Equinoxes and solsticesAs we saw on Figure 1-6, the ecliptic and the celestial equator are different circles tilted 23½° with respect to each other on the celestial sphere. This occurs because Earth’s rotation axis is tilted 23½° away from a line perpendicular to the ecliptic (Figure 1-14 and see Figure 1-7). These two circles intersect at only two points, which are exactly opposite each other on the celestial sphere (Figure 1-15 and see Figure 1-6a). Each of these two points is called an equinox. Recall from Section 1-5 that on these two days, the Sun is directly over Earth’s equator, resulting in 12 hours of daytime and 12 hours of nighttime everywhere on Earth on that day.

Except for tiny changes each year, Earth maintains this tilted orientation as it orbits the Sun. Therefore, Polaris is above the North Pole throughout the year. For half the year, the northern hemisphere is tilted toward the Sun, and as a result, the Sun rises higher in the northern hemisphere’s sky than it does during the other half of the year (Figure 1-16). Equivalently, when the southern hemisphere is tilted toward the Sun, the Sun rises higher in the southern hemisphere’s sky.

Consider the location of the Sun throughout the year as seen from the northern hemisphere. The day that the Sun rises farthest south of east is around December 22 each year (see Figure 1-16a) and is called the winter solstice. The winter solstice is the point on the ecliptic farthest south of the celestial equator (see Figure 1-15). It is also the day when the Sun rises to the lowest height at noon (Figure 1-16a), and it signals the day of the year in the northern hemisphere with the fewest number of daylight hours.

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As the Sun moves along the ecliptic after the winter solstice, it rises earlier, is more northerly on the eastern horizon, and it passes higher in the sky at midday than it did on preceding days. Three months later, around March 20, the Sun crosses the celestial equator heading northward. As noted in Section 1-5, this is called the vernal equinox and is one of the two days on which the Sun rises due east and sets due west (Figure 1-16b). The vernal equinox is the “prime meridian” of the celestial sphere. Three months after the vernal equinox, around June 21, the Sun rises farthest north of east and passes highest in the sky (Figure 1-16c). This is the summer solstice (see Figure 1-15), the day of the year in the northern hemisphere with the most daylight.

Each day from June 21 through December 21, the Sun rises farther south than it did the preceding day. Its highest point in the sky is lower each succeeding day—the cycle of the previous 6 months reverses. The autumnal equinox occurs around September 22 (Figure 1-16d), with the Sun heading southward across the celestial equator, as seen from Earth.

The seasonsThe higher the Sun rises during the day, the more daylight hours there are. During the days with longer periods of daylight, more light and heat from the Sun strike that hemisphere. Furthermore, when the Sun is higher in the sky, its energy is more concentrated on Earth’s surface (see the footprint that the “cylinder of light” from the Sun makes in Figure 1-16a–d). Thus, during these days more energy is deposited on each square meter of the surface, thereby warming the surface more than when the Sun is lower in the sky. The temperature and, hence, the seasons are determined by the duration of daylight at any place and the height of the Sun in the sky there. (Bear in mind that winds and clouds greatly affect the weather throughout the year—we ignore these effects here.)

To summarize, the Sun is lowest in the northern sky on the winter solstice. This marks the beginning of winter in the northern hemisphere. As the Sun moves northward, the amount of daylight and heat deposited increases daily. The vernal equinox marks a midpoint in the amount of light and heat from the Sun onto the northern hemisphere and is the beginning of spring. When the Sun reaches the summer solstice, it is highest in the northern sky and is above the horizon for the most hours of any day of the year. This is the beginning of summer. Returning southward, the Sun crosses the celestial equator once again on the autumnal equinox, the beginning of fall.

Earth is closest to the Sun on or around January 3 of each year—the dead of winter in the northern hemisphere! While the distance between Earth and the Sun changes by 5 million km (3 million mi) throughout the year, this 3% variation in distance, and hence energy deposited from the Sun, is not great enough to cause the seasons; it has only a minor effect on them.

The Sun’s path across the skyDuring the northern hemisphere’s summer months, when the northern hemisphere is tilted toward the Sun (see Figure 1-14), the Sun rises in the northeast and sets in the northwest. The Sun provides more than 12 hours of daylight in the northern hemisphere and passes high in the sky. At the summer solstice, the Sun is as far north as it gets, giving the greatest number of daylight hours to the northern hemisphere (Figure 1-16c).

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During the northern hemisphere’s winter months, when the northern hemisphere is tilted away from the Sun, the Sun rises in the southeast. Daylight lasts for fewer than 12 hours, as the Sun skims low over the southern horizon and sets in the southwest. Night is longest in the northern hemisphere when the Sun is at the winter solstice (Figure 1-16a).

The Sun’s maximum angle above the southern horizon is different at different latitudes. The farther north you are, the lower the Sun is in the sky at any time of day than it is on that day at more equatorial locations. At latitudes above 66½° north latitude or below 66½° south latitude, the Sun does not rise above the horizon at all during parts of their fall and winter months. During their spring and summer months, those same regions of Earth have continuous sunlight for weeks or months (Figure 1-17) because the Sun is then circumpolar; hence, the name “Land of the Midnight Sun.”

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The Sun takes 1 year to complete a trip around the ecliptic (as noted above, this motion is actually caused by Earth’s orbit around the Sun). Since there are about 365¼ days in a year and 360° in a circle, the Sun appears to move along the ecliptic at a rate of slightly less than 1° per day. The constellations through which the Sun moves throughout the year as it travels along the ecliptic are called the zodiac constellations. We cannot see the stars of these constellations when the Sun is among them (see Figure 1-13), but we can plot the Sun’s path on the celestial sphere to determine through which constellations it moves. Traditionally, there were 12 zodiac constellations whose borders were set in antiquity. Recall from Section 1-3 that in 1930 the boundaries of the constellations were redefined by astronomers. As a result the Sun now moves through 13 constellations throughout the year. (The thirteenth zodiac constellation is Ophiuchus, the Serpent Holder. The Sun passes through Ophiuchus from December 1 to December 19 each year.) Table 1-1 lists all the zodiac constellations and the dates the Sun passes through them. You may not have the “sign” that you think you have.

The Sun’s daily motion through the sky provided our distant ancestors’ earliest reference for time because the Sun’s location determines whether it is day or night and roughly whether it is before or after midday. The Sun’s motion through the sky came to determine the length of the solar day, upon which our 24-hour day is based. Ideally, this is the interval of time between when the Sun is highest in the sky on one day until the time it is highest in the sky on the next day. However, the length of the solar day actually varies throughout the year, up to 30 seconds per day. This occurs because Earth’s orbit around the Sun is not perfectly circular—our planet’s speed along the ecliptic increases as we approach the Sun and it decreases as we move away from it—and because Earth’s rotation axis is tilted 23½° from being perpendicular to the ecliptic. These two effects change the apparent speed of the Sun across the sky from day to day. The average time interval between consecutive noontimes throughout the year is 24 hours, which determines the time we use on our clocks. This is called the mean (or average) solar day.

Along with the solar day, there is also a sidereal day, the length of time from when any star is in one place in the sky until it is next in the same place. The solar and sidereal days differ from each other in length because while Earth rotates, it also revolves around the Sun. This motion of Earth in its orbit day by day changes the location of the stars, bringing them back to their original positions 4 minutes earlier each day, as noted in Section 1-6. Therefore, the sidereal day is 23 hours, 56 minutes, 4 seconds long, while the solar day is 24 hours long (Figure 1-18).

Just as the day is caused by Earth’s rotation, the year is the unit of time based on Earth’s revolution about the Sun. As noted earlier, Earth does not take exactly 365 days to orbit the Sun, so the year is not exactly 365 days long. Basing the year on a 365-day cycle led to important events (such as holidays) occurring on the wrong day. To resolve this problem, Roman statesman Julius Caesar implemented a new calendar in the year 46 b.c.e. Because measurement revealed to ancient astronomers that the length of a year is approximately 365¼ days, this “Julian” calendar established a system of leap years to accommodate the extra quarter of a day. By adding an extra day to the calendar every 4 years, Caesar hoped to ensure that seasonal astronomical events, such as the beginning of spring, would occur on the same date year after year.

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The Julian calendar would have worked just fine if a year were exactly 365¼ days long and if Earth’s rotation axis (currently pointing toward Polaris, as discussed earlier) never changed direction. However, neither assumption is correct. Thus, over time, a discrepancy accumulated between the calendar and the actual time—astronomical and cultural events continued to fall on different dates each year. To straighten things out, a committee established by Pope Gregory XIII recommended a refinement, thus creating the Gregorian calendar in 1582. In the Gregorian system, which we use today, we have a leap year every four years with the exception that century years are leap years only if evenly divisible by 400. For example, the years 1700, 1800, and 1900 were not leap years under the improved Gregorian system. But the year 2000—which can be divided evenly by 400—was a leap year. The Gregorian system assumes that the year is 365.2425 mean solar days long, which is very close to the length of the tropical year, defined as the time interval from one vernal equinox to the next. In fact, the error is only 1 day in every 3300 years. That will not cause any problems for a long time.

As just noted above, the orientation of Earth’s axis of rotation changes slightly with respect to the celestial sphere (that is, it “points” in a slightly different direction over time). While this change is small over our lifetimes, it eventually causes the north celestial pole to drift away from Polaris. This major change in orientation is caused by gravitational forces from the Moon and the Sun pulling on the slight bulge at Earth’s equator created by Earth’s rotation—our planet’s diameter is about 43 km (27 mi) greater at the equator than from pole to pole. Gravitation (gravity) is the universal force of attraction between all matter. The strength of the gravitational force between two objects depends on the amounts of mass the objects have and the distance between them, as we explain in more detail in Chapter 2.

Because of Earth’s tilted axis of rotation, the Sun and Moon are usually not located directly over Earth’s equator. As a result, their gravitational attractions on Earth’s equatorial bulge provide forces that pull the bulge toward them (Figure 1-19a). However, Earth does not respond to these forces from the Sun and Moon by tilting so that its equator is closest to them. Instead, Earth maintains the same tilt (23½° from the ecliptic), but the direction in which its axis of rotation points on the celestial sphere changes—a motion called precession. This is exactly the same behavior exhibited by a spinning top (Figure 1-19b). If the top were not spinning, gravity would pull it over on its side. But when it is spinning, the combined actions of gravity and rotation cause the top’s axis of rotation to precess or wobble in a circular path. As with the toy top, the combined actions of gravity from the Sun and the Moon plus rotation cause Earth’s axis to trace a circle in the sky while remaining tilted about 23½° away from the ecliptic.

In the mid-1990s, astronomers simulated the behavior of Earth and discovered that without a large moon, Earth would not keep to a 23½° tilt, but rather would change its angle relative to the ecliptic dramatically over millions of years. Therefore, while being a major cause of precession, the Moon plays a crucial role in stabilizing Earth and maintaining the seasons as we know them.

Earth’s rate of precession is slow compared to human timescales. It takes about 26,000 years for the north celestial pole to trace out a complete circle around the sky, as shown in Figure 1-19c. (The south celestial pole executes a similar circle in the southern sky.) At the present time, Earth’s north axis of rotation points within 1° of the star Polaris. In 3000 b.c.e., it pointed near the star Thuban in the constellation Draco (the Dragon). In the year 14,000, the pole star will be near Vega in Lyra. As Earth’s axis of rotation precesses, its equatorial plane also moves. Because Earth’s equatorial plane defines the location of the celestial equator in the sky, the celestial equator also changes over time. Recall that the intersections of the celestial equator and the ecliptic define the equinoxes, so these key locations in the sky shift slowly from year to year. This entire phenomenon is often called the precession of the equinoxes. This change was discovered by the great Greek astronomer Hipparchus. Today, the vernal equinox is located in the constellation Pisces (the Fish). Two thousand years ago, it was located in Aries (the Ram). Around the year 2600, the vernal equinox will move into Aquarius (the Water Bearer).

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