Chapter 3 =//= Cycles of the Sky
The Aztecs sacrificed humans and offered their beating hearts to the brilliant star that appeared sometimes in the evening sky and sometimes in the morning sky--the object we know as the planet Venus. The Aztecs saw in the cycle of Venus a metaphor for life, death, and rebirth; and they associated Venus with their principal god, Quetzalcoatl (kwét-zal-ko-ah-tl), who had died, journeyed through the underworld, and returned to life. The Aztecs linked the cycles of their lives on Earth directly to the cycles they saw in the sky.
Even today our lives are linked to sky cycles. The rotation of the earth on its axis makes the sun appear to rise and set, and our bodies follow that cycle of day and night in sleeping and waking. The moon revolves around the earth in its orbit--passing through a cycle of phases--and we divide our calendar into months of roughly one lunar cycle each. The orbital motion of the earth around the sun causes a year-long cycle of seasons by which we regulate our agricultural, political, and social lives.
The cycles in the sky are the cycles of the sun and moon. In this chapter, we will study those motions and see our earth as a rotating planet circling its sun. While we may be studying the sky, we will be learning about our world.
-The Cycle Of The Sun-
Perhaps the most obvious cycles in the sky are those that involve the motion of the sun, but these motions are really produced by the rotation and revolution of the earth. The English language distinguishes between rotation and revolution. Rotation is the turning of a body about an axis that passes through a central point in the body. Thus, we say the earth rotates on its axis once a day. Revolution is the motion of a body about a point located outside the body, and we say the earth revolves around the sun once a year.
Earth's rotation produces the daily cycle of sunrise and sunset. The annual revolution of Earth around the sun makes the sun appear to move around the sky in a year-long cycle that causes the seasons.
-The Ecliptic-
When the sun is above the horizon, its brilliance makes Earth's atmosphere glow with scattered light. Because blue light scatters off of air molecules better than red light does, we see the sky filled with blue light. No matter where we look in the daytime sky, we see this blue light, and we cannot see the fainter stars. If we could make the sun a million times fainter, it would be about as bright as the full moon, and we would be able to see stars even when the sun was above the horizon.
If we noted the position of the sun among the stars day by day, we would quickly notice that it appears to be moving eastward. In early January, for instance, we would see the sun against the background of the stars in Sagittarius. Earth is moving, however, so each day we would see the sun slightly eastward of its previous position. By February it would have moved into the constellation Capricornus, and by March it would be in Aquarius.
Of course, it is not quite correct to say that the sun is "in Aquarius." The sun is only 93 million miles away, and the stars of Aquarius are at least a million times farther away. But in March of each year, we would see the sun against the background of the stars in Aquarius, and thus we could say, "The sun is in Aquarius."
If we continued watching the sun against the background of stars throughout the year, we could plot its path on a star chart. After one full year, we would see the sun begin to retrace this line as it continued its annual cycle of motion around the sky. This line, the apparent path of the sun around the sky, is called the ecliptic. Another way to define the ecliptic is to say it is the projection of the earth's orbit on the sky. If the celestial sphere were a great screen illuminated by the sun at the center, then the shadow cast by Earth's orbit would be the ecliptic. Yet a third way to define the ecliptic is to refer to it as the plane of Earth's orbit. These three definitions of the ecliptic are equivalent, and it is worth considering them all because the ecliptic is one of the most important reference lines on the sky. We will use it, for instance, to discuss the seasons.
The eastward motion of the sun along the ecliptic is consequence of Earth's motion around its orbit. Earth completely circles the sun in 365.25 days, and consequently the sun circles the sky following the ecliptic in the same number of days. This means the sun, traveling 360° around the ecliptic in 365.25 days, travels about 1° eastward each day. The sun is about 0.5° in diameter, so it travels twice its own diameter per day.
The sun's motion along the ecliptic is complicated by the fact that Earth does not rotate perpendicular to the plane of its orbit. Its axis of rotation is tipped 23.5° from perpendicular. Earth, like a spinning top, holds its axis fixed in space as it moves around the sun. We saw in the previous chapter that Earth's axis always points toward a spot on the sky very near Polaris, the North Star. Although the direction of Earth's axis does drift slowly because of precession, we will deffinately not notice any change in our lifetimes.
Because Earth is tipped 23.5° in its orbit, the ecliptic is tipped 23.5° from the celestial equator. Recall that the celestial equator is the projection of Earth's equator and that the ecliptic is the projection of Earth's orbit. Since Earth is tipped 23.5°, its equator is tipped 23.5° from the plane of its orbit. When we project this on the sky, we find that the ecliptic and celestial equator meet at an angle of 23.5°.
The ecliptic and celestial equator cross at two places on the sky called equinoxes. The vernal equinox is the place where the sun crosses the celestial equator moving northward, and the autumnal equinox is the place where it crosses moving southward. The sun crosses the vernal equinox on or about March 21, and it crosses the autumnal equinox on or about September 22. The exact dates of the equinoxes can vary by a day or two because of leap year and other factors.
We can identify two other reference marks on the ecliptic by noting where the sun is farthest from the celestial equator. About June 22, the sun is farthest north at the point called the summer solstice. The winter solstice is the point where the sun is farthest south, about December 22.
Note that the equinoxes and solstices are points on the sky, but the same words refer to the times when the sun crosses those points. You might hear someone say, "This year the vernal equinox occurs at 3:02 AM on March 21." Whether we think of them as places or times, the equinoxes and solstices are important because they mark the beginning of each of the seasons.
-The Seasons-
The seasonal temperature depends on the amount of heat we receive from the sun. To hold the temperature constant, there must be a balance between the amount of heat we gain and the amount we radiate to space. If we receive more heat than we lose, we get warmer; if we lose more than we gain, we get cooler.
The motion of the sun around the ecliptic tips the heat balance one way in summer and the opposite way in winter. Because the ecliptic is inclined with respect to the celestial equator, the sun spends half the year in the northern celestial hemisphere and half the year in the southern celestial hemisphere. When the sun is in the northern celestial hemisphere, the northern half of Earth receives more direct sunlight--and therefore more heat--than the southern half. This makes North America, Europe, and Asia warmer.
The seasons are reversed in Earth's southern half. While the sun is in the northern celestial hemisphere warming North America, South America becomes cooler. Southern Chile has warm weather on New Year's Day and cold in July.
To see how the sun can give us more heat in summer, think about the path the sun takes across the sky between sunrise and sunset. (!!fig3.4pg24!!)...shows these paths when the sun is at the summer solstice and at the winter solstice as seen by a person living at latitude 40°, a good average latitude for most of the United States. Notice that at the summer solstice, the sun rises in the northeast, moves high across the sky, and sets in the northwest. But at the winter solstice, the sun rises in the southeast, moves low across the sky, and sets in the southwest. Two features of these paths tip the heat balance.
First, the summer sun is above the horizon for more hours of each day than the winter sun. Summer days are long and winter days are short. Because the sun is above our horizon longer in summer, we receive more energy each day.
Second, the sun stands high in the sky at noon on a summer day. It shines almost straight down, as shown by your small shadows. On a winter day, however, the noon sun is low in the southern sky. Each square meter of the ground gains little heat from the winter sun because the sunlight strikes the ground at an angle and spreads out, as shown by your large shadows. These two effects work together to tip the heat balance and produce the seasons.
We mark the beginning of the seasons by the position of the sun. Spring begins at the moment the sun crosses the celestial equator going north (the vernal equinox). Summer begins at the moment the sun reaches its most northerly point (the summer solstice), and autumn begins when the sun crosses the celestial equator going south (the autumnal equinox). We mark the official beginning of winter when the sun reaches its most southerly position (the winter solstice).
Of course, the weather does not turn warm the instant spring begins. The ground, air, and oceans are still cool from winter, and they take a while to warm up. Likewise, in the autumn, the ground, air, and oceans slowly release the heat stored through the summer. Due to this thermal lag, the average daily temperatures lag behind the solstices by about 1 month. Although the sun crosses the summer solstice on about June 22, the hottest months at northern latitudes are July and August. The coldest months are January and February, even though the sun passes the winter solstice earlier, about December 22.
The seasons are not related to variations in the Earth-sun distance. The average distance from Earth to the sun is one astronomical unit (1 AU), 1.5 * 10^8 km. Earth's orbit is slightly elliptical, however, so its distance varies. About January 4, Earth reaches perihelion, its closest point to the sun; it reaches aphelion, its farthest point, about July 4. The total variation is only about 3 percent, and it has only a tiny influence on the seasons.
The ecliptic is important to our daily lives because of its connection with the seasons, but it may also be familiar in a different guise. The ecliptic marks the center line of the zodiac, a band 18° wide that encircles the sky. The signs of the zodiac take their names from the 12 principal constellations along the ecliptic. Astrology was once an important part of astronomy, but the two are now almost exact opposites--astronomy is a science that depends on evidence, and astrology is a superstition that depends on faith. Thus the signs of the zodiac are no longer important in astronomy. The zodiac itself is of interest only because it is on the path followed by the planets as they move around the sky.
-The Motion Of The Planets-
The planets of our solar system produce no visible light of their own; we see them by reflected sunlight. Mercury, Venus, Mars, Jupiter, and Saturn are all easily visible to the naked eye; but Uranus is usually too faint to be seen, and Neptune is never bright enough. Pluto is even fainter, and we need a large telescope to find it.
All of the planets of our solar system move in nearly circular orbits around the sun. If we were looking down on the solar system from the north celestial pole, we would see the planets moving in the same counterclockwise direction around their orbits with the planets farthest from the sun moving the slowest.
When we look for planets in the sky, we always find them near the ecliptic because their orbits lie in nearly the same plane as the orbit of the earth. As they orbit the sun, they appear to move eastward along the ecliptic. Mars moves completely around the ecliptic in slightly less than 2 years, but Saturn, being farther from the sun, takes nearly 30 years.
As seen from Earth, Venus and Mercury can never be seen far from the sun because their orbits are inside Earth's orbit. They appear at times above the western horizon just after sunset or above the eastern horizon just before sunrise. Venus is easier to locate because its larger orbit carries it higher above the horizon than does Mercury's. Mercury's orbit is so small that it can never get farther than 27°50' from the sun. Consequently, it is hard to see against the sun's glare and is often hidden in the clouds and haze near the horizon.
By tradition, any planet visible in the evening sky is an evening star, even though planets are not stars. Similarly, any planet visible in the sky shortly before sunrise is a morning star. Perhaps the most beautiful is Venus, which can become as bright as -4.7. As Venus moves around its orbit, it can dominate the western sky each evening for many weeks, but eventually its orbit carries it back toward the sun, and it is lost in the haze near the horizon. In a few weeks, it reappears in the dawn sky, a brilliant morning star.
The cycle of the sun around the ecliptic dominates our lives through the seasons, but there is another moving light in the sky. What the cycles of the moon lack in intensity, they make up in beauty and elegance.
-The Cycles Of The Moon-
Among the changing aspects of the sky, none are more striking than those that involve the cycles of the moon. We are most familiar with the lunar phases, but other cycles include tides and eclipses.
The moon orbits eastward around the earth in 27.322 days. This is called the moon's sidereal period because it refers to the moon's position relative to the stars. The moon takes 27.322 days to circle the sky once and return to the same place among the stars.
The moon rotates on its axis as it circles Earth, keeping the same side toward Earth. Thus we always see the same features on the moon's face. A mountain on the near side of the moon remains facing the earth throughout the moon's circuit around Earth.
The moon moves rapidly across the sky, traveling 13°, about 26 times its apparent diameter, in 24 hours. If you compare the position of the moon to the stars in the background, you will see it move a distance slightly greater than its own diameter in an hour. Because the moon's orbit is inclined 5°8'42" to the plane of Earth's orbit, the moon never travels farther than 5°8'42" north or south of the ecliptic.
Because the moon, like the planets, does not produce visible light of its own, it is visible only by the sunlight it reflects, and we can see only that portion illuminated by the sun. As the moon moves around the sky, the sun illuminates different amounts of the side of the moon facing Earth, and so the moon passes through a sequence of phases.
(!!fig3.7pg27!!)... shows how the phases of the moon are related to its orbital position. When the moon is approximately between Earth and the sun, the side toward us is in darkness. The moon is not visible, and we refer to it as a new moon. A few days after new moon, it has moved far enough along its orbit to allow the sun to illuminate a small sliver of the side toward us, and we see a thin crescent. Night by night this crescent moon waxes (grows), until, about a week later, we see half of the side toward us illuminated by sunlight and refer to it as first quarter. The moon continues to wax, becoming gibbous (from the Latin for humpbacked), and then, when it is nearly opposite the sun, the side toward Earth is fully illuminated and we see a full moon.
The second half of the lunar cycle reverses the first half. After reaching full, the moon wanes (shrinks) through gibbous phase to third quarter, then through crescent back to new moon. To distinguish between the gibbous and crescent phases of the first and second half of the cycle, we refer to gibbous waning and crescent waning when the moon is shrinking, and to gibbous waxing and crescent waxing when it is growing.
The cycle of lunar phases takes 29.53 days, the synodic period of the moon, or about 4 weeks. Thus new moon, first quarter, full moon, and third quarter occur at nearly 1-week intervals. In general, an object's synodic period is its orbital period with respect to the sun. (Synodic comes from the Greek words meaning "together" and "path.") To see why the moon's synodic period is longer than its sidereal period, imagine we begin observing at new moon--that is, when the moon is near the sun in the sky. After 27.322 days, the moon's sidereal period, it has circled the sky and returned to the same place among the stars where it was last new, but the sun has moved about 27° eastward along the ecliptic. The moon needs slightly more than 2 days to catch up with the sun and reach new moon again. Thus the moon's synodic period is longer than its sidereal period.