
– 1 degree = 60 arcminutes
– To convert from degrees to arcminutes, set up
a ratio so the unit you want to get rid of
cancels
– Example: how many arcminutes is 0.5
degrees?
0.5 degree 60 arcminutes

 30 arcminutes
1
1 degree
Units conversion
• Start with a relationship like
– 1 parsec = 3.26 light-years
– To convert from parsec to light years, set up a
ratio so the unit you want to get rid of cancels
– Example: How many light-years are in 5
parsecs?
#6
• In the image, suppose that a star in the
constellation Cygnus appears exactly at
an observer's zenith (the dotted line) at 8
pm local time. After 24 solar hours have
passed, where would the constellation
appear to be?
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – finish lecture tutorial
The Moon in its orbit
Math Review – converting units and
scientific notation
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.
Thinking about rotation
In the last lecture I had you do an
experiment with a quarter to illustrate this
point:
When one object “B” rotates about another
object, the number of times it rotates with
respect to something in the distance
depends on if “B” is rotating on its axis.
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
Summary
• When the coin slipped across the table, it
did not rotate at all. When a coin slipped
around another coin, it rotated once with
respect to the “distance”.
• When a coin rolled across a table the
distance of its circumference, it rotated
once. When it rolled the same distance,
but around another coin, it rotated twice
with respect to the “distance”.
What to know
• When thinking about rotation, you need to
account for rotation about its own axis and
rotation about another object.
• The number of times you see something in
the distance will be different than the
number of times you look at the object that
you are rotating around.
Top view of
classroom
Someone in back of
room (distant object)
Stage
Student
Instructor
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.
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
• Sidereal
Time = star
time
• Solar Time
= sun time
• Which is
longer?
1. Sidereal day
2. Solar day
by ~ 4 min.
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
Which way is Andromeda at 8:00 pm
local time for the person in California?
1. West
2. East
3. Vertical
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.
Quiz Discussion
Rotation – review generally
The Seasons – finish lecture tutorial
The Moon in its orbit
Math Review – converting units and
scientific notation
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.
What causes the seasons?
1. Distance of the sun from earth
2. Tilt of Earth with respect to the
ecliptic which causes
•
•
Change in length of time sun is visible
Change in height of sun in sky
3. Both
4. None of the above
5. Primarily 2., but with a small contribution
from 1.
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
Important! The angle of the light to the ground.
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.
Thinking about light
• It is often useful to think of photons as very
small particles.
• When I point a flashlight at you, you are
getting hit with a bunch of little pellets.
• Suppose you were hit by 10 pellets in an
area the size of a quarter.
• How does this compare with getting hit
with 10 pellets over an area the size of a
book?
• See Seasons Lecture Tutorial at end
A
D
F
Outline
1.
2.
3.
4.
5.
Quiz Discussion
Rotation – review generally
The Seasons – finish lecture tutorial
The Moon in its orbit
Math Review – converting units and
scientific notation
Eventually we
want to be able to
explain …
A simple model
• Moon executes circular orbit
• Moon orbit is in Earth’s ecliptic plane
What is wrong with this picture?
B
Earth
C
View of Moon from Earth at one of the
positions (A-E) above.
Sun’s rays
A
1. Fill in the dark and light
parts of the Moon for A-D
(from this perspective)
2. From the perspective of
someone on Earth what
position of A-E best fits
the Moon view in the
E
lower-left-hand corner?
3. In the blank boxes below,
sketch how the Moon
would appear from Earth
from the four Moon
D
positions that you did not
choose for Question 2.
Label each box with a
letter.
F
H
Earth
I
View of Moon from Earth from one of the positions (F-I) above.
Sun’s rays
G
4. Shade in the part of the
Moon that is not
illuminated by the sun
when it is at positions F-I.
5. Which Moon position (FI) best corresponds with
the Moon phase shown in
the lower-left corner?
6. How much of the Moon’s
surface is illuminated by
the sun during this
phase?
7. How much of the Moon’s
illuminated surface is
visible from Earth for this
phase of the Moon?
Model can explain the phases
of the Moon
• The phases of the Moon
occur because light from
the Moon is actually
reflected sunlight
• As the relative positions
of the Earth, the Moon,
and the Sun change, we
see more or less of the
illuminated half of the
Moon.
What does the Earth look
like from the Moon at
•
•
•
•
Full Moon
New Moon
First Quarter
Third Quarter
What are 2 observations simple
model does not predict?
1.
2.
What are 2 observations simple
model does not predict?
1. Why there are not eclipses every month
2. Why there are “annular” and “total”
eclipses
Eclipses occur only when the Sun and Moon
are both on the line of nodes
What are 2 observations simple
model does not predict?
1. Why there are not eclipses every month
2. Why there are “annular” and “total” eclipses
of the sun
Solar eclipses can be
either total, partial, or
annular, depending
on the alignment of
the Sun,
Earth, and Moon
Lunar eclipses can be either total, partial, or
penumbral, depending on the alignment of
the Sun, Earth, and Moon
Question
• If you were looking at Earth from the side
of the Moon that faces Earth, what would
you see during
– A total lunar eclipse?
– A total solar eclipse?
The Moon’s rotation always keeps the same face
toward the Earth due to synchronous rotation
Time and the Moon
• Two types of months are used in
describing the motion of the Moon.
• With respect to the stars, the Moon
completes one orbit around the Earth in a
sidereal month, averaging 27.32 days.
• The Moon completes one cycle of phases
(one orbit around the Earth with respect to
the Sun) in a synodic month, averaging
29.53 days.
•
•
•
•
sidereal month, averaging 27.32 days.
sidereal day – 23 hr 56 min
synodic (lunar) month, averaging 29.53 days.
solar day – 24 hr
Question
• On a certain date the Moon is in the
direction of the constellation Gemini
as seen from Earth. When will the
Moon next be in the direction of
Gemini?
1. One year later?
2. 366.2425 days later?
3. One sidereal month later?
4. One synodic month later?