ABrister-AST201-Lab3
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Northern Arizona University *
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Course
201
Subject
Astronomy
Date
Dec 6, 2023
Type
Pages
8
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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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NAME & USERNAME: ALEXANDRA BRISTER
SECTION: 011
LAB3-4
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]
s
= _____8.3_in_____________________________________________________________________________________________
5.
Find the ratio of Gnomon height to Shadow length.
[0.5pt]
h/s = ___1.289_in____________________________________________________________________________________________
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) = _____52.199_deg_________________________________________________________________________________
7.
How does this angle compare to the angle you measured for the north celestial pole, or the angle of your latitude?
[0.5pt]
90-Arctan(h/s)= B
90-52.199= 37.8 deg
They are complementary angles.
O U T D O O R S K Y - W A T C H I N G E X E R C I S E
NAME & USERNAME: ALEXANDRA BRISTER
SECTION: 011
LAB3-5
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?
9/23/23 at 6:22pm
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: ___9/23/23__5:56pm________________________________________________________________________ (
Q2a
)
Copy Sunset Start photo here:
NAME & USERNAME: ALEXANDRA BRISTER
SECTION: 011
LAB3-6
Sunset End Time:
Obtain a photo just before the upper edge of the
Sun’s
disk disappears below the western horizon, and note the
date and time on your phone. Record them below.
Date & Time: _______9/23/23____6:14pm___________________________________________________________________ (
Q2b
)
Copy Sunset End photo here:
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NAME & USERNAME: ALEXANDRA BRISTER
SECTION: 011
LAB3-7
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
= ______5:56
–
6:14 = _18_min____________________________________________________
2.
Calculate the time of setting for the center of the Sun:
[0.5pt]
Average the times of
Q2a
and
Q2b
= ________6:05_pm______________________________________________________________
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
): ___12:19 pm________________________________________________________
Length of half day at Equinox:
How much time is between 2. just above and Solar Noon Time? _____6:05
–
12:19 =_5:46____________________________
Total Length of Daylight:
Double the time of the Length of half day at Equinox (previous answer) = ____11_hrs_32_min________________________________
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
): __6:14_pm_________________________________________________________________
From website: _____6:22_pm_____________________________________________________________________________________
Day Length Times:
Your measurement (copy from
Step 3, Part 3
): _____11_hrs_32_min______________________________________________________
From website: __12_hrs_6_min___________________________________________________________________________________
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]
I calculated 11 hrs 32 mins for the day length, it is not the same. This is because of human error in recording times. I probably
took the photo early and the setting photo late this could cause the discrepancy between my recorded time and the websites time.
NAME & USERNAME: ALEXANDRA BRISTER
SECTION: 011
LAB3-8
Watch the Equinox videos recorded in Spring 2020/2021 (for Spring semester) or Fall 2020 (for Fall semester), by Lowell astronomers
and public educators on YouTube. You can find the videos by searching
Equinox Lowell Observatory
on YouTube, and your instructor
will let you know the appropriate one to watch. Watch the videos and write one paragraph summary describing 3 things that you learned
from the video. The video previews are shown below:
A L T E R N A T I V E S T O O B S E R V A T I O N S
(2021)