Chapter 3: The Cycles of the Sky
 Instructor: M. Azad Islam

3-1: The Cycle of the Sun

The Ecliptic
The Seasons
Astrology & Pseudoscience: Ignoring the rules of Science
The Motion of the Planets
 

3-2: The Cycles of the Moon

Phases of the moon
Tides
Lunar Eclipses
Solar Eclipses
Predicting Eclipses
 

3-3: Astronomical Influences on Earth's Climate

The Milankovitch Hypothesis
Conflicting Evidences
The Foundation of Science: Evidence

KEY CONCEPTS:

The key concepts are the effects of the motion of the earth around the sun and the moon around the earth. The change of seasons is caused by the "TILT" (twenty three and a half degrees) of the earth's axis of rotation with the normal to the Ecliptic (orbital plane of the earth). This tilt produces change in the duration of days and nights and causes variation in the angle made by the sunrays heating the earth's surface.

The earth and the moon rotates with the same frequency about their axes. as a result, we see the same surface of the moon all the time. The phases of the moon is caused by sunrays reflecting off the moon's surface while it moves around the earth. The sun illuminates half of the spherical moon at any time while the moon orbits around the earth. We don't get to see all of the illuminated part because of the location of the moon with respect to the earth and sun line. The variation in the angle made by the earth-moon line with respect to the earth-sun line causes change in the phase of the moon.

The moon completes one revolution around the earth in 27.322 days with respect to the background stars. This is called the SIDERIAL period of the moon. During this same time the earth moves about 27 degrees along its orbit around the sun. As a result, the moon takes about two extra days to complete the cycle with respect to the sun-earth line. This longer cycle of the moon that takes about 29.57 days is called SYNODIC period of the moon. The longer cycle is taken as ordinary Lunar month.

The tides in the water bodies such as big lakes, seas and the oceans are caused mainly by the moon's gravitational attraction on the earth. The tides (called SPRING TIDES) are stronger when the sun, moon and the earth are lined up as in new moon and full moon orientations. The attraction of the moon is slightly enhanced by the attraction of the sun.

Smaller tides (called NEAP TIDES) are caused during 1st and 3rd quarters of the moon. At these times, the sun and the moon are at right angles with respect to the earth. This causes the attraction of the moon to be slightly opposed by the attraction of the sun.

The shadows of the earth and the moon made by the sunlight, cause the eclipses. There are two kinds of shadows, called UMBRA (completely dark) and PENUMBRA (partially dark). Whenever the moon in its orbit around the earth, passes through the the cone like Umbra shadow of the earth, we see a Lunar Eclipse. This can only happen in the Full Moon phase of the moon. If the moon's Umbra shadow falls on the surface of the earth, observers in the shadow region will see the Solar Eclipse. This can only happen during the new moon phase.

Rotation of the earth about its own axis produces apparent illusion of the sun rising in the east and setting in the west. The light of the day and darkness of the night play the biological clock of our bodies and all living creatures including plants. Our bodies and senses adjust to the cycle of the day and night so that we may work in the day and sleep at night. In reality, it is the earth that rotates on its axis and moves around the sun in a slightly elliptical orbit. The sun is at the center of Earth's nearly circular annual motion.

The moon revolves around the earth in such a way, that we see the same surface of the moon all the time. The moon passes through different phases over a month. The orbital motion of the earth around the sun, causes the change of seasons every year. This helps to adjust our daily social life and to regulate the agricultural production.

So, the cycles of the sky are the cycles of the sun and the moon.


The cycle of the sun: Rotation and revolution of the earth produces apparent motion of the sun for an observer on earth. Such apparent motions are related to the cycles of the sun. Rotation is the turning of a body about its own axis while revolution is the motion around a center that is usually located outside the body. Earth's rotation causes the sun to rise in the east and set in the west. This seems so because the earth rotates toward in the eastward direction.

When sun is up in the sky, sun rays falling on the atmosphere scatter the light. The red in the white light is scattered off air molecules much less than the blue. This makes sky to appear blue.

The apparent daily motion of the sun in the background of the fixed stars of our galaxy (the Milky way), seems to make the sun repeat a cycle every year. An observer from the earth gets to see the same group of stars in the direction of the sun, in anyone time of the season or year.

 

ECLIPTIC: The line following the path of the sun in our skies with the outshine stars behind it in the background is called the ecliptic. It is also known as the apparent path of the sun's motion as viewed from the earth. Ecliptic can also be defined as the orbital plane of the earth in its motion around the sun.

The sun's motion in the sky along the ecliptic is in 365 days, about one degree everyday eastward in the sky. The ecliptic marks the center line of the 12 Zodiac signs (constellations) within a band of 18 degrees in the sky. The signs of the Zodiac take their names from the 12 principal constellations (for 12 months) along the ecliptic. These make up the basis of Astrology that started as Astronomy for the ancients believing in the supernatural powers of the Zodiac. Modern Astronomy is exactly opposite of astrology. Zodiac band in the sky about the ecliptic has some significance, as most of the planets and moon's orbit follow the same path along the ecliptic (Zodiac band).
SO, IF YOU ARE BORN IN THE ZODIAC SIGN OF CANCER WITH MOON IN ANOTHER SIGN OF ZODIAC OR ANOTHER PLANET HAPPENED TO BE IN THE SAME ZODIAC SIGN, THE FORTUNES AND MISFORTUNES OF YOUR LIFE MAY TOTALLY CHANGE IF YOU TRUST IN ASTROLOGY.

The Celestial Equator and the Ecliptic intersect at two points in the sky. The earth passes through these two points once in April 22, called Vernal equinox and once in September 22, called Autumnal Equinox. In the northern hemisphere, when the sun reaches the highest point in the sky at noon on June 23, it is called Summer Solstice, while the lowest point reached by the sun at noon on December 23, is called Winter Solstice.

There are two reasons for summer being warmer than winter that trace their origin from the same cause. The original cause is the tilt of the earth's axis (23.5o) with the normal to the ecliptic.

1. In summer, the sun's rays fall more directly on the surface of the earth. As a result, it is heated up more intensely.

2. In summer, more surface area of one of the hemispheres is heated by sunrays. This has a cumulative effect resulting in a warmer climate.

We may also point out that in summer days, the sun stays up in the sky for longer hours. Thus, accumulating greater amount of heat, resulting in warmer season. Again, in summer the position of the sun in the sky is as high as possible, resulting in direct intense heat than the inclined days of the winter. Everyone has experienced the difference in the heat of the sun, being up in sky and low in the horizon.

In winter, it turns out, that the sun rays fall on the earth's surface at a greater inclination than direct heating in summer. This results in less heating of the earth's surface. In the days during winter, sun overhead in the sky stays up for short period compared with summer days, resulting in less heating. This is the reason why we have a colder season in winter.

 

NOTE: SUMMER OR WINTER SEASON DOES NOT DEPEND ON THE SLIGHT VARIATION OF THE SUN-EARTH DISTANCE

 

As mentioned earlier, the earth and other planets revolve around the sun in an approximate circle. The average sun-earth distance is 1.5x108 km or one Astronomical Unit (1AU).

On January 3rd, the earth reaches its closest point to the sun, called PERIHELION. On July 6, the earth reaches its farthest point from the sun called APHELION. The total variation in distance is about 3% only.

 

MOTION OF THE PLANETS:

Planets produce no light of their own. Reflected sun rays off the surface of the planet, make them visible from the earth. All nine planets Mercury through Pluto move in nearly circular orbits around the sun. If you could look down the planets from the celestial north pole, we would see the planets moving in a counter clockwise direction with the sun at their center. Further from the sun, the slower is the speed of the planet.

The inner planets (Mercury and Venus) inside the earth's orbit stay close to the sun. During day time, sun rays are so powerful that it obliterates the starlight and reflected light from the planets. After sunset, the inner planets are to be seen above the western horizon. For the same reason, inner planets are to be found above the eastern horizon just before the sun rise. Annual period of Mars is 2 years and of Saturn is 30 years. Morning star and Evening star are two names of Venus. Venus is very bright

(-4.7 in magnitude), easier to locate than Mercury which stays very close to the sun. All the planets more or less stay close to the ecliptic except Pluto.

 

THE CYCLES OF THE MOON

Changes in the size of the moon, eclipses and tides in the water bodies are examples of most dramatic phenomena caused by the motion of the sun, moon and the earth. Like the sun, moon's diameter suspends an angle of about 0.5 degree in the sky. The moon's orbit is at 5o 8' 42" inclined to the plane of the earth's orbit or the ecliptic.

Phases of the moon: The moon revolves eastward around the earth in a period of 27.322 days with respect to the distant stars in the background. This is called the SIDEREAL PERIOD. Note that the sun is also in apparent motion during this time covering about 27o eastward. If we start counting from the new moon to the following new moon, and remembering it is caused by the sun rays striking moon's surface, it is going to take an extra time (about two days) more than the sidereal period of 27.322 days. So the period between the two successive new moons is 29.53 days on the average, and it is called Synodic period, measured with respect to sun's position.

The moon rotates on its axis while revolving around the earth. Moon's period of rotation on its axis is the same as earth, so that moon shows the same face to the earth. The moon moves about 13o in 24 hours.

The moon is visible due to reflection of sunlight off its surface and has no light of its own. As the moon moves across the sky, varying amount of sun light is able to reflect off its surface and reach the surface of the earth. This results in the variation of the lighted-up part of the moon as seen from the earth. And, it is called the phases of the moon. As the moon moves, we get to see only that part of the moon facing us and illuminated by the sun.

When the moon is approximately between the earth and the sun, the face of the moon towards us is in darkness. The moon is invisible, we call it the New moon. A few days after, the new moon has moved far enough for the waxing crescent to become visible in the evening sky. Night by night crescent moon grows bigger (called waxing crescent), until we see half of moon's surface towards us is illuminated by sun light We call this 1st quarter. The moon continues to grow bigger (waxing gibbous), until its position is nearly opposite to the sun. At this point, the entire face of the moon towards us is fully illuminated by the sun light. We call it Full moon. After this, the moon starts shrinking, going to 2nd half of its phase, and reverses its illumination made by the sun light. It passes through the waning gibbous. When half of the moon is illuminated once more, it is called 3rd quarter. Then the moon goes through further shrinking (waningcrescent) until it becomes new moon again. The average cycle of the lunar phase takes 29.53 days. It is roughly 4 weeks, one week for each of the four phases (new moon, 1st quarter, full moon and 3rd quarter).

After a sidereal period of 27.322 days, moon completes a circle with respect to the fixed stars in the background. But sun has moved eastward 27o by this time. So, the moon takes about two extra days to catch up with the sun again. At new moon, moon is nearly in line with the sun and sinks below the horizon soon after the sunset. So, at new moon, there is not much of a moon to be seen. In a few days, the waxing crescent makes its appearance above the western horizon soon after sunset. Later, each evening the crescent is fatter and appears higher in the horizon. The first quarter of the moon does not set in until about midnight. The full moon is visible all night and sets in the west at the sun rise. The waning phase of the moon is less familiar. Because, during waning, the moon does not appear in the evening sky. In the 3rd quarter of the moon, it does not appear until about midnight. For the same reason, the waning crescent can be seen only if we observe it before sunrise in the eastern horizon.

TIDES: Periodic advance and retreat of water near the bank of big water bodies.

The pull of the moon on the earth due to gravitation has remarkable effect easily observed by people who live near sea shores. The side of the earth facing moon is 4000 miles nearer than the center of earth. As a result the pull of the moon on nearside of the earth is much stronger than center. The moon pulls the nearside of the earth a few centimeters towards it. Water in the sea and in the ocean responds by penetrating into the land masses at the sea beaches, causing tidal waves. Again, the moon pulls the center of the earth much stronger than the land masses on the far side of the earth. This causes water in the ocean and sea to rise up into a bulge causing a somewhat smaller tide. The effect develops over a period of time as the rotating earth brings its face closest to the moon. The actual tide at any place depends on the latitude, shape of the shore and the wind direction.

Since tides occur simultaneously on opposite sides of the earth, there are two tides daily at the sea beaches. The pull of the sun on earth's water bodies also affect the tides. At New moon and Full moon, the pull of the moon and the sun can be additive to produce greater effect, hightide is higher and low tide is lower. Such tides are called SPRING TIDES. During 1st and 3rd quarters, the pull of the sun and the moon is at right angle to each other. As a result, their effect is a bit opposed to each other. Hence, the tides are less dramatic than normal tides. Such tides are known as Neap tides.

Tidal forces of the water on the ocean beds have many effects. The friction between the sea bed and water above it, slows down the earth's rotation. The fossil records show that 400 million years ago, each day was 22 hours long. The pull of the earth on the moon causes the moon to keep its same face towards earth. The orbital velocity of the moon is affected by the bulging water on earth, increasing its orbital speed and its orbit radius by 3 cm. every year.


LUNAR ECLIPSE: An eclipse of the moon, called Lunar eclipse occurs during full moon when earth's shadow falls on the passing moon. Shadows are two types, Umbra for total darkness or complete shadow and Penumbra, a partial shadow. When a complete blocking of sunrays by earth occurs in a region where the moon passes through, a total lunar eclipse is seen. If the moon happens to pass through the partial shadow region called penumbra, only a deemed eclipse is observed from the earth. During a typical lunar eclipse, the moon first passes through the Penumbra, becoming dimmer as it moves farther into Penumbra region. In about an hour, the moon reaches Umbra region rendering total darkness. Period of total eclipse may last 1 hour and 45 minutes. Actual time of duration of the lunar eclipse depends on where the moon crosses the shadow. Even in the course of the total eclipse, the moon is not completely dark. Sunlight reflected from the atmosphere reaches moon and lunar surface is at times copper red in color. There may be about two lunar eclipses every year.


SOLAR ECLIPSE:

The shadow of the moon made by sunlight, falling on the earth, produces Solar eclipse. The diameter of the Sun or the Moon subtends nearly equal angles (0.5o). If the moon is able to cover the entire disk of the sun, we have a total eclipse. If moon's shadow covers only part of the sun, we observe a partial solar eclipse. At times the umbra region of moon's shadow reaches part of the earth's surface (168 miles wide) forming a circular area in which total solar eclipse can be seen. If the surface of the earth passes through the Penumbra region of moon's shadow, a partial solar eclipse will be observed. If a person is outside the Penumbra region of the moon's shadow, no solar eclipse will be seen. The small diameter (168 miles) Umbra shadow of the moon sweeps rapidly at 1000 mph due to rotation of the earth and orbital speed of the moon, resulting in total solar eclipse of the sun for about 2 to 3 minutes on the average, and 7.5 minutes maximum.

When moon blocks the Photosphere (bright part) of the sun, images of solar corona and solar flare present in the region of Chromosphere can easily be photographed. The earth or moon orbits are not exactly circular. Moon comes slightly closer to earth at Perigee extending its Umbra shadow on earth and slightly farther away at Apogee diminishing the Umbra shadow on earth. As a result, slight variation in the angular diameter of the moon may produce Annular Solar eclipse instead of total eclipse if the Umbra does not reach the earth. People in the ancient civilizations, were able to predict the eclipses from the knowledge of their cycles in which they occur. Cycles of eclipses, tides, seasons and the lunar phases are immediate experiences of all life forms on earth. Some people believe that the Ice age that took place a long time ago, is also the result of earth's periodic change.


SMALL ANGLE FORMULA: The angle subtended by opposite ends of an object with respect to an observer's eye, can be used as a measure of distance.

DEFINITION: The angle measured in radian is,

Angle (radian) = (Arc length)/(radius of the arc) = Diameter/Distance

Example, 2p = 360 degrees = 4 right angles

60 minutes = 1 degree, 60 seconds = 1 minute

206,265 seconds = 1 radian

Angle = (arc length)/(radius) = (diameter/distance) x 206,265 seconds


THE FOUNDATION OF SCIENCE: Evidence is the key to the understanding of Science. Theories and conclusions must be supprted by the experiments and observations. The knowledge of science is based on the evidence from the experimental measurements and observations.

PREDICTING ECLIPSES: Accurate prediction of eclipses requires sophisticated calculations. However, we can predict the timing of the eclipses in general terms from the CYCLIC MOTIONS of the moon and the earth. Many factors come into play in the prediction of the time of eclipse. We must realize that the moon's orbit is tilted at about 5 degrees with the orbital plane of the earth. As a result the moon often misses the shadow of the earth, passing up or down the ecliptic. And we see NO Lunar eclipse.

For sun to be eclipsed, moon's long and narrow shadow must reach the earth in its orbit around the sun. This can only happen if the earth, moon and the sun are almost in a line. The moon has a greater chance of passing through the Umbra shadow of the earth than the earth passing through the long narrow Umbra shadow of the moon. Both shadows are made by the sunlight. This makes Lunar eclipse more frequent than the Solar eclipse. In the best scenario, the moon's Umbra may sweep the earth in about 168 miles wide diameter throhgh different regions of the world as the earth rotates on its axis. Since both the earth and the moon are also in motion in their orbits, the total Solar Eclipse may last from about 2 to 7.5 minutes maximum. The two nodal points of the moon's tilted and slightly elliptical orbit, crosses the earth's orbital plane twice in a year. For a few weeks (called eclipse seasons), the moon may enter the two nodal points passing through the earth and the sun, causing eclipses at the new moon and full moon at this time. Now the moon's orbit is not fixed in space. It precesses slowly due to the gravitational pull of the earth and the sun on it. This changes the direction of the nodal line. The nodal line completes its cycle in 18.61 years. Since the period is not an integral multiple of a whole year, the eclipse seasons occur 3 weeks earlier as each year passes by. The motion of the line of nodes combined with the periodicity of lunar phases, means every 6585.3 days the eclipse seasons must repeat. This repitition of the eclipse seasons is called "Saros Cycle." The Saros cycle contains a factor of 1/3 of a day. This means, the Saros Cycle at any part of the earth rotates one-third of the way around the world. So, the eastern Pacific region will observe total solar eclipse if North America saw it in the previous Saros Cycle. Many ancienct civilizations predicted the Saros Cycle from the observed periodicity of the total solar eclipse without any knowledge of the actual knowledge of motion of the sun or the earth.


EARTH'S CLIMATIC CHANGES:

Our earth underwent drastic changes in the climate in the past. Fossil records show that 570 million years ago, there was an ice age and again about 280 million years later. The most recent an ice age began 3 million years ago and is still going on. We are living in one of the periodic episodes when the glaciers melt and the earth is slightly warmer. The current warm period started 20,000 years ago. The period of ice ages is about 250 million years. Within each ice age, the cycles of glaciations repeat every 40,000 years. Some scientists think these periods of glaciation and ice age have astronomical origin.

According to Milankovitch Hypothesis, small changes in the orbit of the earth, the precession of the earth's axis and inclination affect the heat balance and modify the climate.

Three factors are in play.

1. Shape of earth's orbit changes from more elliptical to less elliptical in 93,000 years. At present, the elliptic orbit is 2% closer to the sun during the Northern hemisphere winters and 2% away from the sun during Northern hemisphere summers. As a result, the warming trend in the Northern hemisphere may cause the ice to melt.

2. Precession causes the earth's axis to wobble in a period of 26,000 years. This changes the location of the seasons around earth's orbit. Perihelion now occurs at the Northern winters. In 13.000 years aphelion will occur in Northern winterss, making it cooler than usual, perhaps enough for accumulation of glaciers.

3. Inclination of earth's equator presently at 23(1/2) degrees, varies from 22 to 24 degrees in a period of 41,000 years. At large inclination, seasons are more severe while at lower inclination, the seasons are less pronounced.

Milankovitch proposed these three periodic variations due to earth's motion are the causes of ice age. This resulted in formation and melting of glacial structures. This hypothesis is stronly supported by the evidence obtained from the cores of sediments from the ocean floor. The experiment resulted in reconstrcting the history of ocean floor temperatures.

Other evidence opposes the timing of glaciation in the Northern hemisphere as predicted by Milankovitch hypothesis. So it is a partial success to understand the ice age. 


KEY WORDS:

rotation, revolution, ecliptic, vernal equinox and autumnal equinox, summer and winter solstice, perihelion, aphelion, morning and evening stars, sidereal and syndonic period of the moon, spring and neap tides, umra and penumbra, lunar and solar eclipse, photosphere and chromosphere, corona, prominence, diamond ring effect, annular eclipse, perigee and apogee, nodal points and nodal line, Saros cycle and finally Milankovitch hypothesis.


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Updated 07/24/05