2.1: Celestial sphere

	A convenient model of the sky for mapping the apparent positions and motions of celestial bodies as seen from the earth (Fig. 2-1).
	*All celestial bodies are imagined* to attach to the inside of a very large hollow sphere surrounding the earth.**

Fig. 2-1 The celestial sphere models the appearance of the sky. The poles mark the pivots, and the equator divides the sky into halves. Those objects below our horizon are invisible. The earth rotates eastward, making objects in the sky appear to rise along the Eastern horizon and set along the Western horizon.

Self-rotation of the earth from West (W) to East (E).

	celestial bodies appear to move in opposite direction (E to W) in the sky, e.g., the sun rises in the E and sets in the W
	*we can describe this motion by imagining* the celestial sphere to rotate once a day, carrying all celestial bodies from E to W.**

Celestial poles: The North (N), South (S) poles of the celestial sphere are located directly above the N, S poles of the earth respectively. The poles define the axis of daily rotation.

Polaris (the Pole star) is a bright star close to the N celestial pole.

it appears almost stationary.

Position of Polaris depends on the location of the observer on Earth,

e.g.,	*an observer at N Pole* sees Polaris at the zenith (directly overhead),**
	*an observer at Equator* sees Polaris at the northern horizon,**
more generally (Fig. 2-2),

angle of Polaris above the horizon = latitude of the observer

Fig. 2-2 For an observer at latitude L on the earth, the N celestial pole is at an angle q = L above the northern horizon.

Celestial equator: An imaginary line which divides the celestial sphere into the N and S hemispheres.

Precession of the earth's rotation axis (Fig. 2-3).

	celestial poles move slowly in a circle (26,000 yr./cycle).
	Pole star changes e.g. Thuban (a Draconis) was the Pole star 5,000 years ago

Fig. 2-3 The earth's axis currently points towards the star Polaris. 5,000 years ago, it pointed at the star named Thuban in the constellation of Draconis. 12,000 years later it will point to Vega.

Fig. 2-4 Your hand held at arm's length makes a convenient measuring tool. Your fist is about 10° , your finger about 1° wide, and your spread fingers span about 18° .

Apparent sizes and separations of celestial bodies are measured in angles (Fig. 2-4):

		1 circle = 360° (degree), 1° = 60' (minutes), 1' = 60" (seconds)
	e.g.,	apparent diameters of the sun and moon 0.5°,
		width of a finger at arm's length 1°,
		width of the fist at arm's length 10°.

Coordinates on the celestial sphere: Declination and Right ascension are similar to latitude and longitude on earth respectively.