Lunar Cycle Lab Key

The moon, like a flower In heaven's high bower, With silent delight Sits and smiles on the night. William Blake, Night

| Lunar Cycle Index | | New | Waxing Crescent | First Quarter | | Waxing Gibbous | Full | | Waning Gibbous | Third Quarter | | Waning Crescent | | Basic Celestial Phenomena |

What is more familiar than the phases of the Moon? They are recognized by children everywhere, but they are not necessarily simple. There are unsuspected secrets about them that you will discover as you work through this lab.

• Needed materials: bright lamp for sun, styrofoam moonball (opaque ones work better than translucent balls), dark room, red flashlight.
• Select a lab partner. Work in groups of two or three persons.
• Model every step as instructed using a moonball. Stand up and do it! Don't just sit still and secrete answers by sheer force of thought. The answers are not as important as the method: learn how to use the modelling techniques to come up with reliable answers you can have confidence in.
• Complete each step sequentially, before going on to the next.
• Do not ask for help until you have attempted to model that step.

I. Model day and night with Mt. Nose

• Your head is the earth; the lamp is the sun; the styrofoam ball is the moon.
• Mt. Nose is located on the earth's equator.
• Anything straight ahead of you, in front of your nose, is crossing the meridian overhead. (Pretend you are lying on a recliner looking up.)
• Extend your arms out to the side, palms forward. Anything in front of your face or arms is visible "above the horizon." Anything behind you is "invisible" beneath your horizon.
• You will not need to refer to north or south directions in this lab.
• Mt. Nose turns eastward (to the left) as the earth rotates. Stand up, face the sun, and make the earth rotate one time around, now, in the proper direction.
• Mr. and Mrs. Epidermis live on Mt. Nose.

1. Face the center lamp.
   • Where in the sky do Mr. and Mrs. Epidermis see the sun? On the meridian.
   • What time of day is it? Noon.
2. Turn eastward (to the left) until your right ear is toward the sun. Extend your arms so that your right hand is toward the sun, your left hand pointing away.
   • What time of day is it on Mt. Nose? Sunset.
   • Which ear or hand is the eastern horizon for Mr. and Mrs. Epidermis? Left.
   • Which ear or hand is the western horizon for Mr. and Mrs. Epidermis ? Right.
     (These ear-hand directions do not change: to remember them, use labelled gloves or attach "east" and "west" stickers to your hands if necessary!)
3. What time of day is it on Mt. Nose when your back is toward the sun?
   • On what part of your head is it daytime? The back side.
4. What time is it on Mt. Nose when your left hand and left ear are toward the sun? Sunrise.
5. STOP: Before going on to Part II, ask the instructor or lab assistant to check your answers to this part. Be prepared to demonstrate the sunset and sunrise positions, and know which way is east and which way is west for both.

   Instructor's approval: ___________

II. Model the rotation and revolution of the moon

1. Rotation refers to the turning of a body around its own axis.
   • How long is the rotation of the earth?
   • The length of one rotation of the earth is one "earth day"; the length of one rotation of the moon is one "lunar day," and they are not necessarily the same.
2. Revolution refers to the orbit of one body around another.
   • How long is one revolution of the earth around the sun?
   • The length of one revolution of the earth around the sun is one "year"; the length of one revolution of the moon around the earth is one "month."
3. The diagram below shows the Earth and Moon as viewed from space far above the north pole of the Earth.
   
4. Stand in the noon position with the moon held at arm length in the direction of the sun, as in #1. (The arrows coming from the right represent light rays from the sun.)
5. Identify a mark on your moonball (such as a sporting brand label on a baseball or golfball) and turn the moon so that this mark is facing you. Let the marked side always represent the "near side" of the moon.
   • At position #1, is the marked side (near side) the same as the bright side?
   • At position #1, what proportion of the near side of the moon is illuminated? All, half, more than half, less than half, or none?
6. Move the moon to positions #2 and #3. Keep the marked side toward you at every position.
   • At position #3, is the marked side (near side) the same as the bright side?
   • At position #3, what proportion of the near side of the moon is illuminated? All, half, more than half, less than half, or none?
7. Fill in the table below for each position as numbered in the diagram above. Answer with the following phrases:

   • A. None
   • B. Less than half
   • C. Half
   • C. More than half
   • E. All

   #	Proportion of the Near Side of the Moon that is illuminated
   1
   2
   3
   4
   5
   6
   7
   8

8. The rotation of the moon:
   1. Procedure:
      Let partner A watch the model moon from a position above its north pole as partner B pivots in place and moves the moon through positions #1 through #8 and back to #1 again, keeping the near (marked) side always facing toward the earth. Partner A will have to walk around partner B, keeping his or head above the moon as the moon completes one revolution around the earth. Partner B may have to squat while pivoting.
      
   2. Trade places and do it again so that both partners can observe the phenomena.
      
   3. Interpretation:
      • From position #1 back to position #1 again, how many times does partner B observe the moon to turn around its axis?
      • Does it take 24 hours, 1 month, or 1 year for the moon to rotate once around its axis?
      • If one rotation of the moon around its axis equals one lunar day, how many lunar days are in one month?
        
9. Many planets have days (rotation periods) that are quite unlike the 24-hour days we know on earth. Examine the table below and then answer the questions listed beneath it.

   Body	Length of Day (Rotation period)	Length of Year (Revolution period)
   Earth	24 hours	365.26 days
   Moon	29.5 earth-days	29.5 earth-days
   Mercury	58.7 earth-days	0.24 yrs (88 days)
   Venus	-243 earth-days (retrograde)	0.615 yrs (225 days)
   Mars	24 hours 30 minutes	1.88 years (687 days)
   Jupiter	0.410 day (9 hours 50 minutes)	11.86 years
   Saturn	0.426 day (10 hours 14 minutes)	29.5 years
   Uranus	-0.746 day (retrograde)	84 years
   Neptune	0.800 day (19 hours 12 minutes)	165 years
   Pluto	-6.39 days (retrograde)	248.5 years
   Altair, in Aquila the Eagle, vertex of summer triangle	6 hours	NA
   Pulsar of Crab Nebula, in Taurus the Bull	3 rotations per second	NA

   1. How many planets rotate in the opposite direction, i.e., westward instead of eastward? (This is called retrograde rotation.)
   2. Which planet's day is closest to that of the earth's?
   3. Which planet has a day longer than its year?
   4. Which planet's day is nearly a week long?
   5. Must the largest planets have the longest periods of rotation?

III. Phase Definitions

What are the different phases of the moon? The bright portion of the moon as seen from the earth changes shape as it passes through different phases. These phases are described by the following terms:


	New Moon: all of the visible side of the moon is dark
	Full Moon: all of the visible side of the moon is bright
	Crescent: the bright part of the moon is a crescent or thumbnail shape
	Quarter: the bright part of the moon is half of the visible side
	Gibbous: the bright part of the moon is lopsided; more than a Quarter but less than a Full

• Note on Quarter phases:
  • A Quarter moon is often called a "half moon," but really only a quarter of the whole moon is both visible and illuminated.
  • The name derives from the fact that when the moon is in a quarter phase, it has passed through either one-fourth or three-fourths of its monthly cycle.
    
• Waxing and waning are used to describe crescent and gibbous moons.
  • Waxing: Just as a candle dipped in wax grows bigger, the bright part of a waxing moon is growing larger from day to day.
  • Waning: When the bright part of the moon is getting smaller each day.

IV. Model Lunar Phases with Mt. Nose

1. Face the sun. Hold your moon directly in front of Mt. Nose as in position 1 of the diagram below. Hold the moon below eye level so it won't block the sun.
   • What is moon's phase? New
   • Note that there are two circles of moons shown in the diagram, an outer circle to draw in and an inner circle of half-illumined moons.
     • The inner circle shows moons positioned by lines from the earth every 45 degrees. It is as if you were viewing the earth-moon system from space, looking down on the north pole of the earth. The inner circle shows how the sun always illumines half of the moon as it journeys in orbit around the earth each month.
     • The outer circle (containing moons without markings) is for you to draw the appearance of the moon at that position as it appears from earth.
   • In the outer circle at position 1 of the diagram below, draw this phase as it appears from earth by penciling in areas not illumined by the sun.
     
2. Move the moon a little to the left (about 45 degrees) until you observe a thin waxing crescent as in position 2 of the diagram below.
   • Turn the page so that when you look at the diagram below you can sight along the line from earth to the half-illumined moon at position 2 of the diagram below. By inspecting this line of sight on the diagram, note that the dark side of the moon covers more than half (but not all) of the visible or near side of the moon. Use your observation of the moonball to determine the precise shape of the bright part of the moon corresponding to this position (it should appear in a crescent form). Then, keeping the page turned so that the outer circle at position 2 is at the top, draw this phase in that outer circle as it appears from the earth.
   • Obtain the instructor's approval before going on: ______________
   • Does the bright side of the moon face the sun or away from it? Toward
   • Is the bright side of the moon on the left or right side? Right
   • Do the horns of the crescent point toward the sun or away from it? Away
   • Bob Berman, Secrets of the Night Sky (pp. 137-145), explains how the tilt of the crescent moon expresses the seasons.
     
3. Move the moon further to the left (about 90 degrees) until it appears half-lit as in position 3.
   • What is the moon's phase? (Don't answer "half" moon.) First Quarter
   • To make the moon appear more full, do you move it toward the sun or away from it? Away
   • Turn the page to sight along the line from earth to position 3 of the diagram below, then draw this phase as it appears from the earth in the outer circle at position 3.
     
4. What is the moon's phase at position 4? Waxing Gibbous
   • Is the bright side of the moon on the left or right side? Right
   • Turn the page to sight along the line from earth to position 4 of the diagram below, then draw this phase as it appears from the earth in the outer circle at position 4.
     
5. Continue moving the moon around you until the near side (near Mt. Nose) is fully lit as in position 5. You will have to hold the moon above your head.
   • What is the moon's phase? Full
   • Turn the page to sight along the line from earth to position 5 of the diagram below, then draw this phase as it appears from the earth in the outer circle at position 5.
   • Is the moon on the opposite side of the earth from the sun? Yes
   • Is this a good time to observe the moon with binoculars? (No. Cf. Berman, p. 52.)

   

6. Half of the Lunar Cycle, from the New Moon to Full Moon or vice-versa, lasts about two weeks.
   • Continue moving the moon around in a complete circle to represent another two weeks, and fill in the outer circles at positions 6, 7, and 8.
   • The complete synodic cycle averages about 29.5 days, or one "moonth" (Old English for "month").
   • Match the position number in the diagram above with the name of each phase in the table below:
     

     #	Phase
     2	Waxing Crescent
     8	Waning Crescent
     5	Full
     1	New
     4	Waxing Gibbous
     6	Waning Gibbous
     3	First Quarter
     7	Third Quarter

   • In the waning half of the moon's cycle (Waning Gibbous, Third Quarter, and Waning Crescent), is the left or right side of the moon illuminated as seen from earth? Left
     • By this means can you tell the difference between a Waxing and Waning Crescent, or between a First and Third Quarter? Yes
     • Interpret these lines from Christina Rosetti's Sing-Song:
       "O Lady Moon, your horns point toward the east; Shine, be increased.
       O Lady Moon, your horns point toward the west; Wane, be at rest."
       
7. Position the moon for a Full Moon. Let one person hold the moon in a constant Full Moon position while the other acts as the earth and rotates in space. For the following questions, answer with phrases such as "setting in the west," "rising in the east," "crossing the meridian," or "invisible beneath the horizon."
   • Assume the sunset position (see Part I). If Mr. and Mrs. Epidermis, who live on Mt. Nose, observe the Full Moon at sunset, where is the moon located in the sky? Rising in the east
   • Assume the midnight position. If they observe the Full Moon at midnight, where in the sky is it? Crossing the meridian
   • Assume the sunrise position (see Part I). If they observe the Full Moon at sunrise, where in the sky is it? Setting in the west
     
8. Model each phase of the moon again. For each phase determine the location of the moon in the sky for someone on Mt. Nose at sunrise and sunset.
   • Step 1: Let one person hold the moon in position for a given phase.
   • Step 2: Let the other assume the sunset position (remember which hands are east and west!) and determine where the moon would appear in the sky at sunset. Use one of the phrases A-F as listed below. Then trade places.
   • Step 3: Repeat step 2 for the sunrise position.
   • Repeat steps 1-3 for each phase.
     A. Above the eastern horizon
     B. Above the western horizon
     C. Crossing the meridian
     D. Rising in the east
     E. Setting in the west
     F. Invisible beneath the horizon

   #	Location at sunSET	Location at sunRISE
   1	Setting in the west	Rising in the east
   2	Above the western horizon	Invisible beneath the horizon
   3	Crossing the meridian	Invisible beneath the horizon
   4	Above the eastern horizon	Invisible beneath the horizon
   5	Rising in the east	Setting in the west
   6	Invisible beneath the horizon	Above the western horizon
   7	Invisible beneath the horizon	Crossing the meridian
   8	Invisible beneath the horizon	Above the eastern horizon

   • Which types of phases will be above the east or west horizon at sunrise/sunset? Crescents and Gibbous
   • Which phases will be crossing the meridian at sunrise/sunset? Quarters
   • Which phases will be on the east or west horizon (rising or setting) at sunrise/sunset? New and Full
     

   • Henry W. Longfellow wrote that:
     In broad daylight, and at noon,
     Yesterday I saw the Moon...
     • Is this poetic account possible? YES
     • If so, in what phases might the Moon have been? Crescents or Quarters
       
   • Some time when the moon is visible, hold a ball up in the direction of the real moon outside (do not look at the sun!). Light rays from the sun upon the real moon are parallel to light rays from the sun upon the moonball.
     Predict: Will the moonball model and the moon show the same phase? YES
     
   • If the moon is visible all night long, in what phase is it? FULL
     

V. Model Eclipses with Mt. Nose

1. Face the sun with your moon between Mt. Nose and the sun. Stand several steps back from the sun, and make sure the moon is much closer to the earth than it is to the sun.
   • What phase is the moon in? NEW
   • Can your lab partner see the moon's shadow on your face? Can you see a shadow on the face of your lab partner? Yes
   • Is the moon's shadow on your face (the earth) as large as your face (the earth itself)? No
   • Eclipses are named for the body that is hidden; in a lunar eclipse the moon is obscured, and in a solar eclipse, the sun is covered. Do Mr. and Mrs. Epidermis on Mt. Nose see a solar eclipse or a lunar eclipse? Solar
   • Do the Chin children or the people in Eyebrow City see an eclipse? No
   • Why is an eclipse of this type not seen by everyone on the near side of the earth? The moon's shadow is smaller than the earth
   • Why does an eclipse of this sort not happen with every New Moon? The moon is usually above or below the earth
     
2. Turn your back toward the sun and move the moon into the shadow of your head on the far side from the sun.
   • What phase is the moon in? Full
   • Is this a solar or a lunar eclipse? Lunar
   • Can you see the shape of your head when the moon moves into eclipse? Yes
     (When the moon is eclipsed the earth always projects a curved shadow. Does this prove that the earth is spherical? Yes, this was Aristotle's argument)
   • Is this kind of eclipse visible from the entire night side of the earth? Yes
   • Why does an eclipse of this sort not happen with every Full Moon? The moon is usually above or below the earth
     
3. During solar and lunar eclipses the sun, earth, and moon lie in a straight line, but they are not arranged in the same order.
   • Which body lies in the middle for a solar eclipse? Moon
   • Which body lies in the middle for a lunar eclipse? Earth
     
4. In the Hebrew calendar each month began with a New Moon. Christ was crucified soon after the Passover meal, which was celebrated in the middle of the month of Nissan. During the crucifixion of Christ the sky became darkened. Given this information, would it have been possible for the darkening to have been caused by a solar eclipse? No, the moon was Full so only a lunar eclipse would have been possible.
   
5. How does the Man in the Moon cut his hair? Answer

VI. Conclusion: Lunar Phases, basic principles

1. Does the moon shine by its own or by reflected light? Reflected
2. How much of the Moon is illuminated by the Sun? Half
3. Are the phases of the moon caused by the earth's shadow blocking light from the sun? NO! In a video documentary, the vast majority of graduating seniors at Harvard missed this question.
4. Is the far side of the moon the same as its dark side? No, in the New Moon the far side is the bright side.
5. What is the moon's phase when it is visible and closer to the sun than we are? Crescents
6. Does the lighted side of the moon face toward or away from the sun? Toward
7. Does it take a day, a week, a month, or a year for the moon to return to the same phase, e.g., from one New Moon to the next New Moon? Month
8. The moon falls behind the fixed stars along the zodiac just as the sun falls behind the fixed stars along the ecliptic. Which falls behind more quickly, the sun or the moon? The sun slips slowly behind by about 1 degree per day; the moon rapidly falls back about 13 degrees per day. Observe this at sunset on two successive nights!
9. The altitude of the Full Moon at midnight on the meridian is opposite the altitude of the sun on the meridian at local noon. That is, in winter the sun is low, and the Full Moon is high, but in summer the sun is high and the Full Moon is low.
   • On what date and time would you see the Full Moon at its highest in the sky? Midnight of winter solstice.
   • Click here for a poetic evocation and celebration of moonlight.

VII. Discussion: How does the Earth appear from the Moon?

You live in a colony on the near side of the moon and observe the earth to be about four times larger in the lunar sky than the moon is in the earth's sky. Use the ball to represent the earth instead of the moon, if necessary, to answer the following questions.

1. Does the earth shine by reflected light from the sun? Yes
   • What makes our daytime sky blue? Air scatters light rays to blue; dust particles scatter light rays to red.
   • Is the daytime sky on the moon blue or black? Black
2. Does the earth show phases? All phases from New to Full? Yes
   • Which phase is the earth in as seen from the moon when the moon is in any given phase as seen from earth? (Opposite or complementary phase; cf. Berman, p. 142; and earthshine.)
3. Does the earth move across the lunar sky like the moon moves across the earth's? No; it stays in a fixed position
   • Does the moon complete one of its major motions in 24 hours? No
   • Is the earth's altitude above the lunar horizon fixed in place throughout a 24-hour period? Yes
4. How long is a lunar day? Does it equal a day on earth, a month, or a year? Month
   • Given a moon buggy, could you outrace the advance of the sun on the moon's surface? (Yes; the edge of daylight advances at about 10 m.p.h. This may be a future Nat Sci lab pending sufficient funding. Cf. Berman, p. 53.)
5. Your friend at OBU observes a lunar eclipse. From the near side of the moon at the same time, what do you see? Solar eclipse
   • (You could model this by letting the ball be the earth, and your eye be the moon.)
6. If you haven't done so already, while the lab is still fresh in your mind read the assigned texts listed below.
   • Bob Berman, Secrets of the Night Sky, chs. "Moonstruck," "Everything you never thought to ask about the Crescent Moon," "Eclipsing it all," and "Harvest Moon."
   • Michael J. Crowe, Theories of the World, pp. 10-15.
   • Original for this lab

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