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Agenda
LAB (Inst. Dickinson):
Lab Constellation/Star Quiz
Angular Measurement Lab
LECTURE (Prof. Canales):
Discuss Formal Lab Report on FOV- Due Tues 2/15
LAB PREP:
• Unit Conversion
• Review Dec. & RA and degree, minute second (Norton?)
• Arc length formula and small angle formula – do fill in the blanks for Angular
Measurement Lab.
LECTURE:
• Scaling, Distance (parsec) Magnitudes (apparent and absolute)
Tutorial: motion CS (3-4)
LAB (Inst. Dickinson)
Planetarium FYI
Intro Moon Project & Journal
Labs- Norton Coordinates and
Measuring Angular Size/Distance
HOW BIG IS IT? WHERE DO I LOOK?
RADIAN - SEC CONVERSION
Angle in degress = Angle in radians X 57.29
Angle in arcsec = Angle in radians X 206,265
Unit Conversion (if time)
Week 5
Motion of C.S., Scaling, Distances
& Magnitude of Stars
Earth’s rotation causes
the Sun, Planets, Moon
and stars to appear to
move (nightly/daily) when
viewed from Earth
Will the North Celestial Pole
(Earth’s Northern Axis)
always point toward Polaris?
Currently it is within 1 degree of Polaris, but it will
take thousands of years for our North Star to
change to another star.
Daily Motion of the Stars
(Sun, Moon, Stars & Planets)
• Do the human animation, neglect tilt of
Earth! (blank paper with cardinal
directions)
• Do stars (etc) rise above your Eastern
or Western horizon?
• Does the moon rise later, earlier or at
the same time each day?
Nightly Motion of the Stars
Do we view the
C.S. (Celestial
Sphere) from
above as this
top arrow
indicates?
Celestial Sphere Rotation
Star B
2
Star A
1
2
Celestial Sphere
Celestial Sphere
3
1
4
3
Does the C.S.
appear to rotate
CW or CCW as
viewed by
Earthlings?
4
Celestial Sphere
Rotation
Figure 2
Horizon
Nightly Motion (diurnal motion) of
the Stars (in Northern Hemisphere)
• For stars (is similar for the Sun,
Moon and planets) they first rise near
the eastern horizon, move upward
and toward the south, and then move
down and set near the western
horizon.
Nightly Motion of the Stars
• Looking North: Stars
appear to move
counter-clockwise
around the stationary
North Star (Polaris) –
we call these
circumpolar stars.
Looking North: Circumpolar
Stars
– Circumpolar stars seem to move counter-clockwise
around the stationary North Star.
– These constellations and stars are visible any night
of the year in the NORTHERN sky because they
never rise or set!
– Examples: Ursa Major, Ursa Minor, Draco,
Cepheus, and Cassiopeia
What happens over time in the
Northern Sky?
What
direction is
the camera
facing in
this picture
(HINT: see
Tutorial
book or
next slide)
Nightly Motion of the Stars
Do we view the
C.S. (Celestial
Sphere) from
above as this
top arrow
indicates?
Celestial Sphere Rotation
Star B
2
Star A
1
2
Celestial Sphere
Celestial Sphere
3
1
4
3
Does the C.S.
appear to rotate
CW or CCW as
viewed by
Earthlings?
4
Celestial Sphere
Rotation
Figure 2
Horizon
Tutorial: Motion – pg. 3-4
(SKIP pg. 5 & 6, but show SUN )
• Work with a partner!
• Read the instructions and questions carefully.
• Discuss the concepts and your answers with
one another.
• Come to a consensus answer you both agree
on.
• If you get stuck or are not sure of your answer,
ask another group.
• If you get really stuck or don’t understand what
the Lecture Tutorial is asking, ask your
Professor to help.
Celestial Sphere
Rotation

Path of
Star B 1
Celestial
Sphere
Path of
Star A
4
North Star
2


North
Star
3
Earth’s
Equator
Horizon
6 PM

North
Celestial
Sphere
Rotation
At what time will Star B be located high in the
Northwestern sky?
A. 4:00 am
B. 10:00 am
C. 2:00 pm
D. 7:00 pm
E. 1:00 am
Celestial Sphere
Rotation

Path of
Star B 1
Celestial
Sphere
Path of
Star A
4
North Star
2


North
Star
3
Earth’s
Equator
Horizon
6 PM

North
Celestial
Sphere
Rotation
If you were able to see the motion of star B at
Noon, over a period of 15 minutes what direction
would it appear to move?
A. west (to the left)
B. east (to the right)
C. South (out of the page)
D. away from the horizon (up)
E. toward the horizon (down) & east
If you could see stars during the day, the drawing
below shows what the sky would look like at noon on
a given day. The Sun is near the stars of the
constellation Gemini. Near which constellation would
you have expected the Sun to be located at sunrise
on this day? Sun
A. Leo
Gemini
B. Cancer
Taurus
Cancer
C. Gemini
Leo
D. Taurus
Aries
 East
West 
South
E. Aries
0/0
Thousands of km
Astronomical Unit
A few to about 1,000 Light-years
10,000 to 100,000 Light-years
Millions of Light-years
Billions of Light-years
Parsec = 3.26 light years
Do all stars appear
the same? How are
they different?
Which one looks
the coolest?
Hottest?
Are they all the
same brightness?
Do they all look the
same size?
• the brightest star Sirius at -1.44.
• the brightest planet Venus varies in brightness and is about -4.4 magnitude at
maximum brightness.
•the Moon is -12.7 magnitude at maximum brightness
•the Sun is -26.75 magnitude.
As the Sun sets, some stars are visible. These are the
first magnitude stars. Later, when twilight is over,
more stars are visible. These are the second magnitude
stars, and so on…Is this apparent magnitude or
absolute magnitude?
Two Kinds of Brightness
Apparent Magnitude, m: How bright the
object appears to us on Earth.
Absolute Magnitude, M: How bright a star
actually is, its intrinsic brightness.
(determine a star’s absolute brightness by imagining
moving it to 10 pc away from the observer)
Apparent Magnitude
is a number that
represents the apparent
brightness of stars as
seen on Earth
The larger the number the
dimmer the object will
appear from Earth
Note we use the letter “m”
for apparent magnitude
Apparent Magnitudes
• Which would look brighter?
Sirius, m = -1.4
Venus, m = -4.4
• Which would look brighter?
Vega, m = 0.03
Antares, m = 1.06
Apparent Magnitudes
• Which would look brighter?
Sirius, m = -1.4
Venus, m = -4.4
• Which would look brighter?
Vega, m = 0.03
Antares, m = 1.06
Smaller/negative
numbers
correspond to
BRIGHTER stars
and
Bigger/positive
numbers
correspond to
DIMMER stars
Why do stars in the night sky
appear considerably different
in brightness?
The distance to stars are not all the same.
Some stars are intrinsically brighter than
others – they simply give off more light.
Which star looks like
it is giving off more
light?
•But, which star is actually giving off more light?
How bright a star appears depends on both how
much light it releases (its actual brightness or
luminosity) and how far away it is (distance)
according to the inverse square law
The Inverse Square
Law
Power or Luminosity (Watts)
apparent magnitude 
Surface Area (in meters2 )
m
 L
4 d 2
Problem
• Rigel (m = 0.18)
• Spica (m = +1.0)
• Which looks brighter from Earth?
• Rigel (m = 0.12)
• Spica (m = +1.0)
• Which looks brighter? Rigel
BUT... It turns out that Spica actually gives
off 1000 times more light than Rigel!!
SO..If Spica is giving off more light, why
would it appear dimmer in the sky here at
Earth?
ANSWER : Because Spica is much farther
away from Earth than Rigel!
PROBLEM: Stars are at different
distances from Earth and so it’s hard to
know which stars are ACTUALLY
brighter versus which APPEAR brighter…
SOLUTION: We imagine having them
all lined up together at the same distance
(10 parsecs or 32 light years), then
compare the brightness of each star
SOLUTION: We imagine having them
all lined up together at the same distance
(10 parsecs or 32 light years), then
compare the brightness of each star
(1 parsec = 206.26×10^3 AU = 3.26156 ly)
This allows us to determine how bright
the star actually is – the Absolute
Magnitude of the star - M
Absolute Magnitude “M”- compares
the brightness of all the stars as if they
were all the same distance away from
Earth (10 pc (32.6 light-years)) and gives
a number that indicates the actual
brightness or luminosity of the star.
Compare some stars:
Absolute
MSun = 4.8
MSirius = 1.4
MBetelgeuse = -5.6
Apparent
mSun = -26
mSirius = -1.46
mBetelgeuse = 0.50
1) Which star looks brightest from
Earth?
A) Sun B) Sirius C) Betelgeuse
2) Which star is brightest?
A) Sun B) Sirius C) Betelgeuse
Absolute
(recall at 10 pc)
distance)
I) MSun = 4.8
II) MSirius = 1.4
III) MBetelgeuse = -5.6
Apparent
(recall at actual
mSun = -26
mSirius = -1.46
mBetelgeuse = 0.50
1) Which is closest to us? Rank them from least distance to farthest.
A) I = II < III
B) I < II < III
C) II <I <III
D) III <II <I
E) III <I <II
By comparing the apparent (m) and
absolute magnitude (M) numbers we
can estimate a stars distance from
Earth.
• When m = M, then the star is located exactly 10
pc away
• When m<M, then the star appears brighter than
it would if it were 10 pc away so it must be
closer than 10 pc
• When m>M, then the star appears dimmer than
it would if it were 10 pc away so it must be
farther than 10 pc
By comparing the apparent (m) and
absolute magnitude (M) numbers we
can estimate a stars distance from
Earth.
OR
• m = M, then the distance = 10 pc
• m < M, then the distance < 10 pc
• m > M, then the distance > 10 pc