The

Phases of the Moon Return to the laboratory website (www.ric.edu/psci103/Earth&Moon) Select Exploring 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 phase. There are two buttons to start and stop the animation. Click  to begin the animation. the changing phases of the moon while the moon orbits the earth.

Stop the animation at a by clicking the button.

From which direction of the screen is the sun located?

How much of the surface of the moon is illuminated by the sun?

How much of the surface of the earth is illuminated by the sun?

How much of the illuminated surface of the moon is visible from earth?

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?

As viewed from earth, what side of the moon (right or left) is the moon illuminated?

As viewed from earth, how much of the illuminated moon’s surface is observed?

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?

As viewed from earth, how much of the illuminated moon’s surface is observed?

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?

As viewed from earth, how much of the illuminated moon’s surface is observed?

1 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.

Earth Sun

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 45o . 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 new 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?

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?

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 . 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.)

Appearan Sun-Earth- % Diagram of Phase Name Moon Angle Illuminated Phase

3 ANALYSIS 1. What is meant by the term “waxing”? What is meant by the term “waning”?

2. When the moon is waning, is it located to the right or to the left of the sun in the sky?

3. Which will set first, the sun or the moon when the moon is waxing? Which will rise first when waxing?

4. Which will set first, the sun or the moon when the moon is waning? Which will rise first when waning?

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.

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?

7. What phases of the moon can be observed only during the day (while the sun is above the horizon)?

8. What phases of the moon can be observed only during the evening (while the sun is below the horizon)?

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?

10. Google “solar ”. What is the orientation of the sun-earth-moon for a to occur? What phase must the moon be in to have a solar eclipse?

11. Google “”. 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?

12. Why are solar and lunar so rare?

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 , 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 = ______mm Scale of Image #1 = ______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 = ______mm Distance Image #2 = ______mm

Magnification = ______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!)

Measured Diameter Calculated Diameter Calculated Actual Crater Image #2 (mm) Image #1 (mm) Diameter (km) Diameter (km) Plato

Cassini

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.

M S T In this diagram MB represents the height of a sunlight B surface feature, such as a mountain, BC is the moon’s radius, MS is the length of the shadow as C 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 = (Equation 1) MS 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!)

Distance to Moon’s Length of Height (MB) Calculated Known Height Feature Terminator Radius (BC) Shadow (MS) (mm) Height (MB) (km) (BT) (mm) (mm) (mm) (km) Mons Pico Mons

Piton

6

Image #1:

Lunar Surface at 1st Quarter

Image #2: Magnified Portion

Crater Plato

Mons Pico

Crater Cassini Mons Piton

7

8