We observe the sky as it looks, not as it is. You feel like you are on top of the Earth (the result of gravity drawing you toward the Earth's center). In the example, you are at a latitude (your location along an arc from the Earth's equator to the rotation pole, given by lower case Greek letter Phi) of 45°, halfway between the Earth's equator and the north pole. The latitude of the north pole is 90°, that of the equator 0°. The Earth appears to lie at the center of a fictional celestial sphere. You pretend that you are inside the sphere at the center looking out around you. Above your head is your zenith, while directly below you is your nadir (both of which are points on the celestial sphere). In between is the great circle of the horizon, which is the circle on the celestial sphere cut by a plane tangent to the Earth at your feet. Everything in the sky above the horizon is visible, while everything below it is not.
The celestial sphere is tipped relative to the observer in the same way as is the Earth. The extension of the Earth's rotation axis to the sky defines the North and South Celestial Poles (the NCP and SCP), while the extension of the Earth's equatorial plane defines the celestial equator. The NCP is in the constellation Ursa Minor (the Smaller Bear) close to the direction of the star Polaris, otherwise called the North Star. The SCP is in the modern constellation Octans, the Octant, in the general direction of the faint southern pole star Sigma Octantis (Polaris Australis).
The circle that runs through the zenith, nadir, NCP, and SCP is the celestial meridian. The intersection of the celestial meridian and the horizon define north (N) and south (S), while that between the equator and the horizon define east (E) and west (W). The intersection of the celestial meridian and the celestial equator (upper case Greek letter Sigma) is down from the zenith by an angle equal to the latitude.
The Earth rotates about its poles from west to east (counterclockwise as viewed from above the north pole), which makes the sky seem to rotate in the other direction about the north and south celestial poles parallel to the celestial equator. The elevation above the horizon (the altitude) of the NCP always equals the observer's latitude. If you are in the southern hemisphere, the south celestial pole (the SCP) is above the horizon, the NCP below it. A star on the celestial sphere seems to go around the observer on a daily path (red circle). The perpendicular angle of a star north or south of the celestial equator is given by its declination, indicated by lower case Greek letterDelta. When the star drops below the horizon, it sets, while when it comes up above the horizon it rises. A star on the celestial equator rises exactly east, sets exactly west. The greater the declination, the farther north of west the star both sets and rises. If far enough north (declination 90° - latitude), the star misses the horizon and is circumpolar, that is, always visible. If the declination is far enough south, the star does not get above the horizon and is always invisible.
THE ECLIPTICThough in truth the Earth orbits the Sun, we feel stationary, which makes the Sun appear to go around the Earth once a year in the counterclockwise direction (from west to east, counter to its daily motion across the sky) along a steady path called the ecliptic. Since there are 365 (actually 365.2422...) days in the year and 360° in the circle, the Sun moves to the east at the slow pace of only a bit under a degree per day. At the same time it is constantly moving (rather, appearing to move) from east to west as a result of the Earth's rotation, just at a pace slightly slower than the stars because of its simultaneous easterly drift. The perpendiculars to the ecliptic plane define the ecliptic poles. The North Ecliptic Pole (NEP) is in Draco, the South Ecliptic Pole (SEP) in Dorado.
The Earth's axis is tilted relative to the perpendiculars to the ecliptic plane by an angle of 23.5° (actually closer to 23.4°). The tilt separates the celestial and ecliptic poles by the same angle, which causes the circle of the ecliptic to be tilted relative to the celestial equator again by the same angle, which as a result is called the obliquity of the ecliptic. As it moves along the ecliptic against the background stars, which are there even if you cannot see them against the blue sky, the Sun, therefore, appears also to move north and south of the celestial equator.
