The celestial sphere

Although the ability to measure distances to celestial objects is a relatively recent development in astronomy, the actual positions of the stars in the night sky have been defined and recorded on maps for thousands of years. Irrespective of whether a star is 1 or 1,000 parsecs from earth, its position can be pinpointed on an imaginary sphere surrounding the earth— the celestial sphere.
The concept of a star-studded celestial sphere was designed to enable the positions of the stars to be located in the same way that positions on earth are defined, in terms of latitude and longitude. The imaginary celestial sphere is divided into a grid system that corresponds directly to the terrestrial grid of lines of latitude and longitude. In the astronomical system, however, the two coordinates are right ascension (abbreviated to RA), equivalent to celestial longitude, and declination, equivalent to celestial latitude. These coordinates are measured with respect to an imaginary celestial equator, which is the extension into space of the earth’s equator. Similarly, the celestial poles are extensions of the earth’s axis and lie, therefore, directly above the earth’s true North and South poles. Thus a star on the celestial equator has a declination of 0°. Just as the earth’s North Pole has a latitude of 90° N, Polaris (the polestar), located almost exactly at the north celestial pole, has a declination of about 90° N.
The ecliptic (an imaginary circle on the celestial sphere) represents the plane of the earth’s orbit around the sun. Because the earth’s axis is inclined at an angle of 23.44° to the plane of the ecliptic, the celestial equator is also inclined by 23.44° to the ecliptic. The celestial equator and the ecliptic meet at two opposite points, which mark the equinoxes. The sun rises at one of these points (the vernal, or spring, equinox, also called the First Point of Aries), on March 20 or 21, and at the other (the autumnal equinox, or the First Point of Libra) on September 22 or 23.
Just as the terrestrial longitude system needs a zero point, so does the celestial sphere, from which all measurements of right ascension can be made. The earth’s was arbitrarily chosen, and internationally agreed upon in 1884, to be the Greenwich meridian. The celestial sphere’s point was defined—in a similarly arbitrary way—by the ancient Greeks, who chose the vernal equinox as the zero point of right ascension, a system that has remained unchanged to this day.

Instead of measuring right ascension in degrees, it is usually expressed in terms of hours, minutes, and seconds, so that the position of a star is related to its apparent motion across the sky. Thus, the imaginary lines of right ascension on the celestial sphere are spaced at intervals of one hour.
The declination of a heavenly body is measured in degrees north (designated by a plus sign) or south (designated by a minus sign) of the celestial equator—in the same way that latitude on earth is measured relative to the terrestrial equator.

n the celestial sphere the lines of right ascension—the astronomical equivalent of terrestrial longitude—are spaced one hour apart, each interval corresponding to 15° of a circle. This system is used because, to an observer on earth, the imaginary celestial sphere appears to rotate through a complete 360° circle every 24 hours. Thus, it revolves through 15° every hour. The zero point of right ascension is the vernal equinox, one of the two equinoctial points at which the celestial equator crosses the ecliptic. The right ascension coordinate of a celestial body can be measured in degrees but is more usually expressed in hours and minutes. The other celestial coordinate, declination, is measured in degrees north (denoted by 4-) or south (denoted by —) of the celestial equator. Thus A in the illustration has a right ascension of about 4 hours and a declination of about 4-25°

Star time

As a result of dividing the celestial sphere into hours of right ascension (one hour being the time taken for one hour of right ascension to pass overhead), the time-keeping system used to locate a star is governed by the positions of the stars on the celestial sphere rather than by the position of the sun in the sky.
The movements of the sun and stars are solely apparent motions caused by the rotation of the earth about its axis. Nevertheless, the star day (called the sidereal day) is slightly shorter than the normal solar day. This is a result of the earth’s yearly orbit around the sun. By the time a day has passed, the earth has moved through of its orbit, which is equivalent to a time period of 3 minutes, 56 seconds. Thus, a solar day is this length of time longer than a sidereal day. Astronomers use sidereal time because it gives the right ascension of a celestial object, without the need to compensate for the longer solar day.

The ecliptic and precession

Slight variations in the mutual gravitational attraction between the sun, moon, and earth cause small perturbations in the movement of the earth. This, in turn, affects the celestial coordinate system. The most marked of the perturbations is known as procession. Analogous to the circular motion of the spindle of a spinning top, procession is a periodic, slow, continuous rotation of the earth’s axis; it takes 25,800 years for the axis to complete one cycle. At present the earth’s axis points toward Polaris but, as the axis precedes, it will point to other stars. Eventually, in 25,800 years time, it will again point to Polaris.
Because of procession of the earth’s axis, the relationship between the celestial equator and the ecliptic also changes over a period of 25,800 years. During this cycle the positions of the equinoctial points relative to the ecliptic slowly change, moving through successive signs of the zodiac. A few thousand years ago, the vernal equinox (the zero point for measuring right ascension) was in the constellation of Aries, but today it is in Pisces and is slowly approaching the next sign, Aquarius. Thus procession affects the celestial coordinates of heavenly bodies. This means that in addition to giving the right ascension and declination of a star, the date on which the star had these coordinates must also be given to enable the star to be located precisely.

Observing the stars

Because of the earth’s rotation, the celestial sphere also rotates about its axis, with the result that the stars appear to rise and set at different angles from different parts of the earth. On the equator, the stars rise perpendicularly to the horizon. Moreover, all stars, irrespective of their declination, can be seen during the course of the year; Polaris appears just above the horizon. At the terrestrial North Pole, however, only stars with northern declination are visible, Polaris being directly overhead. In middle latitudes, the stars appear to rise obliquely from the horizon and some the circumpolar stars never rise or set, but follow circular paths around the celestial poles.

A sundial makes use of the sun’s apparent motion across the celestial sphere (caused by the earth’s 24-hourly rotation about its axis). In this portable eighteenth-century example, the inclination of the horseshoe-shaped dial can be altered to match the instrument’s latitude.