AST201L.Lab3.Word

NAME & USERNAME: SECTION: LAB 3 EQUINOX AND CALENDAR INTRODUCTION Equinoxes occur when the Earth’s rotational axis is tilted perpendicular to a line of sight to the Sun, shown in Figure 3.1. When this happens, the Sun appears on the Celestial Equator (declination zero degrees), rises due east (Azimuth 90 degrees) and sets due west (Azimuth 270 degrees), and day and night times have equal lengths (Equinox literally means equal night). Some ancient indigenous cultures aligned poles, buildings, etc., with the solar Equinox rise and set positions and presumably celebrated the occasion with ceremonial activity. The Cahokia Woodhenge 1 (Figure 3.2), part of the greater Cahokia Mounds, is a classic example where 11th century concentric poles and mounds were excavated in Illinois and found to mark a solar calendar that included Equinox alignments. In Meso-America, the Maya observatory at Chichen Itza (El Caracol) has window alignments that mark the Equinoxes 2 (Figure 3.3). The Equinox occurs precisely when the central coordinate of the Sun crosses the Celestial Equator (remember, however, that the Sun is half a degree in diameter, so some part of it will be above or below the Celestial Equator at this time). 1 See Cahokia Mounds Museum Society page at cahokiamounds.org/ . 2 See Yucatan Today’s article— The Mayas: The Equinox and the Solstice, at yucatantoday.com/mayas- Equinox -and-solstice/?lang=en . Figure 3.1: Earth’s position in relation to the Sun during the Equinox (not to scale, image from timeanddate.com). Arctic Circle Earth Axis Tropic of Cancer Equator Tropic of Capricorn Antarctic Circle Sun Rays Figure 3.3: At Chichen Itza, the Equinox sunset is visible through a window in Caracol observatory tower (image from Yucantan Today). Figure 3.2: Artist rendition of setting up the Cahokia Woodhenge (by Lloyd K. Townsend, image from Cahokia Mounds Museum Society). LAB3-1

NAME & USERNAME: SECTION: In this lab you will locate the equinoctial solar set position on the horizon and measure the height of the Sun at transit by analysis of its shadow. Since the Sun’s position changes little over the course of a day, the following observations can be carried out at sunset or Solar Noon, the day before or after the Equinox. Look up the precise time of the Equinox in the Astronomical Calendar in the Preamble section. Make sure to check the weather ahead of time! For this exercise, you will need 1) a smart phone/tablet with a camera (or just a camera) , and 2) a location with a relatively low and clear western horizon . It should be a location that you will easily be able to return to for a later assignment . You will also need to identify 3) a suitable “gnomon” at this location. This is a vertical pole that casts a shadow on flat ground. The pole can be one that is already in place (e.g., a fence post) or one that you erect. If the latter, you will need to use some kind of vertical level to ensure that the pole is not tilting in any direction. You will also need 4) a measuring tape or a yardstick to measure the height of the pole and the length of its shadow at Solar Noon. LEARNING GOALS The points below are the expected topics to understand by the end of this lab period. Remember to review these points before completing the lab. If you do not understand one, review the steps that cover it and discuss with your instructor.  Use shadows to learn about the position of the Sun  Determine where the Sun is located in the sky during at Equinox  Determine the length of the day at Equinox  Learn the significance of the Equinox in Indigenous astronomies LAB3-2

NAME & USERNAME: SECTION: 4. At Solar Noon, on the day of Equinox (or one day before or after), measure the length of the Sun’s shadow cast by your gnomon. What is the length of your Gnomon Shadow, i.e., s in Figure 3.5? [1pt] 2ft 5. Find the ratio of Gnomon height to Shadow length. [0.5pt] h/s = 3/2 6. Now calculate the inverse tangent of h/s, tan -1 (h/s), or arctan(h/s) in degrees (not “radians”) on a calculator, or on the internet, with trig functions. [0.5pt] Arctan(h/s) = 56.31% 7. How does this angle compare to the angle you measured for the north celestial pole, or the angle of your latitude? [0.5pt] Outdoor sky-watching exercise LAB3-4

NAME & USERNAME: SECTION: STEP 2: THE EQUINOX DAY LENGTH AND SUNSET 1. Travel to your sunset location by about half an hour before the sunset estimated time. Remember to pick a location where you can best see the sunset at the horizon. Use the timeanddate.com website again in Step 1 to determine the time of sunset at your location. What is your Sunset Time from the website? Sunset Time is at 6:20 pm 2. Prepare to photograph the appearance of the solar disk as it just grazes the western horizon with your camera. It is best not to look directly at the Sun, but at the screen of your phone/camera. When the Sun is low in the sky, most of the radiation that could harm your eyes is attenuated by having to travel sideways through the atmosphere. It is safest, however, simply to point your camera in the Sun’s direction and view only the screen. To submit the photo assignments below, you can 1) download the lab Word file and paste the digital photo in the file, or 2) submit them directly on Canvas as attached files. Make it clear to your instructor on how you submit your photos. [2pt] Sunset Start Time: Obtain a photo when the Sun’s limb first touches the western horizon, and note the exact date and time on your phone. Record them below. Date & Time: September 25, 2023 6:15pm ( Q2a ) Copy Sunset Start photo here: LAB3-5

NAME & USERNAME: SECTION: LAB3-7

NAME & USERNAME: SECTION: STEP 3: SIMPLE CALCULATIONS 1. How long did it take the Sun to disappear below the horizon from the first time it touched the horizon to the final disappearance of its upper edge? [0.5pt] Subtract the time of Q2a and Q2b = 10 minutes 2. Calculate the time of setting for the center of the Sun: [0.5pt] Average the times of Q2a and Q2b = 6:20pm 3. Write down below the time of Solar Noon from Step 1 Part 1 again. This is the time that the center of the Sun will cross the “meridian”, an imaginary line that runs north to south going directly overhead in the sky. Calculate the time difference from Solar Noon to sunset by subtracting the setting time of the center of the Sun, i.e., Part 2 above, from the time of Solar Noon. This is approximately half the length of a full day at Equinox. Double it to calculate the length of daylight on the date of your observation. [1pt] Solar Noon Time (copy from Step 1 Part 1 ): 12:18pm Length of half day at Equinox: How much time is between 2. just above and Solar Noon Time? 6:02 Total Length of Daylight: Double the time of the Length of half day at Equinox (previous answer) = 12:04 STEP 4: EQUAL LENGTHS OF DAY AND NIGHT To conclude, let’s compare your results for the full length of daylight with that listed on timeanddate.com . For example, in Figure 3.4, it is 12:07:13 long on Mar. 19, 2020 in Flagstaff. They should be close but may not exactly the same, since the website measures day length from the beginning of sunrise to the very end of sunset. Sunset Times (time of complete disappearance): Your measurement (copy from Q2b ): 6:25pm From website: 6:19pm Day Length Times: Your measurement (copy from Step 3, Part 3 ): 12:04 From website: 12:02 Account for the similarities and differences between the website and your measurements, answer the following questions. How do your Equinox Day lengths compare? Do they both support the equal-day, equal-night picture of what happens at Equinox? Why or why not? [2pt] The length I gave was 2 minutes more than what the website said. Its seems like it doesn’t support the equal-day and equal night because the guess that I got says that there are 4 more minutes of day time than night time and that doesn’t make a whole lot of sense since there are only supposed to be 24 hours in a day. (2021) LAB3-8