A diagram of the Celestial Sphere surrounding the earth showing the Celestial Equator, the North Celestial Pole, and lines of Right Ascension (analogous to longitude) and Declination (analogous to latitude).  Also shown are the Big Dipper, Polaris (at the NCP), and Orion.

The earth's axis is the axis about which the celestial sphere appears to rotate. The extensions of the earth's axis through the north pole (NP) and south pole (SP) of the Earth intersect with the north celestial pole (NCP) and the south celestial pole (SCP), respectively. The projection of the Earth's equator on the celestial sphere defines the celestial equator (CE). The celestial sphere can then be divided up into a grid in a similar manner to the way in which the Earth is divided up into a grid of latitude and longitude. On the celestial sphere, we call this "longitude" right ascension (RA) which is measured in units of time (hours, minutes, seconds). It takes about one hour for one hour of right ascension to pass overhead. Celestial latitude is called declination (decl.) which is measured in degrees. See the page on coordinate systems.

Finding the NCP: For northern hemisphere observers, the star Polaris (a Ursae Minoris) is located very near the NCP making it easy to locate (see Fig. 2-10, page 17 of the text).  To find Polaris, first find the Big Dipper.  The two stars at the end of the "bowl" of the dipper point nearly at Polaris (for this reason they are often called "the Pointers").  The southern hemisphere has no such easily identifiable star to mark the SCP.

As the observer moves farther north in latitude, the north celestial pole moves closer to the zenith until they become coincident when the observer is at the north pole. At the north pole, the celestial equator lies on the horizon. As the observer moves further south in latitude, the north celestial pole moves further away from the zenith until it lies at the horizon when the observer is at the Earth's equator. At the Earth's equator, the celestial equator passes through the zenith. 

The Earth rotates from west to east so that stars, planets, the sun and the moon appear to revolve from east to west about the celestial poles on circular paths parallel to the celestial equator once per day. Some stars never set and remain visible all night all year. These are called circumpolar stars. A circumpolar star at its maximum elevation above the horizon is said to be at its upper culmination. Similarly, a circumpolar star at its minimum altitude above the horizon is said to be at its lower culmination. Stars farther from the pole rise, attain a maximum altitude above the horizon (when they are said to transit, or cross the meridian, a north-south line through the zenith) and then set below the horizon. These stars are visible at night only during that part of the year when the Sun is in the opposite part of the sky.

Summary (see also Fig. 2-9, page 17 of the text): 

• In Ontario, the NCP is 34° above the northern horizon (because Ontario's latitude is 34° N), the CE is a circle 90 – 34 = 56° above the southern horizon and meeting the horizon at the due east and due west points.  The SCP is 34° below the southern horizon and is not visible.
• At the NP, the NCP is at the zenith, and the CE is on the horizon.  The SCP is at the nadir.
• At the SP, the SCP is at the zenith, and the CE is on the horizon.  The NCP is at the nadir.
• On the equator, the NCP is on the northern horizon, the SCP is on the southern horizon, and the CE is a circle that passing through the zenith and meeting the horizon at the due east and due west points.
• In Buenos Aires, Argentina (latitude 35° S), the SCP is 35° above the southern horizon, the CE is a circle 90 – 35 = 55° above the northern horizon and meeting the horizon at the due east and due west points.  The NCP is 34° below the northern horizon and is not visible.

Motions on the Celestial Sphere: The stars are sufficiently distant that for our purposes we can assume that they are fixed to the celestial sphere. This is not true of solar system objects (e.g. the Sun, Moon, planets, comets, asteroids and spacecraft) which move (albeit slowly) with respect to the celestial sphere. We will address the motion of these objects now..

The "Motion" of the Sun: The Sun has two main apparent motions in the sky. The first is its diurnal rising and setting which are, as we know, simply reflections of the rotation of the earth. The second motion is a bit more subtle...

As the earth revolves around the Sun, a process which takes one year , we see the Sun against different background stars and constellations (or we would, if the Sun were not so bright!). For example, in January the Sun lies in the same direction as the constellation Sagittarius (shorthand: the Sun is in the constellation Sagittarius), while by February the motion of the earth around the Sun has changed things enough so that the Sun is in the constellation Capricornus.  When school starts in September, the Sun is in the constellation Leo.

This apparent path that the Sun sweeps out in the sky over the course of a year is called the ecliptic. A band 9° on either side of the ecliptic is called the zodiac, and the constellations that the Sun passes through during the year are called the zodiacal constellations. These are the ones that astrologers use to cast horoscopes (or almost:  the ecliptic passes through a thirteenth constellation (Ophiuchus) between Scorpius and Sagittarius that  the astrologers never seem to include). Since there are 365.25 days in a year, and since the sun travels around the entire celestial sphere in that year (an angle of 360°), then it stands to reason that the sun moves eastward about 1° per day.

Another way of thinking of the ecliptic is that it is the intersection of the plane of the earth's orbit around the Sun and the celestial sphere. Most of the other planets (except Pluto) lie in nearly the same plane, and so they are always found close to the ecliptic, and within the zodiac. Likewise, the moon is always within 5° of the ecliptic.  The reason for all of these objects being near the ecliptic is that all of the major solar system objects are pretty much in the same plane.
 

The "Motion" of the Planets: Planet comes from the Greek work meaning wanderer . As noted above, all of the planets but Pluto can always be found near the ecliptic. The order of the planets, outward from the Sun is  Mercury, Venus, Earth, Mars, Jupiter Saturn, Uranus, Neptune, Pluto.  Also, you may have heard that Pluto is presently closer to the Sun than Neptune, but this is no longer true: Pluto's motion along its orbit carried it beyond Neptune's orbit in 1999.

As seen from Earth, Mercury and Venus can never move far away from the Sun. This is because their orbits are smaller than the Earth's. Draw it and see! These two planets, known as inferior planets because their orbits lie inside the earth's orbit, can therefore be seen only around sunrise and sunset, when they are traditionally known as morning stars or evening stars. They don't both have to be "morning stars" at the same time, though, since their orbits have different periods.

The Seasons: The earth's axis is not perpendicular to the ecliptic, but is tilted at an angle of about 23.5 °. The angle is known as the obliquity of the ecliptic and is currently 23°27'. The ecliptic and the celestial equator intercept at two points, associated with the zodiacal constellations of Aries and Libra. The first point of Aries is defined to be the point where the Sun, moving along the ecliptic, crosses the celestial equator from south to north and forms the basis of the most often used celestial coordinate system. This occurs at the spring equinox (or vernal equinox), on March 21, when day and night are of equal length (hence the name) and marks the beginning of spring in the northern hemisphere. Day and night are also of equal length at the autumnal equinox, on September 21, when the Sun crosses the celestial equator from north to south in the constellation of Libra. The autumnal equinox marks the beginning of autumn in the northern hemisphere.  Midway between the equinoxes are the solstices (summer and winter), which define the beginning of summer and winter.

The maximum altitude of the Sun in the sky, as viewed from the northern hemisphere, gradually increases from the spring equinox until it reaches a maximum on June 21 - the summer solstice (when the Sun appears to `stand still' in the sky before starting to move back towards the celestial equator). At the summer and winter solstices the Sun is directly overhead at noon at the Tropics of Cancer and Capricorn, respectively, these being the zodiacal constellations associated with those parts of the ecliptic where the Sun is at these times. The summer solstice marks the beginning of northern hemisphere summer. Similarly, the Sun reaches its minimum altitude in the sky when viewed from the northern hemisphere on December 21 - the winter solstice - which marks the beginning of northern hemisphere winter. Note that all of this is from the point of view of someone in the northern hemisphere: a person living in Australia, for example, has all of her seasons reversed with respect to ours.

Climate: The tilt of the earth's axis is responsible for the climate associated with our seasons. Look at Fig. 2-15 on page 22 and Fig. 2-16 on page 23 in the text and consider an observer in the Northern hemisphere. In the summer, from his point of view, the Sun rises early, reaches a point very high in the sky, and sets late, while in the winter the Sun rises late (or not at all), doesn't get very far over the horizon, and sets early. The amount of heat delivered to the northern hemisphere is thus much less in the winter than in the summer for two reasons:

1) The sun spends much less time above the horizon in the winter than in the summer.

2) The angle with which the Sun's rays hit the surface is much less steep in the winter than in the summer, so the incoming energy is spread out over a much larger area (see Fig. 2-17, page 24 of the text).

Remember that seasons are NOT due to variations in the earth-Sun distance! (If they were, how would you explain the reversal of seasons in the southern hemisphere??) In fact, the Sun is at perihelion (closest approach to the Sun) on about January 2, and at aphelion (farthest distance from the Sun) in the first week of July. Since the earth's orbit is nearly circular, these distances only vary by about 2%. It is interesting to note that when the earth is closer to the sun in January, it receives about 4% more energy from the Sun than it does in July. In January, the hemisphere with the most ocean coverage receives the most direct solar radiation.  In July, the hemisphere with the most land coverage receives the most direct solar radiation.
 

Precession (see Fig. 2-12, page 19 of the text): Hipparcos (the magnitude guy) also compared his observations with those made by a more ancient culture, the Babylonians, and established that the earth's axis doesn't point in a constant direction but slowly circles with time. This phenomenon is similar to what you would observe with a spinning gyroscope: the axis wobbles in a conical motion, known as precession . Because the earth is not a perfect sphere but bulges out at the equator, the Moon's gravity tends to make the earth wobble just like a gyroscope. Since the earth is very massive, the period for it to complete one wobble is very long: about 26,000 years . This means that, several thousand years ago, the earth's axis did not point at Polaris, and no star marked the north celestial pole.

Climate and Ice Ages: In the past, the earth has experienced many glaciations, when the average temperature drops and sheets of ice engulf much of both hemispheres. The process seems to be periodic, in the following way:

There are Ice Age periods occurring about every 250 million years. The latest started only about 3-5 million years ago. However, just because we are in an Ice Age does not mean that there are always sheets of ice covering the earth.

Within an Ice Age, there are periods of glaciation , occurring about every 40,000 years and lasting about 20,000 years. Between these periods, there is an interglacial period, when the ice sheets melt back. We are living in such a period.

There are many possible explanations for the Ice Age/glaciation phenomenon. The most plausible are:
 

1) The changing shape of the earth's orbit. The ellipticity of the earth's orbit varies with a period of about 93,000 years.

2) Precession of the earth's rotational axis, with a period of about 26,000 years

3) The changing inclination of the earth's axis. The inclination (now 23.5 degrees) varies from 22 to 28 degrees with a period of about 41,000 years.

4) Passage of the earth and Sun through giant molecular clouds located around our Galaxy, causing apparent dimming of the Sun. It is an interesting conincidence that the period of our Sun's revolution around the galactic center is about 250 million years.
 

Probably the true cause is a combination of all of the above.

Astronomical Angles: Angles are measured in degrees, minutes (of arc), and seconds (of arc). There are 360 degrees in a circle, 60 minutes in a degree, and 60 seconds in a minute. Don't confuse minutes of arc with minutes of time!