Astro Lecture #3: The Celestial Sphere (The Geocentric Model of the Universe)
1. Handouts
a. Scales of the Universe with discussion
i. What is bigger the distance from NY to Tokyo or the diameter of the Earth?
ii. How many times larger is the distance to the Sun compared to the distance to the
Moon?
iii. How many times larger is the diameter of our Solar System compared to the
distance to the Moon?
iv. How many times larger is the distance to the nearest star beyond the Sun
compared to the diameter of the Solar system?
v. How many times larger is the diameter of the Milky Way compared to the
diameter of the Solar System?
vi. How many times larger is the diameter of the observable Universe compared to
the diameter of the Milky Way?
2. Introduction
a. Problems?
b. Connect Problems?
c. HW is due on _________
3. The Night Sky (Unit 5)
a. Intro
i. Does anyone know the difference between a constellation and an asterism?
1. Constellation is an officially designated area of the sky with well-defined
boundaries in the celestial coordinates of Right Ascension and
Declination. There are 88 official constellations.
a. Important point: Stars follow their lines of declination
2. An asterism is an easily recognized pattern of stars. e.g. The Big Dipper,
Orion’s Belt, The Summer Triangle. There are hundreds, if not
thousands, of asterisms.
ii. What function do you think constellations serve today?
1. Help astronomers and observers find objects in the sky.
2. Horoscopes
3. Story telling
iii. What function do you think constellations served our ancient ancestors in preliterate societies?
1. Knowledge in pre-literate societies was passed on by oral transmission.
2. They allowed stories to be imprinted upon them. Stories of origins,
moral values, practical time-keeping or calendric purposes.
3. The stars were a “book” that could never be lost, before books even
existed.
4. It should be of little surprise that stars still hold a spiritual attraction
today since they were an essential part in the development of western
civilization.
b. The Celestial Sphere: Draw the model (Figure 5.1)
i. The stars appear to be sprinkled on a giant sphere that surrounds the Earth. We
can only see a portion of the sphere of stars at night due to the solid Earth hiding
the lower half of this celestial sphere.
ii. Stars are so far away, that only very sensitive measuring instruments can
distinguish between near and far stars. To the naked eye all, stars appear equally
far away.
iii. Use the UNL Rotating Sky to illustrate the celestial sphere.
iv. Even though the concept of the Celestial Sphere is not physically true, it is still a
very useful conceptual tool in understanding the night sky. Read Kuhn – yellow
book mark.
c. Daily Apparent Motion
i. Illustrate with the movie Stars over Greece from APOD
ii. Further illustrate with Starry Night
iii. Some simple rules
1. The cause of the daily apparent motion of the stars is the rotation of the
Earth eastward on its axis once every 23h 56m 4.09s (Demonstrate this
with Starry Night) This time period is called the Sidereal Day (Unit 7)
2. Two points on the sky do not appear to move. The NCP (which is very
close to Polaris, the North Star) that is always above the horizon as seen
from northern latitudes and the SCP which always below the horizon as
seen by northern observers. The celestial poles are located directly
above the Earth’s north and south geographic poles.
3. Halfway between the celestial poles lies the Celestial Equator that
intersects the horizon due (exactly) East and West for all observers.
Stars near or on the Celestial Equator spend equal amount of time above
and below the horizon (about 12 hours each).
a. Read Aristotle (See Hot Tips)
4. The altitude of Polaris (NCP really) equals the observer’s latitude. (See
proof on Hot Tips)
5. The details of the apparent motion of the stars depend on your latitude on
the Earth. See Figure 5.7
6. For Northern Hemisphere observers:
a. Looking North, stars appear to move in counterclockwise circles
around Polaris (NCP really). Some stars never set because they
are so close to Polaris their daily circles never take them below
the horizon (a.k.a. Circumpolar stars). Northern stars are above
the horizon longer than they are below the horizon.
b. Looking East (or West), stars appear to rise (or Set) along a
slanted path toward (away from) the South whose angle from the
vertical equals the observers latitude.
c. Looking South, stars appear to make shallow clockwise
downward-curving arcs about the hidden SCP. Some stars never
appear above the horizon because they are too close to the SCP
for their daily circles to carry them above the horizon. Southern
stars are above the horizon less than they are below the horizon.
d. See Figure 5.5
7. Latitude and Longitude
a. The latitude of an observer determines what fraction of the entire
celestial sphere he/she can see. Demo with the Rotating Sky
modules.
i. At the North Pole, the observer sees only ½ of all the
celestial sphere. Same for the South Pole.
ii. At the Equator, the observer can see the entire celestial
sphere in one single night – if we lived on a perfectly
spherical smooth Earth with no atmosphere.
iii. The longitude of an observer only effects when (i.e. the
time of day) an object is seen.
iv. Since the Earth turns at 15/hour, a star that passes
through the zenith at one location, will pass through the
zenith at another location, at the same latitude, after a
time period proportional to the difference in longitude
between the two locations. See class exercise.
4. Summary
a. The Review Questions at the end of each unit will be a source of exam questions, as
well as some of the Quantitative Problems.
i. Please write and answer the Review Questions out in your notes. The answers
can be found in the reading of the Unit or you can search the web – be careful
though on the web – no all sources are reliable. Wikipedia is pretty good for
astronomy
5. The Apparent Motion of the Sun (Units 7 & 6)
a. The Key concept: The Sun acts like a moving star, behaving like the stars around it on
any given day, but slowly moving through the stars over the course of a year.
b. The Apparent Daily Motion of the Sun
i. Show’em with Starry Night
ii. Write the conclusion with it’s caveat
1. 23h 56m 4.09s = 86164.09s = 1 sidereal day
2. 24h = 86,400s = 1 mean solar day
3. Difference = 235.91s
4. Calculate the number of sidereal days required for the Sun to fall so far
behind that it is back where it started (365.241 sidereal days)
c. The Apparent Annual Motion of the Sun
i. Show’em with Sky Gazer
ii. Define the Ecliptic, solstices and equinoxes
iii. Describe the daily apparent motion of the sun on the solstices and equinoxes
iv. Demo the apparent movement of the Sun in SOHO.