1.3 Earth’s Orbital Motion

DAY-TO-DAY CHANGES

Figure 1.10 Solar and Sidereal Days The difference between a solar and a sidereal day can be easily explained once we understand that 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 one year (365 days), it moves through nearly 1° in one day. Thus, between noon at point A on one day and noon at the same point the next day, Earth actually rotates through about 361°. Consequently, the solar day exceeds the sidereal day (360° rotation) by about four minutes. Note that the diagram is not drawn to scale, so the true 1° angle is in reality much smaller than shown here.

We measure time by the Sun. Because the rhythm of day and night is central to our lives, it is not surprising that the period of time from one noon to the next, the 24-hour solar day, is our basic social time unit. The daily progress of the Sun and the other stars across the sky is known as diurnal motion. As we have just seen, it is a consequence of Earth’s rotation. But the stars’ positions in the sky do not repeat themselves exactly from one night to the next. Each night, the whole celestial sphere appears to be shifted a little relative to the horizon, compared with the night before. The easiest way to confirm this difference is by noticing the stars that are visible just after sunset or just before dawn. You will find that they are in slightly different locations from those of the previous night. Because of this shift, a day measured by the stars—called a sidereal day after the Latin word sidus, meaning "star"—differs in length from a solar day. Evidently, there is more to the apparent motion of the heavens than simple rotation.

The reason for the difference between a solar day and a sidereal day is sketched in Figure 1.10. It is a result of the fact that Earth moves in two ways simultaneously: It rotates on its central axis while at the same time revolving around the Sun. Each time Earth rotates once on its axis, it also moves a small distance along its orbit about the Sun. Earth therefore has to rotate through slightly more than 360° (360 degrees—see More Precisely 1-1) for the Sun to return to the same apparent location in the sky. Thus, the interval of time between noon one day and noon the next (a solar day) is slightly greater than one true rotation period (one sidereal day). Our planet takes 365 days to orbit the Sun, so the additional angle is 360°/365 = 0.986°. Because Earth, rotating at a rate of 15° per hour, takes about 3.9 minutes to rotate through this angle, the solar day is 3.9 minutes longer than the sidereal day (that is, one sidereal day is roughly 23^h56^m long).

For more on astronomical timekeeping, and for a working definition of the mean solar day, the time measured by our clocks, consult More Precisely 1-3.

SEASONAL CHANGES

Figure 1.11(a) illustrates the major stars visible from most locations in the United States on clear summer evenings. The brightest stars—Vega, Deneb, and Altair—form a conspicuous triangle high above the constellations Sagittarius and Capricornus, which are low on the southern horizon. In the winter sky, however, these stars are replaced as shown in Figure 1.11(b) by several well-known constellations that include Orion, Leo, and Gemini. In the constellation Canis Major lies Sirius (the Dog Star), the brightest star in the sky. Year after year, the same stars and constellations return, each in its proper season. Every winter evening, Orion is high overhead; every summer, it is gone. (For more detailed maps of the sky at different seasons, consult the star charts at the end of the book.)

These regular seasonal changes occur because of Earth’s revolution around the Sun: Earth’s darkened hemisphere faces in a slightly different direction in space each evening. The change in direction is only about 1° per night (Figure 1.10)—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 1.12. After six months, Earth has reached the opposite side of its orbit, and we face an entirely different group of stars and constellations at night. Because of this motion, the Sun appears (to an observer on Earth) to move relative to the background stars over the course of a year. This apparent motion of the Sun on the sky traces out a path on the celestial sphere known as the ecliptic.

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.

As illustrated in Figure 1.13(a), the ecliptic forms a great circle on the celestial sphere, inclined at an angle of 23.5° to the celestial equator. In reality, as illustrated in Figure 1.13(b), the plane of 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.

	Figure 1.13 Seasons (a) The apparent path of the Sun on the celestial sphere and (b) its actual relation to Earth’s rotation and revolution. The seasons result from the changing height of the Sun above the horizon. At the summer solstice (the points marked 1), the Sun is highest in the sky, as seen from the Northern Hemisphere, and the days are longest. In the "celestial sphere" figure (part a), the Sun is at its northernmost point on its path around the ecliptic; in reality (b), the summer solstice corresponds to the point on Earth’s orbit where our planet’s North Pole points most nearly toward the Sun. The reverse is true at the winter solstice (point 3). At the vernal and autumnal equinoxes, day and night are of equal length. These are the times when, as seen from Earth (a), the Sun crosses the celestial equator. They correspond to the points in Earth’s orbit when our planet’s axis is perpendicular to the line joining Earth and Sun (b).

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"). As shown in Figure 1.13, 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, points north of the equator spend the greatest fraction of their time in sunlight on that date, so the summer solstice corresponds to the longest day of the year in the Northern Hemisphere and the shortest day in the Southern Hemisphere.

Six months later, the Sun is at its southernmost point, or the winter solstice (December 21)—the shortest day in the Northern Hemisphere and the longest in the Southern Hemisphere. These two effects—the height of the Sun above the horizon and the length of the day— combine to account for the seasons we experience. In summer in the Northern Hemisphere, the Sun is high in the sky and the days are long, so 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 the Northern Hemisphere), as the Sun crosses from the Northern into the Southern Hemisphere, we have the autumnal equinox (on September 21). The vernal equinox occurs in northern spring, on or near March 21, as the Sun crosses the celestial equator moving north. Because of its association with the end of winter and the start of a new growing season, the vernal equinox was particularly important to early astronomers and astrologers. It also plays an important role in human timekeeping. The interval of time from one vernal equinox to the next—365.242 mean solar days (see More Precisely 1-3)—is known as one tropical year.

LONG-TERM CHANGES

Figure 1.14 Precession (a) Earth’s axis currently points nearly toward the star Polaris. About 12,000 years from now—nearly halfway through one cycle of precession—Earth’s axis will point toward a star called Vega, which will then be the "North Star." Five thousand years ago, the North Star was a star named Thuban in the constellation Draco. (b)The dashed circle shows the precessional path of the north celestial pole among some prominent Northern stars. Tick marks indicate intervals of 1000 years.

Earth has many motions—it spins on its axis, it travels around the Sun, and it moves with the Sun through our Galaxy. We have just seen how some of these motions can account for the changing nighttime sky and the changing seasons. In fact, the situation is even more complicated. Like a spinning top that rotates rapidly on its own axis while that axis slowly revolves about the vertical, Earth’s axis changes its direction over the course of time (although the angle between the axis and a line perpendicular to the plane of the ecliptic always remains close to 23.5°). Illustrated in Figure 1.14, this change is called precession. It is caused by torques (twisting forces) on Earth due to the gravitational pulls of the Moon and the Sun, which affect our planet in much the same way as the torque due to Earth’s own gravity affects the top. During a complete cycle of precession—about 26,000 years —Earth’s axis traces out a cone.

The time required for Earth to complete exactly one orbit around the Sun, relative to the stars, is called a sidereal year. One sidereal year is 365.256 mean solar days long—about 20 minutes longer than a tropical year. The reason for this slight difference is Earth’s precession. Recall that the vernal equinox occurs when Earth’s rotation axis is perpendicular to the line joining Earth and Sun, and the Sun is crossing the celestial equator moving from south to north. In the absence of precession, this would occur exactly once per sidereal orbit, and the tropical and sidereal years would be identical. However, because of the slow precessional shift in the orientation of Earth’s rotation axis, the instant when the axis is next perpendicular to the line from Earth to the Sun occurs slightly sooner than we would otherwise expect. Consequently, the vernal equinox drifts slowly around the zodiac over the course of the precession cycle.

The tropical year is the year that our calendars measure. If our timekeeping was tied to the sidereal year, the seasons would slowly march around the calendar as Earth precessed—13,000 years from now, summer in the Northern Hemisphere would be at its height in late February! By using the tropical year, we ensure that July and August will always be (northern) summer months. However, in 13,000 years’ time, Orion will be a summer constellation.

Concept Check

In astronomical terms, what are "summer" and "winter," and why do we see different constellations during those seasons?