The Motion of the Sun Lab Instructions Fall 2023
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School
University of North Texas *
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Course
1052
Subject
Astronomy
Date
Dec 6, 2023
Type
Pages
12
Uploaded by MajorExploration12487
THE SUN’S MOTION IN THE SKY: DAILY AND ANNUAL
Objectives • You will become familiar with how the altitude of the Sun changes when in different positions on the globe during different times of the year. • You will use Stellarium to gather data on the Sun's altitude and azimuth for different cities on the globe, at different times of the day, on the equinoxes and solstices. • You will then plot this information on a set of graphs to visualize how a day may look on different parts of the globe. You will upload an image or scan of these graphs. • You will also discuss the applicability of this experiment in your everyday lives in a discussion board. Equipment • Stellarium web version (
www.stellarium-
web.org
) – watch tutorial posted in Canvas for overview and features helpful for this lab • Calculator • A pen or pencil • A set of different colored pencils/pens • The data table and graphs provided for each of the locations. Background Information This class should be widening your perspective on not just the universe around you, but also to those people on other parts of our globe. Their constellations, their stories, their cultural touchstones may be broadly similar yet specifically unique to yours and this lab will shed light on a small part of that experience: the position of the Sun in the sky and the length of the day. Let’s say you walk outside and want to measure the position of the Sun right now (assuming it’s not cloudy). How would you do it? Well, you’d need some kind of measurement system! You can’t just point to it and say “There it is!” and expect that to translate well to a description that others not currently in your location at that time would understand. Instead, we will use a local coordinate system
that defines the position of any object in the sky by way of placing a grid on the sky that is centered on your position on the Earth. This contrasts with a celestial coordinate system
which places a grid on the sky centered on the Earth itself, using the Earth’s equator and geographic rotational poles to define specific points. The local coordinate system
, shown in Figure 1, uses 2 axes of measurement. One axis is the planar location of the object. If we imagine that the whole sky is projected onto a flat circle, the
planar location would be best to measure as an angle away from some specific line drawn from the center of the circle to a point on the edge of the circle. For our system, this line is the line Figure 1: Local Coordinate System drawn from you straight towards geographic north
. So if you face directly north and start to rotate eastward
until the Sun is directly in front of you, you have physically measured what we call the azimuth
of the Sun. It is the angular displacement eastward from north whose values will go from 0° to 360°. The second axis is a description of height away from your horizon and we call this measurement the altitude
. If you’re familiar with the word altitude
, then you probably already understand this measurement. The altitude
is the angle of deviation from the horizon to the object whose values go from 0° to 90°, where 90° is the position directly over your head – the zenith
. Now you’re not the first person to measure the position of the Sun and through careful measurement over the whole year, those people noticed that the Sun seemingly moves with respect to the background stars. When the Sun sets, the constellation that was setting with the Sun that they could see would change through the year. From any day to day, the position change is a bit less than 1 degree for the Sun, so hard to notice, but over the whole year we could draw a line that represents this ecliptic
on a map of the whole sky. The path that the Sun takes throughout the whole year is the ecliptic
and it runs through the constellations you’re probably the most familiar with, the zodiac. Use Figure 2 as you try to understand the next explanation about the ecliptic, the celestial equator, the equinoxes, and the solstices. Figure 2: Ecliptic, Celestial Equator, and Equinox As we are plotting the position of the Sun throughout the whole year, there are 4 days that are important to note: the spring equinox, the summer solstice, the autumnal equinox, and the winter solstice. The word equinox
comes from the words equal and night and it’s when there is an equal amount of day and night almost everywhere on the Earth, so about 12 hours of daylight. The word solstice
comes from the words for Sun and stopped or stationary and it’s when the Sun reaches its most northerly position or southerly
position in the sky before heading in the opposite direction. The Sun moves northerly during the northern spring time until the northern summer solstice and then it moves southerly through the northern autumnal equinox until the northern winter solstice where it turns around heading back northerly to the northern spring equinox. So it may be easy to place the Sun’s position on the sky map when we’re talking about the solstices but what about the equinoxes? There’s one more line we can draw on the sky map and that is the celestial equator
which is simply the projection of the Earth’s equator onto the sky map. On the equinoxes
, the Sun is directly over the Earth’s equator and the ecliptic crosses the celestial equator. On the solstices
, the Sun is furthest north or south from the celestial equator. In this lab you will record the altitude and azimuth of the Sun at two locations on the Earth at different times during the day on three specific days (winter solstice, spring equinox, and summer solstice). You will share your data with classmates who selected different cities, and analyze the group’s results. Pre-Lab Questions 1.
The points where the ecliptic and celestial equator cross are called__________. a)
Equinoxes b)
Longitudes c)
Solstices d)
Latitudes 2.
Altitude refers to __________. a)
the angular height away from the horizon b)
the number of meters you’re standing at sea level c)
the angular distance from the celestial equator d)
the angular height of Polaris above or below the horizon 3.
Azimuth refers to __________. a)
The angular displacement eastward from north b)
The angular displacement westward from north c)
The angular displacement eastward from the vernal equinox d)
The angular displacement westward from the autumnal equinox 4-7.
In this lab you will collect data for two cities: Denton, Texas and a city of your choice. The city you choose must have a latitude that is at least 25 degrees higher or lower than Denton's latitude. Some interesting locations are those near the equator, the North Pole, and the South Pole.
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Use Stellarium to find the latitude and longitude for Denton and your chosen city using the Location option in the bottom left corner and searching for each city. Record your answers rounded rounded to the nearest degree. Sometimes, longitudes are given in east/west and some are given in +/-. Negative longitudes are West longitudes, but record them as +/- numbers. City Latitude (Degrees) Longitude (Degrees) Denton, Texas 4.
5.
6.
7.
Use the website “
Time and Date
” (https://www.timeanddate.com/calendar/seasons.html) as your source for questions 10-12. 8.
What is the date of the Spring Equinox for 2023 (for northern hemisphere)? a)
March 19 b)
March 20 c)
March 21 d)
March 22 9.
What is the date of the Summer Solstice for 2023 (for northern hemisphere)? a)
June 19 b)
June 20 c)
June 21 d)
June 22 10.
What is the date of the Winter Solstice for 2023 (for northern hemisphere)? a)
Dec 19 a.
Dec 20 b.
Dec 21 c.
Dec 22
Instructions for Setup You will notice icons on the menus that we will reference. If you click on something that you can’t undo then just reload the page. IMPORTANT NOTE: The time in the online version of Stellarium is always in local (your) time, even when you change location. Pay very close attention when you collect data for your selected city – you need to find out which time zone it is in and add or subtract hours from the time shown in Stellarium. A.
Open Stellarium web version. B.
In the menu along the bottom of the screen, turn on the Azimuthal Grid. C.
Click the button in the bottom left and search for a city. Instructions for Data Collection Click the button in the bottom right to view the date and time settings. a.
Make sure the time isn’t continuing to progress by clicking the pause button. b.
Set the date and time to the first date and time for the data taking on Table 1. This should be for Denton, on the spring equinox, at 6:00 AM. Since your dates are for 2023, make sure to set the year to 2023
. Leave this window up, you will be using it to move forward in time.
D.
Click in the top center to search and type ‘Sun’ into the search field and click enter
. a.
This should bring up the Sun as the centralized object in the sky. b.
As you’ll be looking through the ground at the Sun below the horizon, likely you won’t see the Sun if you followed the setup instructions well. c.
As long as you don’t click elsewhere on the screen (except on a menu, like the date/time menu) the screen will stay locked onto the Sun as its centered object. d.
If you find that when you change the time that the Sun is no longer centered, just repeat these steps to get it centered again. E.
You should be able to see in the top left-hand corner the Altitude and Azimuth of the Sun. Record these values in Table 1 below and round to the nearest degree value
. Angle values are given in Degrees, Minutes, and Seconds where 1 degree is 60 minutes and 1 minute is 60 seconds. So 10° 33’ 54.26” would round up to about 11° in recording. a.
Advance the time 2 hour to 8:00 AM and repeat the process. b.
Do this for all times listed on the table for the spring equinox c.
Then switch the day to the summer solstice and repeat the whole process again. d.
Then switch the day to the winter solstice and repeat the whole process again. F.
After completing all the measurements for Denton, switch locations to your selected city and repeat the process.
Graphing You will create one Cartesian graph for Denton, Texas. You will create one polar graph for each location.
You will plot data for the three days all illustrated on the same graph for the location listed in the title. Finish graphing one day at a time and use a unique colored pencil to make that day unique to the other days. If the data point doesn’t fit on the graph, don’t graph that point, just illustrate what fits on the given graph.
What you are looking at when the graph is complete is the path of the Sun for each of those days. Compare the graphs between cities. What kind of relationship do you see between the latitude of the city and the altitude of the Sun in the northern hemisphere? To graph the data you recorded in Table 1 on the Cartesian graphs
, you will use the azimuth as your x-coordinate
and the altitude as your y-coordinate
. The example in Figure 3 should help. Figure 3: Example Cartesian Graph
– If you unrolled the sky onto a sheet of paper, the path the Sun makes in a day would look like this. Azimuth
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Figure 4: Polar Graph Example
– If you flattened the sky from its dome shape onto a piece of paper, the path the Sun makes in the sky looks like this. To graph the data you recorded in Table 1 on the Polar graphs
, think of them as if you are looking down on the local sky for that location. So, 0
o
azimuth is North, 90
o
azimuth is East, 180
o
azimuth is South, and West is 270
o
azimuth. All azimuth is measured along the outermost circle which you can think of as the horizon
. The altitude is then simply the radial distance from the outer circle, inwards
which is indicated by concentric circles. Negative altitudes can be plotted as if they were positive, but remember that the line must first go to the horizon before curving to negative altitudes. Every bold line is 30° change
and all dashed lines are 15° changes
. You will draw an approximate ‘best fit’ line through the data as the example in Figure 4 shows. If you’re having trouble imagining what the polar graphs should represent, follow these instructions to have a live view of the phenomena we’re trying to have you graph.
Rotate the camera by clicking and dragging with the mouse on the screen till your view is roughly pointed straight up (towards your zenith)
Zoom Out using the scroll wheel until you can see the sky as a full circle. This circle should have the Cardinal Directions (N, S, E, W) listed on it
Rotate your view if you need to using the arrow keys so that South (S) is at the bottom of the circle in your view.
On each of the days we’ve asked you to observe, and at each location, watch the position of the Sun over the course of the day in this view. Drag the time bar back and forth to watch how the Sun moves across this circle in Stellarium
11.
For Denton, Texas what is the length of daylight on summer solstice? __________ hrs 12.
For Denton, Texas what is the length of daylight on winter solstice? __________ hrs 13.
For your selected city, what is the length of daylight on summer solstice? __________ hrs 14.
For your selected city, what is the length of daylight on winter solstice? __________ hrs 15.
Which of the locations from your discussion board has the largest change in daylight time between winter and summer solstice? 16.
Which of the three locations has the smallest change in daylight time between winter and summer solstice? 17.
For Denton, in which month does the Sun reach the highest altitude? a)
Dec b)
Jun c)
Sep For Question 18
you will need to scan or take a picture of your Data Table If necessary, you can copy and paste each file into a word or text document and upload them that way. DO NOT FORGET TO ANSWER THE QUESTIONS IN THE DISCSSION BOARD
Data Table 1: ALT/AZI of Sun
. Times listed are local times – you must add the number of hours indicated next to the season to the “Time” in the table because Stellarium displays times in Central time.
(Example: for Juneau Alaska, you would set Stellarium to 5:00 to collect 2:00 data; 7:00 to collect 4:00 data…)
DENTON, TEXAS
MY CITY = Spring Summer Winter Spring (subtract ____ hours)
Summer (
subtract _____ hours
) Winter (subtract ______ hours) Time AZI ALT AZI ALT AZI ALT Time AZI ALT AZI ALT AZI ALT 6:00 6:00 8:00 8:00 10:00 10:00 12:00 12:00 14:00 14:00 16:00 16:00 18:00 18:00 20:00 20:00
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DENTON
MY CITY =
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