THE CELESTIAL SPHERE

Key Concepts

The sky as seen from Earth is divided into 88 constellations .
It's convenient to imagine that the stars are attached to a celestial sphere.
Positions of stars are measured relative to the celestial poles and celestial equator.
East and West of the Sun

(1) The sky as seen from Earth is divided (for fairly arbitrary historical reasons) into 88 constellations.

Imagine you are outside on a clear, cloudless night, looking up at the stars. The stars form distinct patterns, the same from one night to the next. Traditionally, the stars we can see from Earth have been grouped together into different constellations.

The oldest known constellations (Leo, Taurus, and Scorpius) are mentioned on cuneiform tablets from Mesopotamia, dating to the earliest days of writing, ca. 3000 BC. In the 2nd century AD, the Greek astronomer Ptolemy made a list of 48 constellations, mainly in the northern sky. During the 16th to 18th centuries, European astronomers, traveling in the southern hemisphere, filled the remaining sky with constellations, making a total of 88 altogether.

The constellations are largely arbitrary. Different cultures have adopted different constellations. Consider, for example, the stars that make up the Big Dipper. The Big Dipper is not an official constellation; in the list of 88 constellations sanctioned by the International Astronomical Union, it is part of the constellation Ursa Major, representing the rump and implausibly long tail of a celestial bear. To the ancient Egyptians, the Big Dipper represented the leg of a bull; to the Chinese, it was a grain measure; to medieval Germans, it was a wagon; to the Mayans it was a macaw; and so on.

Not only are the patterns of stars we see given arbitrary names which differ from culture to culture, the actual patterns of stars that we see are an accident of where we are in space. For instance, the stars in the Big Dipper are at very different distances from the Sun. The closest star in the Big Dipper, known as Alioth, is a mere 60 light years away, while the most distant, named Alkaid, is 210 light years away. Someone viewing the stars of the Big Dipper from a different angle would not see a dipper shape at all. The patterns of stars we see in the sky depend on when we view them, as well as where we view them from. The stars in our galaxy move slowly with respect to each other. Although we see basically the same constellations that Ptolemy did 18 centuries ago, over time scales of 100,000 years or more the slow drifting of the stars distorts the shapes of the constellations. 100,000 years ago, the Big Dipper looked like a Big Spear. 100,000 years from now, it will look like a Big Nothing-In-Particular.

(2) It's convenient to imagine that the stars are attached to a celestial sphere.

As you look up at the constellations, it is impossible to tell, using only your unaided eyes, how far away the stars are. A particular point of light might be a very bright star 1000 light years away, a dimmer star 10 light years away, or a planet only a few astronomical units away. For convenience in computing the motions of the stars and planets, it is convenient to pretend that the stars are all at the same distance, attached to the celestial sphere, an imaginary sphere centered on the Earth, with a radius much larger than the Earth's radius. (Ancient astronomers believed that the celestial sphere was real; we now know that the stars are all at different distances from Earth, and are moving through interstellar space.)

To calculate the positions of stars on the celestial sphere, it is important to have landmarks. Important landmarks on the celestial sphere are:

North Celestial Pole: the point on the celestial sphere directly above the Earth's North Pole. The star Polaris is very close to the North celestial pole.
South Celestial Pole: the point on the celestial sphere directly above the Earth's South Pole. There don't happen to be any bright stars close to the South celestial pole.
Celestial Equator: the circle on the celestial sphere directly above the Earth's Equator.

The distance of a star relative to another star, or relative to the North Celestial Pole, or relative to another landmark on the celestial sphere, is an angle measured in degrees, arcminutes, and arcseconds.

Interpolated note: Measuring angles

360 degrees in a circle
60 arcminutes in a degree
60 arcseconds in an arcminute
Therefore, 60 x 60 x 360 = 1,296,000 arcseconds in a full circle

(3) Positions of stars are measured relative to the celestial poles and the celestial equator.

In order to plot the positions of stars accurately, we need a coordinate system on the the celestial sphere. The problem of building a coordinate system on the surface of a sphere has already been solved, since we live on the surface of a spherical object, called the Earth. The location of any point on the Earth's surface can be specified using two numbers:

(1) Latitude: angle north or south of the Equator.
(2) Longitude: angle east or west of the prime meridian, which runs, by international agreement, through Greenwich, England.

The latitude of Medina is 40 degrees north of the equator. The longitude of Medina is 83 degrees west of Greenwich, England. The position of any point on the Earth's surface is uniquely specified by its latitude and longitude, as shown below in the case of Columbus.

[Image credit: Richard Pogge]

Similarly, the position of any star on the celestial sphere is uniquely specified by the celestial equivalent of latitude and longitude.

(1) ``Celestial Latitude'': angle north or south of the Celestial Equator.
(2) ``Celestial Longitude'': angle east or west of the celestial prime meridian, which runs, by international agreement, through the Vernal Equinox (in the constellation Pisces).

The ``celestial latitude'' is referred to by astronomers as ``declination'' and the ``celestial longitude'' is called ``right ascension''. The illustration below shows a star which lies on the celestial meridian and has a declination of 45 degrees; that is, it's 45 degrees north of the Celestial Equator.

(4) East and West on the Celestial Sphere

It is useful to define east and west directions on the celestial sphere, as illustrated in the following figure.

Thus, objects to the west of the Sun on the celestial sphere precede the Sun in the diurnal motion of the celestial sphere (they "rise" before the Sun and "set" before the Sun). Likewise, objects to the east of the Sun trail the Sun in the diurnal motion (they "rise" after the Sun and "set" after the Sun). Generally, one object is west of another object if it "rises" before the other object over the eastern horizon as the sky appears to turn, and east of the object if it "rises" after the other object.

updated: