Content

Celestial Sphere

When we look at the sky, it is difficult to tell how far the stars are. It seems that all the stars lie on a "flat" surface. A similar situation is watching television, the screen of the television represents the three dimensional world.

Everyone knows that the Sun rises from the east and sets in the west. Less well known is that almost everything on the sky, including the Moon, planets and most of the stars, also rises from the east and sets in the west. This is the major movement of objects on the sky and it is due to the rotation of the Earth. We could imagine that the Earth is at the center of a large sphere, called the celestial sphere and the Sun, stars, etc. are located on the sphere. Because the Earth is rotating from the west to the east, everything on the celestial sphere will apparently move from the east to the west. This is why the Sun rises from the east. From the picture, we can see that those stars near the north celestial pole never set. We call them circumpolar stars. One of the circumpolar star, called Polaris, is special because it is very near the north celestial pole. Thus, it appears to be stationary.

The sky "surrounds" us from all directions. We placed ourselves at the center of an imaginary sphere, the celestial sphere. Everything on the sky will appear on the celestial sphere. The celestial sphere does not follow the rotation of the Earth. Thus, stars are fixed on the celestial sphere. The truth is that some stars do move on the celestial sphere. We call this the proper motion of stars. Usually, proper motion of a star is very small and can only be detected if we observe the star for decades.

There is one important exception however. The Sun is also a star, but the Sun does move on the celestial sphere because the Earth revolves around it. It moves from west to east, and completes a full circle in a year. The path that the Sun traces out on the celestial sphere is called the ecliptic.

The ecliptic forms a great circle on the celestial sphere, inclined at an angle of about 23.5° to the celestial equator. In reality, as illustrated in Figure 1.2(b), the plane defined by the ecliptic is the plane of Earth's orbit around the Sun. Its tilt is a consequence of the inclination of our planet's rotation axis to its orbital plane.

The point on the ecliptic where the Sun is at its northernmost point above the celestial equator is known as the summer solstice (from the Latin words sol, meaning "sun," and stare, "to stand"). It represents the point in Earth's orbit where our planet's North Pole points closest to the Sun. This occurs on or near June 21—the exact date varies slightly from year to year because the actual length of a year is not a whole number of days. As Earth rotates on that date, points north of the equator spend the greatest fraction of their time in sunlight, so the summer solstice corresponds to the longest day of the year in Earth's Northern Hemisphere and the shortest day in Earth's Southern Hemisphere. Six months later, the Sun is at its southernmost point below the celestial equator, and we have reached the winter solstice (December 21)—the shortest day in Earth's Northern Hemisphere and the longest in the Southern Hemisphere. These two effects—the height of the Sun above the celestial equator and the length of the day—combine to account for the seasons we experience. In northern summer, the Sun is high in the sky and the days are long, with the result that temperatures are generally much higher than in winter, when the Sun is low and the days are short.

The two points where the ecliptic intersects the celestial equator are known as equinoxes . On those dates, day and night are of equal duration. (The word equinox derives from the Latin for "equal night.") In the fall (in Earth's northern hemisphere), as the Sun crosses from the northern into the southern celestial hemisphere, we have the autumnal equinox (on September 21). The vernal equinox occurs in spring, on or near March 21, as the Sun crosses the celestial equator moving north. The vernal equinox plays an important role in human time keeping. The interval of time from one vernal equinox to the next—365.242 solar days—is known as one tropical year.

Although the stars are fixed the stars' positions in the sky do not repeat themselves exactly from one night to the next. Each night, the whole celestial sphere appears shifted a little compared with the night before. To understand this shift we make a distinction in time measurements. A solor day is the period of time between the instant when the Sun is directly overhead (i.e. at noon) to the next time it is directly overhead. It is this time we use in our day to day lives for one day of 24 hours. However the Earth revolves around the Sun at the same time as it rotates on its axis. A solar day is the time from one noon to the next. In that time, Earth also moves a little in its solar orbit. Because Earth completes one circuit (360°) around the Sun in 1 year (365 days), it moves through nearly 1° in 1 day. Thus, between noon at point A on one day and noon at the same point the next day, Earth rotates through about 361°. Thus, the interval of time between noon one day and noon the next (a solar day) is slightly greater than the true rotation period. This true rotation period is the time required for the Earth to rotate exactly once, relative to the stars. This time is called a sideral day. The additional angle is 360°/365 = 0.986°. Because Earth takes about 3.9 minutes to rotate through this angle, the solar day is 3.9 minutes longer than the sidereal day.

Because Earth revolves around the Sun, our planet's darkened hemisphere faces in a slightly different direction each night. The change in direction is only about 1° per night (Figure 1.1)—too small to be easily noticed with the naked eye from one evening to the next but clearly noticeable over the course of weeks and months, as illustrated in Figure 1.3. In 6 months, Earth moves to the opposite side of its orbit, and we face an entirely different group of stars and constellations at night. The 12 constellations through which the Sun passes as it moves along the ecliptic—that is, the constellations we would see looking in the direction of the Sun if they weren't overwhelmed by the Sun's light—had special significance for astrologers of old. These constellations are collectively known as the zodiac .