Understanding Lunar Phases and Their Appearance, Study notes of Geometry

Download Understanding Lunar Phases and Their Appearance and more Study notes Geometry in PDF only on Docsity! Lunar Phase Simulator The changing appearance of the moon is the most commonly observed astronomical phenomenon. The moon's cycle of phases has importance in almost all cultures, and even today we use periods of time — the week and month — which likely have their origin in lunar cycles. A common assumption is that the earth's shadow falling on the moon causes its phases. In fact, the dark part of the moon is the half of the moon that is on the opposite side from the sun — the nighttime half of the moon. While half of the moon is always in darkness, keep in mind that there is no permanent 'dark side' since the moon rotates. However, since the moon rotates at the same rate it orbits around the earth it always keeps the same side toward us. In the pictures below features stay in the same relative place. The other side of the moon, the far side, cannot be seen from earth. Waxing First Waxing Full Waning Third Waning Crescent Quarter Gibbous Gibbous Quarter Crescent The sequence of images above shows the phases of the moon in their relative order. During the first half of the cycle (new to full) the moon is illuminated on the right hand side, and during the second half of the cycle (full back to new) it is illuminated on the left hand side. Another way to remember this is the following: “When the light is on the right, it will soon be bright.” To describe how much of the moon appears illuminated we can calculate the percent illuminated, or the fraction of the moon's lit as seen from earth. A new moon is 0% illuminated (completely dark) and a full moon is 100% illuminated (fully lit). Both first quarter and third quarter occur when the moon is 50% illuminated. When the percent illumination is increasing we say that the moon is waxing, and when the percent illumination is decreasing we say that the moon is waning. When the moon is more than 50% illuminated it is gibbous, and when it is less than 50% illuminated it is a crescent. The fraction of the moon that appears illuminated changes since the moon is orbiting the earth. The time it takes the moon to complete one orbit around the earth (with respect to the sun) is also the amount of time it takes to complete one cycle of phases. This period, known as the synodic month, is about 29.5 days. It follows that in one week the moon completes about a quarter of its orbit. So if the moon is at first quarter today, then in one week it should be near full. The diagram below shows the relationship between the position of the moon in its orbit and its appearance from earth. Here we are looking down from far above the earth's North Pole. From this direction, the moon orbits the earth in a counter-clockwise direction. Phase Phase 1 New Moon 5 Full Moon 2 Waxing Crescent 6 Waning Gibbous 3 1st Quarter 7 3rd Quarter 4 Waxing Gibbous 8 Waning Crescent Visualizing Phases A simple illustration can be used to determine the appearance of the moon based on the orientation of the moon. Using the figure below you will bisect the moon twice. a) Draw a line (perpendicular to the direction of sunlight) that shows the half of the entire moon that is illuminated and shade the shadowed region. b) Draw a line (perpendicular to the Earth-moon line) that shows the half of the moon visible for an observer on earth. c) Mark the region that is both visible from earth and illuminated by the sun. That region will be the phase of the moon we on earth see. The phases of the moon are drawn with the terminator (the dividing line between light and shadow) from the north pole to the south pole of the moon. Use the drawing above to draw the appearance of the moon in the box to the right. Moon Earth sunlight PART II: RISING, SETTING, AND MERIDIAN TIMES When observing the moon one thing we might like to know in advance is when it is visible – what time it sets, rises, and crosses the meridian (due south at it’s greatest altitude above the horizon.) Question: At what time of day can the moon be found due south during a new moon? Using the Horizon Diagram, move the moon to the new mooon position. Rotate the earth until the moon is centered on the meridian (due south). You may need to play with the orientation to get a better view of the positions. Note that the transit time of the new moon is 12:00 PM (noon). Question: What is the setting time for a full moon? With the moon at the full position, rotate the earth while keeping an eye on the horizon diagram in the lower right corner. Rotate the earth until the moon just disappears below the western horizon. You should verify that this occurs at 6:00 AM.  Complete the rest of the rising and setting times in the table above.  During the waxing phases of the cycle, which rises first, the sun or the moon? The sun rises first and sets first.  Which side of the moon (right or left) is illuminated during the waxing phases? side is illuminated so the moon is left of the sun (looking south).  During the waning phases of the cycle, which rises first, the sun or moon? The moon rises first and sets first.  Which side of the moon (right or left) is illuminated during the waxing phases? Left side of the moon is illuminated so the moon is right of the sun (looking south). PUTTING IT TOGETHER On the following page are three examples of analyzing the positions of the observer, sun and moon. Using the Sun-Earth-Moon geometry and the orientation of the observer to the sun, you will plot the positions of the moon and sun on the diagram to the right and complete the table for each situation. Phase Rising Meridian Crossing Setting New 6:00 AM 12:00 PM 6:00 PM Waxing Crescent 9:00 AM 3:00 PM 9:00 PM First Quarter 12:00 PM 6:00 PM 12:00 AM Waxing Gibbous 3:00 PM 9:00 PM 3:00 AM Full 6:00 PM 12:00 AM 6:00 AM Waning Gibbous 9:00 PM 3:00 AM 9:00 AM Third Quarter 12:00 AM 6:00 AM 12:00 PM Waning Crescent 3:00 AM 9:00 AM 3:00 PM Time of Day Noon Phase Waxing Crescent Sun–Earth-Moon Angle 45o Azimuth of Sun South (on meridian) Azimuth of Moon SE % Illumination 25% Time of Day Sunset (6 PM) Phase Waxing Crescent Sun–Earth-Moon Angle 45o Azimuth of Sun West (at horizon) Azimuth of Moon SE % Illumination 25o Time of Day Mid-morning Phase First Quarter Sun–Earth-Moon Angle 90o Azimuth of Sun SE Azimuth of Moon SW % Illumination 50% Sun-Earth-Moon Geometry Su n lig h t Sun – Moon Positions Su n lig h t Su n lig h t ANALYSIS 1. What is meant by the term “waxing”? What is meant by the term “waning”? Waxing: Approaching full moon. Waning: Approaching 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 is illuminated so the moon is to the right (west) of the sun (looking south). 3. Which will set first, the sun or the moon when the moon is waxing? Which will rise first when waxing? Sun sets first and the sun rises first. 4. Which will set first, the sun or the moon when the moon is waning? Which will rise first when waning? Moon sets first and the moon rises first. 5. It’s a full moon . If I see the sun setting in the west where will I find the moon? Explain your reasoning. The Sun-Earth-Moon angle is 180o for a full moon. The moon will be rising in the east. 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 right side of the moon is illuminated so it is left (east) of the sun. It would be found in SE sky. 7. What phases of the moon can be observed only during the day (while the sun is above the horizon)? All, except the full and new moon. 8. What phases of the moon can be observed only during the evening (while the sun is below the horizon)? Only the waxing phases can be seen in the evening after the sun has set. 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 takes 29 days for the moon to rotate. This is called a synchronous orbit. 10. Watch the YouTube video on the eclipses. 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 between the sun and earth –the moon casts a shadow on the earth. This is a new moon. 11. 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 – the earth casts a shadow toward the moon. This is a full moon. 12. Why are solar and lunar eclipses so rare? Why don’t eclipses occur twice a month? The orbit of the moon is tilted about 5o above the plane of the earth and sun (the ecliptic). Therefor the moon is not always in line with the sun and earth to cast a shadow.