The Celestial Sphere

Several different systems of coordinates exist in astronomy to describe positions of the various celestial objects. Each coordinate system has its own class of situations in which it is convenient. We shall borrow from the ancient Greeks the concept of the celestial sphere on which all the heavenly bodies reside. This sphere, centered upon EArth, is very, very large in comparison to Earth. While modern astronomers know that the heavenly bodies actually do not lie on a celestial sphere, the concept is still useful in describing hte positions and motions of these objects.

Before introducing the different coordinate systems in astronomy, some of the common terms should be explicitly stated. Referring to Figure 1, the extension of Earth's equatorial plane onto the celestial sphere is known as the celestial equator, while the extensions of the poles determine the north celestial pole (NCP) and the south celestial pole (SCP). The apparent path of the sun throughout the year on the celestial sphere is known as the eccliptic, tracing out a circle inclined about 23.5° with respect to the celestial equator. The two points at which the ecliptic intersects the celestial equator are known as equinoxes. The vernal equinox (VE) is that point at which the sun is "ascending" into the northern celestial hemisphere, while the autumnal equinox (AE) corresponds to the point at which the sun is "descending" into the souther celestial hemisphere. The solistices, on the other hand, are those positions along the ecliptic which are furthest from the celestial equator. The summer solstice (SS) is the northern-most point on the ecliptic, while the winter solstice (WS) is the southern-most point. It is evident that this terminology is biased towards observers living in the northern hemisphere, since the seasons are opposite in the southern hemisphere than would be expected from the solistices and equinoxes. When the sun is at the summer solstice, the southern hemisphere is deep within the winter season while the northern hemisphere enjoys summer. Similarly, when the sun is at the vernal equinox, the soutern hemisphere is experiencing autumn.

Now, concentrate on that portion of the sky visible to a given observer as illustrated in Figure 2. The point on the sky directly above the observer is known as the zenith (Z). The horizon is then defined as the circle of points on the celestial sphere at a 90° angle from the zenith with respect to the observer. Theoretically, the observer's visible sky is determined by his or her horizon. Thus, each observer should be able to see one half of hte celestial sphere at any given time during the night. However, trees, buildings, and other obstructions usually limit significantly the portion of the sky that can be seen. The familiar directions make up the north point (N), south point (S), east point (E), and west point (W) on the horizon. Then, the semi-circle NZS is known as the meridian. Furthermore, note that the angle between the celestial equator and Z with respect to the observer is known as the latitude of the observer.

Because of th eeastward rotation of the Earth, the celestial sphere exhibits an apparent westward rotation about an axis through NCP and SCP. The stars and other objects located on the celestial sphere appear to rise in the east and set in the wset as they cross an observer's horizon into and out of the visible sky. However, depending upon the latitude of the observer, there exist some stars that never set. Those stars with paths between NCP and N for northern hemisphere observers (between SCP and S for southern hemisphere observers) are visible all night throughout the year. Because these stars tend to be relatively close to the visible pole, they are known as circumpolar stars.

One system for describing hte positions on the celestial sphere is the altitude-azimuth coordinate system, or alt-azimuth system. Consider a star at point P relative to an observer's horizon as illustrated in Figure 3. The relevant arc of the semi-circle connecting Z and P is also illustrated in the figure. The first coordinate in this system, the altitude, is the angular displacement above the horizon measured along this arc by an observer at O. The azimuth is the angular displacement of this arc from the north point N measured in the plane of the horizon. The altitude ranges from 0°at the horizon to 90° at the zenith, while the azimuth spans the entire scale 0° to 360° with N, E, S, and W at 0°, 90° 180°, and 270°, respectively. It is important to note that because the celestial objects are constantly moving across the sky, the altitude and azimuth of a given object continuously change throughout the night. Thus, the alt-azimuth system is not good for assigning stars permanent coordinates, rather it is beneficial in describing the position of an object relative to an observer's horizon at a particular time.

A second system, more widely used by astronomers than the first, is the equatorial coordinate system. It is analogous to the latitude-longitude scheme for the surface of Earth. Consider a star at point P and the semi-circle connecting the NCP, SCP, and P as illustrated in Figure 4. The declination (Dec) of the star is its angular displacement from the celestial equator measured along this semi-circle by an observer at O. The right ascension (RA) of the star is the angular displacment of this semi-circle from VE measured in an eastwardly direction within the plane of the celestial equator. The declination ranges from -90° to 90° with the SCP, celestial equator, and NCP at -90°, 0°, and 90°, respectively. The right ascension is measured in units of time rather than degrees, where the 360° is equivalent to 24 hours beginning with 0 hr at VE. Because the equatorial system uses as references the celestial equator and vernal equinox (which rotate on the celestial sphere at the same rate as the stars), the RA and Dec of a star do not change throughout the night. However, over the course of decades and centuries, the RA and Dec doordinates of a star will change significantly due to the precession of Earth's axis.

Questions

1. At what latitude or latitudes do none of the visible stars rise or set? At what latitude or latitudes do all of the visible stars rise and set?

2. What is the altitude of the north celestial pole for an observer at latitude L in the northern hemisphere?

3. A star has a declination of 40° At what latitude or latitudes can an observer be located to see the star all night throughout the year?