## How much of the surface of the Moon is illuminated by the Sun? Half. How much of the surface of the Earth is illuminated by the Sun?

The Moon Phases of the Moon Return to the laboratory website (www.ric.edu/psci103/Earth&Moon) Select Exploring Earth Visualization In this simulation ...
Author: Kerry Lee
The Moon Phases of the Moon Return to the laboratory website (www.ric.edu/psci103/Earth&Moon) Select Exploring Earth Visualization In this simulation there is a composite view of the phases of the moon as seen from earth, and a view as seen from the perspective high above the earth-moon system. You will use both of these during the simulation. The simulation starts with the position of the earth and moon during the Full Moon phase. There are two buttons to start and stop the animation. Click  to begin the animation. Watch the changing phases of the moon while the moon orbits the earth. Stop the animation at a New Moon by clicking the

button.

From which direction of the screen is the Sun located? Left How much of the surface of the Moon is illuminated by the Sun? Half How much of the surface of the Earth is illuminated by the Sun? Half How much of the illuminated surface of the Moon is visible from Earth? None Start the animation and stop the lunar cycle at a First Quarter Moon. How much of the surface of the Moon is illuminated by the Sun? Half As viewed from Earth, what side of the moon (right or left) is the moon illuminated? Right As viewed from Earth, how much of the illuminated moon’s surface is observed? Half of one side Start the animation again and stop the lunar cycle at a Full Moon. How much of the surface of the Moon is illuminated by the Sun? Half As viewed from Earth, how much of the illuminated Moon’s surface is observed? Full side Start the animation again and stop the lunar cycle at a Third Quarter Moon. As viewed from Earth, what side of the Moon (right or left) is the moon illuminated? Left As viewed from Earth, how much of the illuminated Moon’s surface is observed? Half of one side

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More Details of the Lunar Cycle Return to the laboratory website (www.ric.edu/psci103/Earth&Moon) Select Lunar Cycle Simulation This simulation is very similar to the previous one, except that it provides a bit more information regarding the phases of the moon. In the previous simulation you stopped the motion of the moon in its orbit around the earth every one quarter of an orbit (90o). In this simulation you will stop the simulation every 45o to determine the percent illumination, the names for each of the phases, and the angle formed by the sun-earth-moon for each phase. The controls for navigating this site are very straightforward. Start and stop the animation and complete the diagram below, listing the names of the phases and drawing the appearance of the moon and its direction (clockwise or counter-clockwise) as it orbits the earth.

Third Quarter

Waning Crescent

Sun

New

Waxing Crescent

Waning Gibbous Earth

Full

Waxing Gibbous First Quarter

The reason why we only see a portion of the half-illuminated moon is due to the sun-earth-moon angle. While half of the earth is illuminated and half of the moon is illuminated at all times, because of the position of the moon and earth we are only able to see varying amounts of the illuminated side of the moon. Notice that each of the names for the phases of the lunar cycle are in increments of 45 o . Starting with a New Moon, notice that the sun, moon, and earth are in alignment, with the moon in between the earth and sun. This is an angle of 0o. Since the moon orbits the earth in a counter-clockwise direction, the angle formed between the sun and moon as observed from earth increases, with the moon on the left-side of the sun. Since the moon is to the left of the sun, this means two things: 1. The right side of the moon (as observed from earth) is illuminated. 2. The moon is following the sun in the sky as they both make their way from the eastern horizon (where they rise) to the western horizon (where they set). Complete the table at the end of the laboratory collecting the information from the simulation. 2

MODELING THE MOTION OF THE MOON Use the globe, the yellow sphere as the sun, and the ping pong ball as the moon to illustrate the orientation of the sun-earth-moon system. Place the sun on the laboratory table and orient the moon between the earth and sun to represent a full moon. Place the side of the ping pong ball with the insignia towards the earth so to show that this side of the moon remains facing earth. Move the moon counter-clockwise around the earth approximately 45o while keeping the insignia pointed toward the earth. What lunar phase is represented? Did you rotate the moon to achieve this phase? The ping pong ball (Moon) must be rotated in order to keep the same side facing the Earth. Move the moon counter-clockwise again so that the sun-earth-moon angle is 90o, again while keeping the insignia pointed toward the earth. What lunar phase is represented? Did you rotate the moon to achieve this phase? First Quarter Moon, and yes, the ball must be rotated. Continue moving the moon through the entire lunar cycle, noting the sun-earth-moon angle. You should see that the same side of the ping pong ball always faces the earth, that is the moon rotates with the same rotational period as its orbital period. The moon is said to have a synchronous rotational period so that the same side of the moon is always oriented toward the earth. (Go to the link from ExploreLearning to observe the moon’s synchronous orbit in action.)

Diagram of Phase

Phase Name

Sun-EarthMoon Angle

% Illuminated

New

0o

0%

Waxing Crescent

45o

25% Right

First Quarter

90o

50% Right

Waxing Gibbous

135o

75% Right

Full

180o

100%

Waning Gibbous

135o

75% Left

Third Quarter

90o

50% Left

Waning Crescent

45o

25% Left 3

ANALYSIS 1. What is meant by the term “waxing”? What is meant by the term “waning”? Approaching a Full Moon. Approaching a New Moon 2. When the moon is waning, is it located to the right or to the left of the Sun in the sky? The left side of the Moon is illuminated so it is located on the right side (west) of the sun. 3. Which will set first, the sun or the Moon when the Moon is waxing? Which will rise first when waxing? The right side of the Moon is illuminated when waxing so it is located on the left side (east) of the sun. The Sun will set first when waxing and the Sun will rise first. 4. Which will set first, the sun or the moon when the moon is waning? Which will rise first when waning? The left side of the Moon is illuminated when waning so it is located on the right side (west) of the sun. The Moon will set first when waning and the Moon will rise first. 5. The angle formed by the full moon and the sun is 180o . If I see the sun setting in the west, where will I find the rising moon? Explain your reasoning. East, it will be rising. The Moon will be found in the opposite horizon of the Sun when full. 6. The angle formed by the first quarter Moon and the Sun is 90o. If the Sun is setting, would I be able to see the Moon? Where in the sky would I look to see the Moon? The Moon is illuminated on the right. The Sun is setting in the west. 90o from west is south. 7. What phases of the Moon can be observed only during the day (while the Sun is above the horizon)? Every phase except a New Moon (which can’t be seen anyway) and a Full Moon which rises above the horizon in the east as the Sun is setting in the west. 8. What phases of the Moon can be observed only during the evening (while the Sun is below the horizon)? The waxing phases (crescent, first quarter, and gibbous). 9. We see only one side of the moon. Does the moon rotate on its axis? If it takes 29 days for the Moon to complete one lunar cycle, how long does it take the moon to rotate one about its axis? Yes, it rotates. The time for the Moon to make one complete rotation (rotational period) is equal to the time required for the Moon to make one complete orbit around the Earth (orbital period). 10. Google “solar eclipse”. What is the orientation of the sun-earth-moon for a solar eclipse to occur? What phase must the moon be in to have a solar eclipse? The Moon is located between the Sun and Earth blocking the Sun from the Earth’s perspective. A new moon. 11. Google “lunar eclipse”. What is the orientation of the sun-earth-moon for a lunar eclipse to occur? What phase must the moon be in to have a lunar eclipse? The Earth is between the Sun and Moon and the Moon travels through the Earth’s shadow. A full moon. 12. Why are solar and lunar eclipses so rare? The orbital plane of the Moon is inclined 4o from the ecliptic therefore the moon is not in line with the Earth and Sun every month. 4

Lunar Features Because the moon spans 3476 kilometers, about a quarter the diameter of Earth, and lies only a quarter million miles away, it exhibits a wealth of detail in a small telescopes and binoculars. Both will reveal the Moon's desolate landscape punctuated by bright highlands, dark plains, and rayed craters. At every phase except when full, you'll notice that the lunar globe is divided by the terminator, the line separating the Moon's bright, sunlit side from the side hidden in shadow. Here is where surface features stand out best. Seen in a small telescope or high-power binoculars, the landscape near the terminator stands out in bold contrast and detail. The terrain looks very rough near the terminator because here the Sun is near the lunar horizon. Thus every low hill casts a long, black shadow that creates an exaggerated impression of height. The term 'meteorite impact' is used to describe the process of surface bombardment by cosmic objects. The objects themselves are variously referred to as impactors or 'projectiles'. The impact process is explosive, impacting the surface at more than 20 km/sec (45,000 mi/hour). Upon impact, the impactor vaporizes and the planetary or lunar material is compressed and is tossed out of the target area, piling up around the hole with the bottom of the crater lower than the original ground surface with the piled up material on the rim higher. PART I: SIZE OF LUNAR FEATURES To determine the size of any lunar feature you must first determine the scale of the photograph. Using a ruler, measure the diameter of the Moon (Image #1) to the nearest millimeter. The moon’s actual diameter is known to be 3476 km. Determine the scale of your photograph in km/mm. Diameter of lunar image = 221 mm

Scale of Image #1 = 15.7 km/mm

To determine the magnification of Image #2 measure the distance from the centers of the craters Plato and Cassini on Image #1 and Image #2. From these measurements determine the magnification of Image #2. Distance Image #1 = 25 mm

Distance Image #2 = 116 mm

Magnification = 4.6 times The surface features on the full image are blurry making accurate measurements difficult. By knowing the scale of the lunar image and the magnification of the inset (Image #2), you can now calculate the diameters of the two craters, Plato and Cassini with greater accuracy as they appear in Image #1. Compare your results with the known diameters of the two craters (Google it!) Crater

Measured Diameter Image #2 (mm)

Calculated Diameter Image #1 (mm)

Calculated Diameter (km)

Actual Diameter (km)

Plato

27

5.8

92

109

Cassini

16

3.5

55

57

5

Height of Lunar Features The height of a certain lunar feature such as mountains or craters can be calculated by analyzing the length of their shadows. In the figure below you are viewing the moon from above one of its poles. S

M

sunlight

T

B C

In this diagram MB represents the height of a surface feature, such as a mountain, BC is the moon’s radius, MS is the length of the shadow as seen from Earth, and BT is the distance of the mountain from the terminator. Notice that each of the two triangles are right triangles so that the ratios of the sides are equal. So that: MB

BT =

MS

(Equation 1) BC

Since we are interested in the height of the surface feature, rearranging results in: (MS) (BT) MB =

(Equation 2) BC

Remembering your algebra, we must know all of the terms on the right hand side of the equation to determine the height of the crater. BC is the Moon’s radius, which is known (from Part I) and BT, the distance of the mountain from the terminator can be measured from the full lunar photograph (Image #1). The length of the shadows (MS) is difficult to measure from the full lunar photograph, but can be determined by measuring the shadow on the enlarged image and scaling it to the size of Image #1. Now you have all the needed information to calculate the height of a lunar feature. 1. The mountains Mons Piton and Mons Pico have been identified on the magnified lunar photograph. Measure the length of their shadows on the magnified image (Image #2) and from this determine the length of the shadows (MS) on the full image (Image #1) using the scale of the enlarged photo. 2. Measure the distance from the mountain’s center to the terminator from Image #1. (BT) 3. Use Equation 2 to calculate the height of the mountain (in millimeters) as it appears in Image #1. Use the scale of Image #1 to determine the calculated height of the mountain (in kilometers). 4. Compare your answers with the known heights (Google it!) Feature

Distance to Terminator (BT) (mm)

Mons Pico

9.0

110.5

Mons Piton

15.0

110.5

7.0/4.6 1.52 4.0 / 4.6 0.86

Height (MB) (mm)

Calculated Height (MB) (km)

Known Height (km)

0.123

1.94

2.4

0.117

1.84

2.3

6

Image #1: Lunar Surface at 1st Quarter

Image #2: Magnified Portion

Crater Plato

Mons Pico

Crater Cassini Mons Piton

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