The View from Earth

1.  Earth in Motion
    *  Rotation:  24 hrs
        >  CCW about north pole
        >  750 mi/hr at State College
        >  Night/Day
        >  Earth bulges due to rotation
    *  Revolution:  365.25 days
        >  CCW about north pole
        >  Avg speed:  67,000 mi/hr
    *  Orientation of Earth in Space
        >  23.5o tilt of polar axis
    *  Precession:  26,000 yrs
        >  'Wobble' of Earth's rotation (polar) axis
        >  Due to gravity of Moon & Sun
    *  Motion relative to nearby stars
        >  Video:  Jack Horkheimer describes motion of Arcturus
    *  Orbit about the Milky Way:  230 million yrs
        >  Orbit radius:  28,000 ly
        >  Speed:  500,000 mi/hr
        >  Vertical oscillation
    *  Motion within Local Group
        >  Expected collision with M31 (Andromeda Spiral)
    *  Expansion of the Universe
        >  Space itself is expanding (raisin-cake model)
2.  Latitude, Longitude & All That
    *  Latitude:  angle between equator plane & your location (0o < Lat < 90o)
    *  Latitudes of tropic & polar circles are related to orientation of Earth
    *  Longitude:  Measured east/west of Prime Meridian (0o to 180o E/W)
    *  State College:  Lat = 41o N, Long = 78o W
3.  Celestial Sphere:  A Model of the Sky
    *  Horizon (plane), Meridian, Zenith
    *  Celestial poles, Equator
    *  Polaris
4.  Rising & Setting
    *  Due to rotation of Earth
    *  Stars follow circles centered about a celestial pole
    *  Circumpolar stars
5.  The Sky & Your Latitude
    *  Altitude (elevation) of celestial pole = your latitude
    *  Daily motion of sky at various latitudes
    *  Drift of celestial pole relative to stars (Precssion)
6.  Different Stars in Different Seasons
    *  Due to orbit of Earth about sun
7.  Constellations
    *  Traditional and Modern definitions
    *  Constellation stars distributed in space
 

Diagrams


FIG 1


FIG 2


FIG 3


FIG 4



 

FIG 5



 

FIG 6


FIG 7


FIG 8


FIG 9


FIG 10



Questions

1.  Ques. #11, pg. 26.

2.  All points on Earth rotate with the same period, namely 24 hrs.  So, why does a point on Earth's equator rotate about Earth's axis with a speed greater than the rotation speed of State College?

3.  Ques. #2, pg. 48.

4.  Ques. #4, pg. 48.

5.  Ques. #6, pg. 48.

6. Ques. #7, pg. 48.  [Hint:  Have a look at FIG 10 above.]

7.  Prob. # 2, pg. 49.  [Hint #1:  As reported in class, for State College:  Lat = 41o N; Long = 78o W.  Hint #2:  A study of FIG 2 (above) may prove useful in responding to this question.]

8.  In FIG 2 above, what is the value of the angle (in degrees) between celestial equator and celestial pole (either pole will do).

9.  Suppose the angle between Earth's equatorial and ecliptic (orbit) planes were only 16.5o.What would be the latitude of the Tropic of Cancer and the Arctic Circle?  [Hint:  Take a look at FIG 1 above & note that angle I is identical to the angle between equatorial and ecliptic planes.]

10.  Your spaceship lands on the mysterious planet Xenon at a locale where all stars appear to circle a point elevated 57o above your northern horizon.  What's your latitude on Xenon?  [Hint #1:  Assume Xenonians measure latitude in exactly the same way we do; i.e., equator lies at 0o lat & north pole lies at 90o lat.  Hint #2:  Take a look at FIG 6 above.]

11. As observed from State College, a star that rises directly East must set where on the horizon?  A star that sets in the southwest must have risen where?  [Hint:  Have a look at FIG 5 above.]

12.  The image in FIG 7 above was taken in the northern hemisphere.  Are we looking east or west?

13. [Multiple-Choice] A certain star appears on your zenith at midnight on a certain night.  About how much time must pass before this same star appears again at your zenith?

a)  One hour
b)  One day
c)  One month
d)  One  year

14.  Where on Earth does the celestial equator coincide with the horizon?

15.  Where would you be standing on Earth if no visible stars are circumpolar?

16.  Take a look at Figure 2.13 (pg. 34) in your textbook.  (a)  The center of all of the arcs of circles traced by stars in this picture is what special point on the sky? (b)  Is the star Polaris found in this picture?  Explain.  (c)  How would this picture change if the viewer were standing at Earth's south pole, instead of in Utah?  (Apart from the obvious change in topography!)

17.  The constellation Pegasus appears directly overhead at midnight.  One month later, at midnight, will Pegasus be found west of your meridian, or east of your meridian?  Explain.  [Hint:  Take a look at FIG 10 above.]

18.  Precession has what effect on the appearance of the sky?

19.  Ques. #1, pg. 48.

20.  Ques. #3, pg. 48.


Answers

1.  The motions of Earth (from rotation to participation in the expansion of the Universe) were well summarized in lecture; consult your notes.

2.  Have a look at Fig 1.16 on pg. 19 in your text.  A person standing on Earth is carried around on a circle once every day (24 hours).  The size of that circle depends on latitude (the smaller the circle as we get closer to either pole).  Now, the larger the circle, the greater the distance that must be covered in 24 hours.  So, as you move further from the equator, your speed will decrease.

3.  The celestial sphere is an imaginary sphere, essentially infinite in radius, surrounding any oberver on Earth (or any place else, for that matter).  Except for the celestial meridian, the main features of the celestial sphere are nicely identified in FIG 2 above.

4.  Your sky is really the collection of all possible directions you can look outward from your location on Earth.  This collection of directions adds up to a hemisphere (or, dome). Horizon, zenith and meridian are defined very satisfactorily on pg. 31 in your text.

5.  Here's one way to think about the changing sky:  Extend a line from Earth's center through you and on out into space.  This line runs along an Earth radius and points toward your zenith.  As Earth is spherical, the direction toward the zenith thus changes continuously as you move around Earth.  So you see different stars in the zenith depending on where you are.  As your sky is cut-off by the plane (horizon plane)  perpendicular to the zenith direction, your whole sky thus varies as you move around Earth.

6.  It's a matter of Earth moving in an orbit about the sun, giving those on Earth's dark side a constantly changing view of the universe through the year.

7.  a)  State College:  lat = 41o North; long = 78o West.
b)  The NCP lies about 41o elevation above the northern horizon, as viewed from State College (SC).  The south celestial pole lies below the horizon, as viewed from SC.
c)  Polaris is circumpolar in the SC sky; it lies less than 1o from the NCP.
d)  As it does everywhere, the meridian extends from north to south on the horizon, while passing through the zenith.
e)  Celestial equator passes from east to west on horizon, crossing the meridian 49o above the horizon in SC.  (See FIG 3 under Sun & Seasons).

8.  The angle between celestial pole and celestial equator is 90o.

9.  Tropic of Cancer:  16.5o North.  Arctic Circle:  73.5o North.

10.  Your latitude on Xenon is 57o North.

11.  A star that rises directly east must set directly west.  A star observed to set in the southwest must have rises in the southeast.

12.  We're looking west in this picture.  (North must be off to your right, as the stars in this picture are evidently circling a point elevated and to the right - this point must be the NCP.)

13.  b)

14.  The celestial equator coincides with horizon at either of Earth's poles.

15.  If no visible stars are circumpolar, you must be standing on Earth's equator.

16.  a)  The center of the circles traced by the stars is the north celestial pole.  (As the caption indicates, the picture was taken in Utah.)  b)  The star Polaris is represented by the short, very bright arc very near the center of all of the arcs.  We know Polaris is a moderately bright star near, but not at the NCP.  c)  In order to see pattern at Earth's south pole, you'd have to be looking toward the zenith, in which case the landscape would likely lie outside your field of view.

17.  Pegasus will lie west of your meridian one month after your initial observation.  Have a look at FIG 10, which clearly shows that Pegasus lies to the west of directly overhead in September, whereas it was located directly overhead in July.  The general rule illustrated here is a follows:  At the same clock time, all objects in our sky appear to drift westward as we proceed through the year.

18.  Precession is the very slow (but very real) wobble of Earth's rotation axis; 26,000 years is required to complete one full wobble.  The orientation of Earth's rotation axis defines the directions to the north and south celestial poles.  Thus, if the axis is changing direction, the particular stars that lie in thte direction of the poles changes continuously through the precession cycle. As it happens, the north end of the Earth's rotation axis points toward a moderately bright star (Polaris).  This coincidence has not always been so, nor will it be so in the future.

19.  By modern definition, a constellation is a fixed, well-defined piece of the celestial sphere.  All traditional constellation figures (e.g., Ursa Major) are enclosed by thet boundaries of a modern constellation.

20.  The Milky Way in our sky is the projection on the celestial sphere of the disk of the Milky Way galaxy;  we're viewing our galaxy from a vantange point inside of it, of course!