ABrister-AST201-Lab3

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Northern Arizona University *

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201

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Astronomy

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Dec 6, 2023

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NAME & USERNAME: ALEXANDRA BRISTER SECTION: 011 LAB3-1 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 3.3: At Chichen Itza, the Equinox sunset is visible through a window in Caracol observator y 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). 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
NAME & USERNAME: ALEXANDRA BRISTER SECTION: 011 LAB3-2 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
NAME & USERNAME: ALEXANDRA BRISTER SECTION: 011 LAB3-3 STEP 1: THE TRANSITING SUN AT EQUINOX At the Equinox, the Sun is situated on the Celestial Equator at 0 degrees Declination. During the Spring (or Vernal) Equinox, the Sun is at 0 h Right Ascension, but during the Fall (or Autumnal) Equinox the Sun is at 12 h Right Ascension. On the day of the Equinox, the Sun ’ s diurnal path traces out the Celestial Equator and gives us a chance to see where this great circle arcs through the sky at our particular latitude. We should not look directly at the Sun, but we can estimate its elevation angle by comparing shadow lengths with the height of the objects that cast them and using a little trigonometry. This is best done with a gnomon, a vertical pole that casts a shadow used by some indigenous tribes to determine the time of day. It can also be used to determine the Sun ’ s elevation angle. If we measure the Gnomon shadow length at Solar Noon, when the Sun is on the meridian and at its highest point in the sky, we can calculate the elevation angle of the intersection point of the meridian with the Celestial Equator. This angle is linked to our latitude as is the elevation of the north celestial pole (north star location), but in a complementary way. 1. Determine the time of Solar Noon at your location. If you are in Flagstaff, you only need to look up the MST time of Solar Noon on this ephemeris at www.timeanddate.com/sun/usa/flagstaff (see Figure 3.4 for example). If you are not in Flagstaff, simply go to the same website and change the location to where you are. What is your location (city, state)? What is the date of your observation? And what time is the Solar Noon for your observation? [0.5pt] Flagstaff, AZ 9/23/23 at 12:15 2. Pre-measure the length of an existing gnomon, or of one that you have erected. Make sure this post is standing perfectly vertical in advance of your Solar Noontime measurements. Use Figure 3.5 below as a reference. What is the height of your Gnomon, i.e., h in Figure 3.5? Make sure you also record your units. [1pt] h = __10.7_in_____________________________________________ 3. Prepare to make your observations within 10 minutes of Solar Noon or LST time of 0 hours! Figure 3.4: The figure above shows the time of Solar Noon (for example, 12:33pm on Mar 20, 2022) and other data in Flagstaff from the website. α = tan -1 (h/s) h s α Figure 3.5: A gnomon of height h casts a shadow of length s. The elevation angle of the Sun is calculated as the inverse tangent (arctangent) of the ratio h/s.
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