The Celestial Sphere

If you go out on a clear evening and look up at the sky it seems as though you are at the center of a large inverted bowl that comes down and meets the Earth in a big circle. This circle is called the astronomical horizon. Actually, you can only see this if you are out on the sea or a large plain. Usually the astronomical horizon is hidden by trees and buildings, and what is seen is the visible horizon.

Many years ago Greek astronomers imagined that there was another part to the sky below the astronomical horizon. The entire sky, they suggested, was a sphere with half of the sphere hidden by the Earth. Today, the sky sphere is often called the celestial sphere.

Figure 2.1 shows the celestial sphere. Notice that you, the observer, are at the center of the sphere and that the astronomical horizon divides the sphere into two equal parts. The point directly overhead is called the zenith and the point directly underfoot is known as the nadir. Around the horizon are the four cardinal points: north, east, south, and west.
 
 

Because the Earth rotates from west to east, all celestial objects seem to move in the opposite direction, from east to west. This is why objects rise on the eastern horizon and set on the western horizon. The paths that objects trace out in one day are known as diurnal circles and also as declination circles. A few of these circles are shown in Figure 2.1. Notice that these circles make an angle with the horizon but they are all parallel to one another. The diurnal circle that passes through the east and west points is called the celestial equator.

The angle that the diurnal circles and the celestial equator make with the horizon is always equal to 90 degrees minus the observer’s latitude (see Figure 2.2).
 
 

An observer’s astronomical meridian (Figure 2.1) is the circle that passes through the south point on the horizon, the zenith, the NCP, the north point on the horizon, and the nadir. This circle divides the sky into an eastern and a western half. When an object is rising it is to the east of the meridian, and when it is setting, it is to the west of the meridian. The part of the meridian above the horizon is called the upper meridian and that below the horizon is known as the lower meridian.

When an object crosses the upper meridian and is at its greatest angular distance above the horizon, it is said to be at upper transit. At lower transit an object usually lies below the horizon on the lower meridian. Objects are at upper and lower transit once each day.

Because of the Earth’s rotation all objects seem to circle about an imaginary axis passing through the observer and two points in the sky called the north celestial pole (NCP) and the south celestial pole (SCP). The NCP lies directly above the north point on the horizon. The North Star, Polaris, is very close to the NCP. Polaris is the last star in the handle of Ursa Minor, better known as the Little Dipper.

Figure 2.2 is drawn with the Earth at the center of the celestial sphere. An observer is shown on the Earth in the northern hemisphere at middle latitude. The angle between the observer and the equator is the observer’s latitude (about 40 degrees North in this example). As always, the point over the observer’s head is the zenith and the point underfoot is the nadir. The horizon is drawn as a line tangent to the Earth and also as a circle dividing the sky into two hemispheres.

In Figure 2.2  the Earth’s axis of rotation has been extended out to the celestial sphere and intersects it at the north (NCP) and south (SCP) celestial poles. Likewise, extending the Earth’s equator produces the circle called the celestial equator. Thus, the celestial poles and celestial equator are simply the astronomical counterparts of the Earth’s poles and equator. Just as the Earth’s equator divides it into two hemispheres, the celestial equator divides the sky into a northern and southern hemisphere. The celestial poles are located 90 degrees north and south of the celestial equator.

The size of the Earth is really insignificant compared to the distance to even the closest stars. If the Earth in the Figure 2.2 were drawn on the same scale as the sky, it would shrink down to a point at the center of the sky sphere. The observer standing on this point would also be at the center. In fact everyone on the Earth is essentially standing at the same point! Because the Earth is so small, no matter where you are on the Earth's surface you always seem to be at the center of the celestial sphere.

Imagine yourself in Figure 2.2  standing at the Earth’s North Pole (latitude 90 degrees). The NCP pole would be overhead at your zenith 90 degrees from the horizon. Next imagine yourself at the Earth’s equator (latitude 0 degrees). The NCP would lie at the north point on your horizon. But, if you were alongside the observer at latitude 40 degrees North, the NCP would be at 40 degrees above the north point on your horizon. From these observations one can conclude that in general the NCP’s angular distance above the north point on the horizon is always equal to the observer’s latitude.

By measuring the angular distance that the NCP (Polaris) is above the horizon you can actually determine your latitude. For example, if you measured this angle to be 53 degrees you would be standing on the Earth's surface at a latitude of 53 degrees North.
 
 

The Diurnal Motion of Celestial Objects
 

The daily east to west motion of celestial objects is caused by the Earth’s rotation and is known as diurnal motion. Diurnal motion causes the position of objects to  change throughout the day. So, whether or not an object is above the horizon depends, in part, on the time of day.

StarryNight Movie:  Diurnal Motion of Sirius

Project 5: The Diurnal Motion of Sirius

But an object above your horizon at a certain time may not be above the horizon at the same time for another observer at a differrent latitude. As we have seen the angular distance above the horizon of the NCP (and other celestial objects) depends on the observer's latitude. Hence, an object's visibility depends not only on the time of day but also on the observer's latitude .

	StarryNight Movie: Circumpolar Stars viewed From Detroit, Michigan
	StarryNight Movie: Circumpolar Stars viewed From London, England
	Project 7:  Circumpolar Stars

Some objects rise directly at the east point, while others rise north or south of east. It is important to realize that because all diurnal circles are parallel to the celestial equator objects that rise at the east point must set at the west point. Likewise objects that rise in the northeast must set in the northwest, and objects that rise in the southeast must set in the southwest.

The time that an object spends above the horizon depends, essentially, on where it rises. The farther north the rising point the longer an object remains above the horizon while the farther south it rises the longer it remains below the horizon. Objects that rise at the east point are above the horizon for 12 hours and below it for 12 hours. Objects that rise in the northeast remain above the horizon for more than 12 hours and those that rise in the southeast are above the horizon for less than 12 hours.

In addition, at most latitudes, there are some objects that always remain below the horizon and are never seen, while some remain above the horizon and are always visible. Objects that constantly stay above the horizon are called circumpolar objects since they circle around the pole star Polaris.

Any given star always rises and sets at the same point on the horizon and hence is above the horizon for the same amount of time every day of the year. This is not true, however, for the Sun, Moon, and planets. In the summer in the northern hemisphere the Sun rises in the northeast and days are long, while during the winter the Sun rises in the southeast and days are short. The longest day of the year occurs on the summer solstice (June 21) and the shortest on the winter solstice (December 21). Twice a year, on the vernal equinox (March 21) and the autumnal equinox (September 21), the Sun rises at the east point and is above the horizon for 12 hours and below it for 12 hours.
 

In addition to depending on time and the observer’s latitude, an object’s position in the sky also depends on the object and the calendar date. The Sun, Moon, and planets all seem to move against the background of so-called fixed stars. That is, they are not always in the same constellation.

The position of the Earth in its orbit determines the calendar date. As the Earth revolves about the Sun, the seasons change, stars rise 4 minutes earlier each day, and different constellations become visible in the evening sky (see Figure 2.3).

As viewed from the Earth, the constellations out in the Sun’s direction are above the horizon during the day. In the opposite direction are the constellations seen during the evening hours.

Since the Earth moves 360 degrees around the Sun in approximately 360 days, it must move about 1 degree along its orbit each day. This makes the Sun appear to move eastward by 1 degree per day. Expressed in time units 1 degree is equivalent to 4 minutes of time. So as the Sun moves eastward relative to the stars, they rise about 4 minutes earlier each day, eventually becoming visible at night. This results in different constellations being visible in the evening at different times of the year.

Seen from the Earth, the Sun moves through 12 constellations known as the zodiacal constellations. Each month it is in a different zodiacal constellation. The path that the Sun traces out in one year is called the ecliptic. The Moon and planets also appear to move eastward through the zodiacal constellations. However, the time required for their motion is different for each object (see Chapter 1).