1. Using Time Zones and Celestial Navigation to Teach the Phases of the Moon Aileen O’Donoghue, Priest Associate Professor of Physics TIME ZONES Teaching about time zones has two primary benefits: 1) Working with the distribution of time zones, students begin to grasp the idea that the time of day on their clock is determined by their position on Earth relative to the Earth-Sun line. The ~15° width of time zones cements the fact that Earth turns 15° per hour. 2) the various clock times of solar noon within a time zone gives the students initial exposure to the association of the observer’s longitude and the clock time of a celestial event. ABSTRACT The phases of the moon are typically presented to introductory astronomy classes in a diagram showing the position of the moon, its appearance and elongation at each phase, and the time of each phase's transit. Though wonderfully compact and efficient at conveying information, I have found it to be overwhelming to non-science major students. Much of their difficulty arises from their vague definition of time which must be broadened for them to understand the different rising, transit and setting times for the phases of the moon. Working with time zones helps them recognize that the time on their watch is relative to a particular longitude and the transit of the sun at that longitude. Celestial Navigation extends this to the transit of all celestial objects and helps them re-define "time of day" to a position on Earth relative to the Earth-Sun line in a practical way. Once they understand why a given object transits at the same time for all time zones, extending this to the moon is much simpler. My students are quickly able to identify the transit times of the various phases of the moon, and with some additional instruction, quickly learn how to figure out their rising and setting times as well. 12 pm 9 pm 6 pm 3 pm 9 am 12 am 6 am 3 am 2 pm 1 pm 4 pm 5 pm Figure 1. Observers at different clock times. In class, this diagram is animated so that the Earth and various observers rotate while the times hover in the sky above each position 1) the altitude of the celestial pole as a direct measure of the observer’s latitude. 2) the fact that the time on a clock is always relative to a particular longitude (reinforcing the idea from the time zone exercises) 3) the ephemeris of transit times gives the positions of objects relative to the Earth-Sun line where they “hover” as Earth turns underneath Clock Noon FOR ALL East side West side Eastern Observer’s Solar Noon Time Zone Rising Time Zone’s Solar Noon Degrees East of TZ center West side Setting Western Observer’s Solar Noon Degrees West of TZ center Transit time gives position of star with respect to the sun 12 pm 9 pm 6 pm 3 pm 9 am 12 am 6 am 3 am 2 pm 1 pm 4 pm 5 pm The transit time of Aldebaran on December 15 is 11 pm. 11 pm Aldebaran’s Position on December 15 nearly opposite Sol! Standard Time FINDING RISING, TRANSIT, AND SETTING TIMES Having worked through time zones and celestial navigation problems, the standard phases diagram can be introduced with elongations in addition to the times. The last hurdle to overcome is to help the students realize that the times shown are the transit times of the moon phase at that position. To facilitate their ability to figure out the rising and setting times, we use a “little observer” printed on transparent film with eastern and western horizons indicated (for looking south). They then use this with the diagram to work out the rising, transit and setting times of the various phases.. CONCLUSION Before I started including time zones and celestial navigation in my course, students truly struggled to understand the different rising, transit, and setting times associated with different phases of the moon. Since I have included these additional topics, they seem to understand it more completely and with much less struggle. The evidence for this is limited to my experience of their having less trouble with the lab exercises and exam questions where they find the rising, transit and setting times of the different phases. With only 24 students per year, statistics are impossible. I am happy to collaborate and supply materials to anyone who wants to do a statistical study of the effectiveness. Figure 2. Clicker questions in class have students practice finding the times of solar noon from the observers’ longitudes (with respect to the time zone center) and positions from observed times of solar noon. Figure 3. Now that students understand the time of day as the position on Earth relative to the Earth-Sun line, they can easily grasp why a given star transits at the same clock time for all observers. waxing gibbous waning gibbous waxing crescent waning crescent 1 st quarter 3 rd quarter Earth 6pm 90  western elongations eastern elongations new noon 6am mdnt full 180  00 90  mdnt noon waxing gibbous waning gibbous waxing crescent waning crescent 1 st quarter 3 rd quarter 6pm new 6am full 9pm 3pm 9am 3am Earth rotation Rising Moon to East Observer’s Time Above E W Setting Moon to West Transiting Moon Above Figure 4. The standard moon phase diagram and an example of finding the rising, transit and setting times of the waning gibbous moon using the little observer. Little Observers … take one! Time EW CELESTIAL NAVIGATION Calculations of observer’s longitudes from celestial observations, the time and an ephemeris (of transit times) promote student understanding of Figure 5. Solutions to student exercises on Time Zones, Celestial Navigation, and Phase of the moon (answers in green). Solar noon is (Degrees)  (4 minutes/degree) Later than clock noon Solar noon is (Degrees)  (4 minutes/degree) earlier than clock noon