Moon Phases and Tides in the Planning the D-Day Invasion Part I: The Phases of the Moon

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2 The apparent motion of the moon relative to the sun as seen from Earth Moon s orbit around the Earth Apparent direction of motion east = 12 per day Direction of Earth rotation (once in 24 hours) Day 2 Waning crescent moon angle SME = 156 (obtuse) Earth 24 Parallel rays from sun North Pole Direction of moon s apparent motion as seen from Earth (2 days x 12 /day = 24 ) Day 0 New moon (not seen) angle SME = 180 The angle SME is the angle between the sun, the moon, and the Earth. The moon is located at the vertex of this angle. Not drawn to scale. 2

4 determining the timing of the phases of the moon is that as seen from earth, the moon appears to move by 12 degrees per day toward the east relative to the sun. Let us investigate these changes with the use of the accompanying diagram and possibly, a laboratory simulation. A note about the view of the earth shown in the diagram: the diagram shows a polar view of the earth and the moon s orbit, as though we were looking down on the earth from far above the North Pole. The view of the earth that you are probably most familiar with is an equatorial view, with the equator horizontal, the northern hemisphere on the top and the southern hemisphere on the bottom. In this different view, any movement in the counterclockwise direction is toward the east, and any movement in the clockwise direction is toward the west. You can simulate this with a globe. Point the North Pole toward you, and spin the globe toward the east; it will appear to be moving counterclockwise. Laboratory simulation of the phases of the moon: In a darkened room, let a centrally seated observer represent the earth, a small bright ball represent the moon, and a flashlight represent the sun. As the angle between the sun, the moon and the earth changes, the moon will to go through phases, similar to those of the real moon. Complete the data table below. Also, using a protractor, show the location and apparent shape (phase) of the moon on the diagram on each of the days indicated. Data table: Day of Motion of moon on orbit Angle SME Category of angle Phase of moon cycle (degrees toward east) open new (not seen) obtuse waxing crescent new (not seen) Answer the following questions with reference to the diagram and/or the simulation. Fill in the accompanying data table as you go. 5. What time is it for the observer on earth shown in the diagram (Hint: where is the sun?) 6. Why is the moon not seen on the night of a new moon? 4

6 Answers to questions Part I 1. Why was the moon important to the Allied invasion plan? Why would the use of artificial lighting, like flashlights, be dangerous for the paratroopers? Since the aerial assault would be beginning slightly after midnight, the paratroopers would need light to see by. The use of flashlights or any other artificial light would attract the attention of the Germans and reveal their location. 2. In order to be useful to the Allies, on the night of the invasion, by what time should the moon be high in the sky? It should be high in the sky by midnight, when the aerial assault was scheduled to begin. 3. In order to be useful to the Allies, on the night of the invasion, until what time should the moon remain above the horizon? The moon should remain above the horizon until the first light of dawn. 4. During the times referred to in questions 3 and 4, in order to provide the most possible light to the paratroopers, what phase should the moon be in? Ideally, the moon should be full, or nearly so. 5. What time is it for the observer on earth shown in the diagram (Hint: where is the sun?) Since the sun is on the western horizon, it is sunset. 6. Why is the moon not seen on the night of a new moon? Because since it lies in the same direction as the sun, it sets when the sun sets, and does not rise until sunrise. 7. Would the night of a new moon be a good night to begin the invasion? Why or why not? No, because there would be no moonlight at all. 8. On the night of a waxing half moon, where is the moon seen at sunset? (Hint: Analyze the diagram.) Moving to the east at 12 degrees per day, in the 7.5 days since new moon it will have separated from the sun by 90 degrees. Therefore when the sun sets in the west, the moon will be at its highest point in the sky. 9. On the night of a waxing half moon, at what time does the moon set? (Hint: The moon and the entire sky appear to move from east to west by 15 degrees/ hour due to the rotation of the earth in the opposite direction.) As seen in question 8, at sunset, the moon would be separated from the sun by 90 degrees. Due to the apparent rotation of the sky by 15 degrees per hour toward the west, it will set by approximately midnight (six hours after sunset). ( 15 degrees/hour x 6 hours = 90 degrees) 10. Would the night of a waxing half moon be a good time for the invasion? Why or why not? No, because by the time the aerial assault would have begun at about midnight, the moon would have set. 6

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