The Celestial Sphere

Celestial Sphere Defined

Imagine the sky as a great, hollow, sphere surrounding the Earth. The stars are attached to this sphere -- some bigger and brighter than others -- which rotates around the stationary Earth roughly every 24 hours. Alternatively, you can imagine the stars as holes in the sphere and the light from the heavens beyond the sphere shines through those holes. This imaginary sphere is called the celestial sphere, and has a very large radius so that no part of the Earth is significantly closer to any given star than any other part. Therefore, the sky always looks like a great sphere centred on our position. The celestial sphere (and, therefore, the stars) appears to move westward -- stars rise in the east and set in the west.

Even though we now know that this ancient model of a stationary Earth is incorrect, we still use this model because it is a convenient way to predict the motions of the stars and planets relative to a location on the Earth. We now know that a star's apparent brightness is determined by its distance, as well as its physical size and temperature. We also know that the stars' apparent motion around us is due to the Earth rotating once every 24 hours on its axis. The stars are stationary and the Earth rotates, in a west to east direction. This rotational motion makes the stars appear to move from east to west around us. You should carefully distinguish between the convenient artifact of the celestial-sphere model and the way things really are.

Why a sphere? The Earth is spherical! This was known much earlier than Columbus' time. Sailors had long known that as a ship sailed away from the shore it not only diminished in apparent size, but it also appeared to sink into the water. The simplest explanation to use was that the Earth was curved (particularly, since those ships did come back without falling off some edge!). They also knew that if one traveled in a north-south direction, some stars disappeared from view while others appeared. The difference in the height of a star's height above the north or south horizon is directly proportional to the difference in the north-south distance of observers looking at the star at the same time. The simplest explanation said that the Earth is round, not flat. Pythagoras noted that the shadow of the Earth falling on the Moon during a lunar eclipse was always curved and the amount of the curvature was always the same. The only object that always casts a circular shadow regardless of its orientation is a sphere. We know about this Pythagorean argument through the writings of Aristotle.

Angles

To measure distances on the imaginary celestial sphere, we use angular separations instead of metres or kilometres. There are 360 degrees in a full circle and 90 degrees in a right angle (two perpendicular lines intersecting each other make a right angle). Each degree is divided into 60 minutes of arc. Each minute of arc is divided into 60 seconds of arc. The ball in the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second across. The Sun and Moon are both about 0.5 degrees = 30 arc minutes in diameter. The pointer stars in the bowl of the Big Dipper are about 5 degrees apart and the bowl of the Big Dipper is about 30 degrees from Polaris, at the north celestial pole (NCP). The arc from the north point on the horizon, through the point directly overhead, to the south point on the horizon is 180 degrees, so any object directly overhead is 90 degrees above the horizon and any object 'half-way up' in the sky is about 45 degrees above the horizon.

Reference Markers

Now for some reference makers: The stars rotate around the North and South Celestial Poles. These are the points in the sky directly above the geographic north and south poles, respectively. The Earth's axis of rotation intersects the celestial sphere at the celestial poles. The number of degrees the celestial pole is above the horizon is equal to the latitude of the observer. Fortunately, for those of us in the northern hemisphere, there is a fairly bright star real close to the North Celestial Pole (Polaris or the North star). Another important reference marker is the celestial equator: an imaginary circle around the sky directly above the Earth's equator. It is always 90 degrees from the poles. All the stars rotate in a path that is parallel to the celestial equator. The celestial equator intercepts the horizon at the points directly east and west anywhere on the Earth.

If you joined Santa Claus last Christmas at the north pole (90 degrees latitude), you would have seen Polaris straight overhead and the celestial equator on your horizon. The point straight overhead on the celestial sphere for any observer is called the zenith and is always 90 degrees from the horizon. The arc that goes through the north point on the horizon, zenith, and south point on the horizon is called the meridian. The positions of the zenith and meridian with respect to the stars will obviously change as the celestial sphere rotates and if the observer changes locations on the Earth. Any celestial object crossing the meridian is at its highest altitude (distance from the horizon) during that night (or day). The angle the star paths make with respect to the horizon = 90 degrees - (observer's latitude).

For each degree you move south with Santa in his sleigh, the North Celestial Pole (NCP from here on) moves 1 degree away from the zenith toward the north, and the highest point of the celestial equator's curved path in the sky moves up one degree from the southern horizon. This effect has nothing to do with the distance between you and a celestial object or marker at different points on the Earth. Observers on a world only ten miles across would see the same effect! The picture above shows the celestial sphere for the northern city of Fairbanks in Alaska (at about the same latitude as Iceland). Since it is 25° south of the north pole, the NCP is 25° away from the zenith for Fairbanks observers.

By the time you reach your hometown, the NCP has moved away from the zenith so it is now a number of degrees above the horizon equal to your latitude on the Earth. Remember that your position on the Earth is specified by a latitude and a longitude co-ordinate. The latitude is the number of degrees north or south of the Earth's equator. On a map or globe, lines of latitude run more or less horizontally (depending on the map projection used), parallel to the equator. The longitude is the number of degrees east or west of the prime meridian that runs through Greenwich. On a map or globe, lines of longitude typically run more or less vertically, perpendicular to the equator. The celestial sphere for observers in Seattle and any other observer at the same latitude on the Earth (47°; roughly the latitude of Switzerland) is shown above.

For another more detailed example, let's choose Los Angeles at latitude 34° N. The NCP is therefore 34 degrees above the north horizon. The diagram for latitude 34° N is shown above. Notice that finding the angle of the NCP above the horizon provides a very easy way of determining your latitude on the Earth (a fact used by navigators even today!). Because the Earth's equator is 90° away from the north pole, the celestial equator as seen in Los Angeles will arc up to 90 - 34 = 56 degrees above the southern horizon at the point it crosses the meridian. It still intercepts the horizon due east and west. The stars rise in the east part of the sky, move in arcs parallel to the celestial equator reaching maximum altitude when they cross your meridian, and set in the west part of the sky. The star paths make an angle of 90 - 34 = 56 degrees with respect to the horizon.

For observers in the northern hemisphere, stars north of the celestial equator are above the horizon for more than 12 hours because we see more than half of their total 24-hour path around us. Stars on the celestial equator are up 12 hours and those south of the celestial equator are above the horizon for less than 12 hours because we see less than half of their total 24-hour path around us. (The opposite is true for observers in the southern hemisphere.)

Notice that stars closer to the NCP are above the horizon longer than those farther away from the NCP. Those stars within an angular distance from the NCP equal to the observer's latitude are above the horizon for 24 hours -- they are circumpolar stars. Also, those stars close enough to the SCP (within a distance = observer's latitude) will never rise above the horizon. (They are also called circumpolar stars by some people, but this is a less common usage.)

To warm Rudolph's frozen nose, Santa headed down to the equator (0 degrees latitude). At the equator, you would have seen the celestial equator arcing from due east to the zenith to due west. The NCP would have been on your northern horizon. At the equator you see one-half of every star's total 24-hour path around us, so all stars are up for 12 hours. Every star rises and sets perpendicular to the horizon (at an angle = 90 - 0 = 90 degrees).

Continuing southward, you would have seen the NCP disappear below the horizon and the SCP rise above the southern horizon one degree for every one degree of latitude south of the equator you went. The arc of the celestial equator would have moved to the north, but the arc still intercepted the horizon at the east/west points.

Here is a summary of the positions of the celestial reference marks (note that 'altitude' means the number of degrees above the horizon):

• Meridian always goes through due North, zenith, and due South points.
• Altitude of zenith always equals 90°.
• Altitude of celestial pole = observer's latitude. Observers in northern hemisphere see NCP; observers in southern hemisphere see SCP.
• Altitude of celestial equator on meridian = 90 - observer's latitude.
• Celestial equator always intercepts horizon at due East and due West points.
• Angle celestial equator (and any star path) makes with horizon = 90 - observer's latitude.
• Stars move parallel to the celestial equator.
• Circumpolar object's distance from celestial pole = observer's latitude.

Motion of Our Star the Sun

Now that we have our bearings, let's take a look at the position and motion of the closest star to us, the Sun. Every day the Sun rises in an easterly direction and sets in a westerly direction; and (on average) it takes the Sun 24 hours to go from noon position to noon position the next day. The 'noon position' is when the Sun is highest above the horizon on a given day. Our clocks are based on this solar day. However, the exact position on the horizon of the rising and setting Sun varies throughout the year.

Furthermore, the Sun appears to drift eastward with respect to the stars (or lag behind the stars) over a year's time. It makes one full circuit of 360 degrees in 365.24 days (very close to 1 degree, or twice its diameter, per day). We now know that this drift eastward is caused by the motion of the Earth around the Sun in its orbit.

The apparent path of the Sun through the stars is called the ecliptic. This circular path is tilted 23.5 degrees with respect to the celestial equator because the Earth's rotation axis is tilted by 23.5 degrees with respect to its orbital plane.

The ecliptic and the celestial equator intersect at two points: the vernal (spring) equinox and autumnal equinox. The Sun crosses the celestial equator moving northward at the vernal equinox around March 21, and crosses the celestial equator moving southward at the autumnal equinox around September 22. When the Sun is on the celestial equator at the equinoxes, everybody on the Earth experiences 12 hours of daylight and 12 hours of night (hence, the name 'equinox' for 'equal night'). The day of the vernal equinox marks the beginning of the three-month season of spring on our calendar and the day of the autumn equinox marks the beginning of autumn.

Let's make sure we understand this. No matter where you are on the Earth, you will see 1/2 of the celestial equator's arc. Since the sky appears to rotate around us in 24 hours, anything on the celestial equator takes 12 hours to go from due east to due west. Every celestial object's diurnal (daily) motion is parallel to the celestial equator. So for us northern observers, anything south of the celestial equator takes less than 12 hours between rise and set, because most of its rotation arc around is hidden below the horizon. Anything north of the celestial equator takes more than 12 hours between rising and setting because most of its rotation arc is above the horizon. For observers in the southern hemisphere, the situation is reversed. However, remember, that everybody anywhere on the Earth sees 1/2 of the celestial equator so at the equinox, when the Sun is on the equator, we see 1/2 of its rotation arc around us, and therefore we have 12 hours of daylight and 12 hours of nightime everyplace on the Earth.

The geographic poles and equator are special cases. At the geographic poles the celestial equator is right along the horizon and the full circle of the celestial equator is visible. Since a celestial object's diurnal path is parallel to the celestial equator, stars do not rise or set at the geographic poles. On the equinoxes the Sun moves along the horizon. At the North Pole the Sun 'rises' on March 21 and 'sets' on September 22. The situation is reversed for the South Pole. On the equator observers see one half of every object's full 24-hour path around us, so the Sun and every other star is above the horizon for exactly 12 hours for every day of the year.

Since the ecliptic is tilted 23.5 degrees with respect to the celestial equator, the Sun's maximum angular distance from the celestial equator is 23.5 degrees. This happens at the solstices. For observers in the northern hemisphere, the farthest northern point above the celestial equator is the summer solstice, and the farthest southern point is the winter solstice. The word 'solstice' means 'sun standing still' because the Sun stops moving northward or southward at those points on the ecliptic. The Sun reaches winter solstice around December 21 and we see the least part of its diurnal path all year -- this is the day of the least amount of daylight and marks the beginning of the season of winter for the northern hemisphere. The Sun reaches the summer solstice around June 21 and we see the greatest part of its diurnal path above the horizon all year -- this is the day of the most amount of daylight and marks the beginning of summer for the northern hemisphere. The seasons are opposite for the southern hemisphere (e.g., it is summer in the southern hemisphere when it is winter in the northern hemisphere). The Sun does not get high up in the sky on the winter solstice. The Sun's rays hit the ground at a shallow angle at mid-day so the shadows are long. On the summer solstice the mid-day shadows are much shorter because the Sun is much higher in the sky.

Co-ordinates

Early astronomy concentrated on finding accurate positions of the stars and planets. This was due in part to the influence of astrology, but later came to be important for determining their physical characteristics. Accurate positions for the stars were crucial for commercial and military navigation (navigation by the stars has only recently been replaced by the use of satellite systems such as the Global Positioning System). But of more importance to astronomers is where to point a telescope to locate some object of interest.

There are a couple of popular ways of specifying the location of a celestial object. The first is what you would probably use to point out a star to your friend: the altitude-azimuth system. The altitude of a star is how many degrees above the horizon it is (anywhere from 0 to 90 degrees). The azimuth of a star is how many degrees along the horizon it is and correspond to the compass directions.

Azimuth starts from due North = 0 degrees azimuth and increases eastwards: due East = 90 degrees, due South = 180 degrees, due West = 270 degrees, and due North = 360 degrees = 0 degrees. However, since a star changes its apparent position throughout the night, its altitude and azimuth change. Also, observers at different locations looking at the same star at the same time will see it at a different altitude-azimuth position.

The second way of specifying star positions is the equatorial co-ordinate system, which is very similar to the longitude-latitude system used to specify positions on the Earth's surface. This system is fixed with respect to the stars so, unlike the altitude-azimuth system, a star's position does not depend on the observer's location or time. Because of this astronomers prefer using this system. You will find this system used in astronomy magazines and in most sky simulation computer software.

Selecting the image link will bring up a short animation of a spinning celestial sphere.

The lines on a map of the Earth that run north-south are longitude; the analogous celestial reference is lines of right ascension. Right ascension (RA) is measured in hours, minutes, and seconds, instead of degrees, and increases in an easterly direction on the sky. Zero RA is where the Sun crosses the celestial equator at the vernal equinox. The full 360 degrees circle is broken up into 24 hours, so one hour of RA = 15 degrees. The lines of RA all converge at the celestial poles, so two stars one hour of RA apart will not necessarily be 15 degrees in angular separation on the sky (only if they are on the celestial equator will they be 15 degrees apart).

The lines on a map of the Earth that run east-west parallel to the equator are lines of latitude; when projected onto the sky, they become lines of declination. Like the latitude lines on Earth, declination (Dec) is measured in degrees away from the celestial equator, positive for objects north of the celestial equator and negative for objects south of the celestial equator. Objects on the celestial equator are at 0 degrees dec, objects half-way to the NCP are +45 degrees, objects at the NCP are +90 degrees, and objects at the SCP are -90 degrees. Polaris's position is RA 2hr 31min, Dec +89 degrees 15 arcmin.

An effect called precession causes the vernal equinox to shift slowly westward over time, so a star's RA and Dec will slowly change (by about 1.4 degrees every century). This precession is caused by the Sun and Moon gravitationally pulling on the Earth's equatorial bulge, to reduce the tilt of the Earth's axis with respect to the ecliptic and lunar orbit plane. Like a rapidly-spinning top, the Earth responds by slowly rotating its rotation axis, with a period of 26,000 years.

This motion was first recorded by Hipparchus in 100 BC; he noticed differences between ancient Babylonian observations and his own. When the Babylonians were the world power, in 2000 BC, the vernal equinox was in the constellation Aries and the star Thuban (in Draco) was the closest bright star to the NCP. At the time of Jesus Christ the vernal equinox had shifted to the constellation Pisces and the star Kochab (in the bowl of the Little Dipper) was the closest bright star to the NCP. Now the star Polaris is close to the NCP and the vernal equinox is close to the border between Pisces and Aquarius (in 2600 AD it will officially be in Aquarius) -- a popular song of some years ago refers to 'this is the dawning of the Age of Aquarius'. In the year 10,000 AD, the bright star in the tail of Cygnus, Deneb, will be the pole star and Vega (in Lyra) will get its turn by the year 14,000 AD.

Star Chart sites

(These sites are in the US and may load slowly.)

1. National Geographic Society's Star Chart with Hubble image enhancements. Select a particular section of the sky on the image map. Locations of objects imaged by Hubble are hyper-linked on the section you selected. The grid lines are lines of right ascension and declination.
2. Interactive Star Chart. Choose a constellation as your starting point for this viewer of the skies. Your browser must be java-enabled.

Formulae

• Altitude varies from 0 to 90°. Vertical position of object.
• Azimuth varies from 0° to 360°. Due N = 0°, due E = 90°, due S = 180°, due W = 270°. Horizontal position of object.
• Right ascension varies from 0 to 24 hours. Horizontal position of object.
• Declination varies from -90° (at SCP) to +90° (at NCP). Celestial equator declination = 0°.
• Meridian altitude of any object = 90 - (observer's latitude) + declination degrees. If declination is negative, then addition of declination becomes a subtraction.

Formulae for Sun's position

• Ecliptic tilted by 23.5° with respect to the celestial equator.
• Sun's declination ranges between -23.5° and +23.5°.
• Vernal equinox right ascension = 0 hours; declination = 0°; Sun rises at 90deg; azimuth and sets at 270° azimuth.
• June solstice right ascension = 6 hours; declination = +23.5°; Sun rises at less than 90° azimuth and sets at greater than 270° azimuth.
• Autumnal equinox right ascension = 12 hours; declination = 0°; Sun rises at 90° azimuth and sets at 270° azimuth.
• December solstice right ascension = 18 hours; declination = -23.5° Sun rises at greater than 90° azimuth and sets at less than 270° azimuth.
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