moon phases & eclipses - jmu homepage · eclipse can only result when a new moon or full moon...

Introduction The Moon orbits the earth roughly once each month, and this orbital motion leads to two well known effects: the cycle of lunar phases and eclipses. Understanding the causes of these phenomena is the subject of this exercise. The material is divided into two parts. The first part treats lunar phases while the second deals with eclipses. After this lab, you should be able to identify a given phase of the Moon, tell the order in which the phases occur, and describe the cause of the phases. You should be able to estimate the approximate rising and setting times of the Moon given the Moon’s phase. You will understand why the Moon always keeps one face toward the Earth. You will learn the types of lunar and solar eclipses and know the phase of the Moon at which they can occur.

Part I: Lunar Phases The Earth, Moon, and planets in our solar system are spherically shaped objects that orbit the source of light, the Sun. Only half of each of these spherical objects or one hemisphere can experience sunlight at any moment. For the Moon, the entire illuminated face cannot usually be seen from the Earth. The relative positions of the Moon, Earth, and Sun at a given time determine what fraction of the illuminated face is visible.

Figure 1 is a view of the Moon’s orbit roughly from the north celestial pole

(NCP) perspective. When the Moon, in its orbit, is in the general direction of the Sun, it cannot be seen. Not only is it located in the bright, daytime sky, but also that hemisphere facing the earth is not sunlit. This is known as new moon. At all other positions in its orbit the Moon is visible, and the changing shape of the illuminated portion of Moon, as different amounts of the sunlit face are seen, is known as the phase cycle. Following new moon, one sees crescent phases for several days. Crescent phase is followed by the first quarter moon, then the gibbous phases until full moon is reached. This waxing (increasing illumination) half of the cycle is followed by the waning (decreasing illumination) half of the cycle, and then back to new moon.

Figure 1

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6:00 pm

6:00 am

Midnight Noon

9:00 pm 3:00 pm

3:00 am 9:00 am

S

U

N

L

I

G

H

T

Waxing Crescent

First Quarter

Waxing Gibbous

Full Moon

New Moon

Third Quarter

Waning Gibbous Waning

Crescent

Moon Phases Solar & Lunar Eclipses1

MOON PHASES & ECLIPSES

ECLIPSE WORKSHOP

MOON PHASES & ECLIPSES The relative angle of the Sun, Moon, and Earth determines the the amount of the Moon’s surface which is illuminated or its phase. When the Moon is behind or in front of the Earth, there is a possibility of an eclipse.

One can use the moon phase diagram to determine rising and setting times. For example, suppose you want to find the time at which a waxing crescent moon sets. When is this Moon overhead? Setting time will be six hours after that time. A waxing crescent moon therefore sets at approximately 9 PM. The full cycle of moon phases over the lunar month is pictured to the below. Each phase will have predictable rising, setting, and meridian crossing times.

Figure 2

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Complete table 1 for the times the Moon crosses the meridian, rises, and sets.

Table 1

Determine the answers to the following questions using table 1 and figure 1:

1. It is 6:00 pm. What Moon is currently rising?

2. The Moon’s right half is illuminated. It is midnight. Where in the sky do you see this Moon?

3. It is 3:00 am and the Moon is setting. What Moon is this?

4. It is 3:00 am and the Moon is rising. Sketch a picture of this Moon:

PHASE MERIDIAN RISE SET

New moon

Waxing Crescent

1st Quarter

Waxing Gibbous

Full Moon

Waning Gibbous

3rd Quarter

Waning Crescent


Part II: Lunar and Solar Eclipses

The Moon’s Revolution The Moon orbits counterclockwise (to the east) and the Earth also rotates counterclockwise (to the east). The time for the Moon to make one complete orbit is called the sidereal period. This is the same time as it takes the moon to rotate on its axis, and is approximately 27.3 days. As a result, the moon always keeps the same face toward earth. In fact, nobody knew what was on the opposite face of the moon until it was photographed by spacecraft in the 1960’s.

Figure 3

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In reality, we see more than half of the Moon’s surface from Earth: about 59%. This results from the fact that the lunar orbit is not perfectly circular and its rotation axis is tilted about 5° relative to its orbit. These two things cause the moon to appear to "rock" a little as it orbits, both from side to side and also a bit up and down. These apparent rocking motions are called librations. Because the Earth is moving in its orbit about the sun, the cycle of phases, or synodic period, of the moon is slightly longer (29.530589 days) than

perigee to perigee or the sidereal period (27.554550 days).

Solar and Lunar Eclipses By this time, you may be wondering why eclipses don't occur on a monthly basis. Doesn't the Moon come between the earth and the sun every 29.5 days? Eclipses require a near perfect alignment of the earth, sun, and Moon. The Moon’s orbit has a 5° tilt compared to the earth's orbit around the sun. The two points where the Moon's orbit intersects with the earth's orbital plane are called the eclipse nodes. Note that the period from node to node is slightly different to the sidereal and synodic periods: 27.212221 days. This is known as the Draconic month. An eclipse can only result when a new Moon or full Moon occurs while the Moon is near one of these nodes. As figure 4 illustrates, this situation only happens twice a year. The months when this happens are called the eclipse seasons.

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During an eclipse either the Sun or the Moon appears to go out. Both can be dramatic events, for properly situated observers on Earth. Total solar eclipses had tremendous psychological impact on ancient cultures because the Sun disappears with no guarantee of return. There are two types of eclipses: lunar and solar. They are produced by shadows cast by the Earth and the Moon, respectively.

2.2 Days

27.3 Day Orbit


A lunar eclipse occurs when the shadow of the Earth strikes the Moon:

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A lunar eclipse typically happens between 10:00 pm and 2:00 am depending on location. Here is what the Moon looks like leading up to, during, and just after a lunar eclipse:

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A solar eclipse occurs when the shadow of the Moon strikes the Earth.

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A total solar eclipse will typically happen around noon. And here is what the Sun looks like leading up to, during, and just after an eclipse:

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A special version of a solar eclipse occurs when the Earth is behind the inflection point of the Moon’s shadow. An observer on Earth will see the Moon not quite

covering the Sun. Such an eclipse is known as an annular eclipse. The situation is illustrated below:

8. Based on the above diagrams and what you know about the sizes of the Earth and the Moon, why do you think a solar eclipse might only last about 7 minutes whereas a lunar eclipse can last for a couple of hours?

9. Looking at the photographs, the Sun disappears at totality however the Moon reappears just after crossing into the Earth’s shadow and appears blood red! Why do you think the Moon is visible during a total lunar eclipse i.e. where does the light come from?


10.It is clear that each type of eclipse can only happen during a specific Moon phase! By looking at your Moon phase diagram, determine the phase of the Moon during which a lunar and solar eclipse can occur.

Eclipses can be total or partial eclipses. A partial eclipse occurs when the Earth (or the Moon) only cover some of the Sun. A total eclipse occurs when the Earth (or the Moon) fully blocks out the Sun. The shadow where partial eclipses occur is known as the penumbra while the shadow of totality is known as the umbra.

The Saros Cycle The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). This value is known as a Saros. The value was known to the Chaldeans (neo-Babylonians) as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well. The cycle arises from a harmony between the three different orbital periods of the Moon: the sidereal, synodic, and Draconic months. One Saros is equal to 223 synodic months,

239 sidereal months, and 242 Draconic months.

Any two eclipses separated by a Saros cycle must share similar geometries. They will occur at the same node with the Moon at nearly the same distance from the Earth and at the same time of year. Because the Saros period is not equal to a whole number of days, its biggest drawback is that subsequent eclipses are visible from different parts of the globe. The extra 1/3 day displacement means that Earth must rotate an additional ~8 hours or ~120º with each cycle. For solar eclipses, this results in the shifting of each successive eclipse path by ~120º westward. Thus, a Saros series returns to about the same geographic region every 3 Saroses (54 years and 34 days).

11. Roughly when will the next solar eclipse that is one Saros after the August 21 eclipse occur? Where will this eclipse occur on Earth? When will the next solar eclipse occur in the U.S. from this similar geometry of the Earth-Sun-Moon?

A Saros series doesn't last indefinitely because the three lunar months are not perfectly in sync with one another (i.e. thy are not perfect multiples of their integers). In particular, the Moon's node shifts eastward by about 0.5º with each cycle. A typical Saros series for a solar eclipse begins when new Moon occurs ~18° east of a node. If the first eclipse occurs at the

TYPE OF ECLIPSE MOON PHASE

Lunar

Solar


Moon's descending node, the Moon's umbral shadow will pass ~3500 km below Earth and a partial eclipse will be visible from the south polar region. On the following return, the umbra will pass ~300 km closer to Earth and a partial eclipse of slightly larger magnitude will result. After ten or eleven Saros cycles (about 200 years), the first central eclipse will occur near the south pole of Earth. Over the course of the next 950 years, a central eclipse occurs every 18.031 years (= Saros) but will be displaced northward by an average of ~300 km. Halfway through this period, eclipses of long duration will occur near the equator. The last central eclipse of the series occurs near the north pole. The next approximately ten eclipses will be partial with successively smaller magnitudes. Finally, the Saros series will end a dozen or more centuries after it

began at the opposite pole. Due to the ellipticity of the orbits of Earth and the Moon, the exact duration and number of eclipses in a complete Saros is not constant. A series may last 1226 to 1550 years and is comprised of 69 to 87 eclipses, of which about 40 to 60 are central (i.e., total, hybrid or annular).

Solar eclipses that take place near the Moon's ascending node have odd Saros numbers. Each succeeding eclipse in a series shifts progressively southward with respect to the center of Earth. On the other hand, solar eclipses occurring near the Moon's descending node have even Saros numbers. Each succeeding eclipse in a series shifts progressively northward with respect to the center of Earth. The current Saros is 145 and some its eclipses are illustrated below:


12.For the following diagrams, use a straight edge to draw the sun’s rays that outline the earth’s and Moon’s shadows. Label the umbra and penumbra on each one. Be specific on the type of eclipse (partial or total, lunar or solar, etc.)


Sun Earth Moon

EarthSun Moon

EarthSun Moon

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