The View From Earth

Outline

  1. Earth in Motion
  1. Rotation: 24 hrs
  2. CCW about north pole
  3. 750 mi/hr at State College
  4. Night/day
  5. Revolution: 365.25 days
  6. CCW about north pole
  7. Avg. speed: 67,000 mi/hr
  8. Orientation of Earth in Space
  9. 23.5o tilt of polar (rotational) axis
  10. Precession: 26,000 yrs
  11. ‘Wobble’ of Earth’s polar axis
  12. Due to gravity of Moon and Sun
  13. Orbit about center of Milky Way: 230 million yrs
  14. Orbit radius: 28,000 ly
  15. Speed: 500,000 mi/hr
  16. Motion within Local Group
  17. Galaxies ‘swarm’ due to mutual gravitational attraction
  18. Collion with M31 (?)
  19. Expansion of the University
  20. Space itself expanding ( ‘raisin-cake’ model)
  1. Latitude, Longitude & All That
  1. Latitude: angle between equator plane & your location (0o < lat < 90o)
  2. Latitudes of tropic & polar circles related to Earth’s orientation
  3. Longitude: measures E/W of Prime Meridian (0o < long < 180o E/W)
  4. State College: lat = 41o N; long = 78o W
  1. Celestial Sphere: A Model of the Sky
  1. Horizon (plane), Meridian, Zenith
  2. Celestial poles (Polaris); Celestial Equator
  3. Rising & Setting
  4. Due to Earth’s rotation
  5. Stars follow circles centered about celestial pole
  6. Circumpolar stars
  1. The Sky & Your Latitude
  1. Altitude of celestial pole = your latitude
  2. Daily motion of sky at various latitudes
  3. Drift of celestial poles due to precession
  1. Different Stars in Different Seasons
  1. Due to orbit of Earth about Sun
  1. Constellations
  1. Traditional and Modern definitions
  2. A few star names

Diagrams

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.

7. Prob. # 2, pg. 49. [Hint: As reported in class, for State College: Lat = 41o N; Long = 78o W.]

8. 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?

9. 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: Assume Xenonians measure latitude in exactly the same way we do; i.e., equator lies at 0o lat & north pole lies at 90o lat]

10. 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?

11. [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

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

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

14. 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!)

15. 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.

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

17. Ques. #1, pg. 48.

Answers

1. Earth: (1) rotates on an axis once every 24 hours; (2) revolves about the Sun with period 365.25 days; (3) accompanies the Sun (and other planets) as it moves relative to other stars in its immediate neighborhood; (4) orbits about the center of the Milky Way galaxy, with period 230 million years; (5) moves with the Milky Way galaxy as the Milky Way moves relative to other galaxies within the Local Group; and (6) partakes, with the Local group as a whole, in the expansion of the universe.

2. Each point on the equator is carried through a larger circle than each point at the latitude of State College. Consequently, points at the equator must be going faster as they must cover a greater distance in the same amount of time (namely, 24 hours).

3. The celestial sphere is an imaginary sphere centered on any observer of the sky on Earth. The celestial sphere is essentially infinite in radius. The sphere is divided into a visible part and an invisible part by the horizon plane; the edge of the horizon plane forms the observer’s horizon. The point directly overhead on the sphere is called the zenith. A half circle running from north to south, and through the zenith, which divides the visible part of the sphere into an east half and a west half is called the celestial meridian. Observation shows that all objects visible on the sphere (stars, planets, Sun, Moon, etc.) appear to pivot every 24 hours about a point elevated above the north point on the horizon (for a northern hemisphere observer). This point is called the celestial north pole. (A similar point exists in the sky visible from Earth’s southern hemisphere.) The poles of the sky are located on the celestial sphere above the north and south poles of Earth. A circle, called the celestial equator, divides the sky into north and south halves; the equator is thus located midway between the north and south celestial poles.

4. The sky looks like a dome because all stars appear approximately equidistant from you – although in fact you have no idea as to their true distances. Horizon, zenith and (celestial) meridian are mentioned in the answer to Ques. #3.

5. As your latitude changes, the altitude (elevation) of the celestial poles changes. For a northern hemisphere observer, this means that the altitude of polaris (the “north star”) changes. Also, constellations visible above the southern horizon change, as well. For example, were you to travel south from State College (say, toward Florida), you would find that polaris’ altitude decreases, fewer constellations are circumpolar, and new constellations, not previously visible, appear above your southern horizon.

6. As Earth circles the Sun in its orbit, the night-time hemisphere (which always points away from the Sun) naturally changes the direction in which it points. For example: the night-time hemisphere points in opposite directions on July 1 and Jan 1. Here’s a diagram that illustrates this situation:

7. b) As viewed from State College, the north celestial pole (which is nearly coincident with Polaris) is elevated about 41o above the north point on the horizon.

c) Yes, Polaris is circumpolar. Polaris circles the pole once every 24 hours, never touching the horizon.

d) The (celestial) meridian sprouts from the north point on the horizon, passes through your zenith, then disappears at the south point.

e) The celestial equator arises from the east point on your horizon, arcs upward to the celestial meridian, crossing the meridian south of the zenith, then arcs downward to the west point on the horizon.

8. Tropic of Cancer: 16.5o North; Arctic Circle: 73.5o N

9. Your latitude is 57o N.

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

11. b) One day.

12. The celestial pole coincides with the horizon at either pole.

13. If no visible stars are circumpolar, you would be standing on Earth’s equator.

14. a) The center of the arcs is the north celestial pole (the picture was taken in the northern hemisphere).

b)Polaris is the bright arc near the center.

c)At Earth’s south pole, the center of the arcs would be elevated 90o above the horizon; i.e., it would appear in your zenith.

15. Pegasus will appear west of your meridian one month later. This shift is due to Earth’s revolution about the Sun.

16. Among other effects, precession causes the location of the celestial poles to wander relative to the stars. At the moment, the north celestial pole happens to lie near a moderately bright star (Polaris). In the future, the pole will wander away from Polaris, and appear near Polaris again in about 26,000 years.

17. In modern terms, a constellation is a specific, well-defined region of the celestial sphere – rather like a state on a map of the U.S. Traditionally, a constellation is the depiction of a person, animal or object among the stars. Each modern constellations have been defined so as to enclose a traditional constellation.