ubject Astronomy
Topic no title
Type Questions-Answers
Level High School
Style MLA
Sources 3
Language English(U.S.)
Description
Background
Shadow Stick Astronomy
Diurnal Motion of the Sun -В Observed with a Gnomon
Purpose
The simple apparatus of a shadow stick board and a vertical stick (gnomon) can be used to make a number of simple and sophisticated measurements of the Sun’s position during a single day or throughout the course of a year. In this experiment you will be measuring shadow lengths and positions during a single day. From this you will be able to:
– determine a north-south line or local meridian.
– determine azimuth and altitude of the Sun.
– determine Local Noon.
– determine local latitude.
Materials Needed
- a) Shadow Stick Dial – click on this link to download the SSD. This file is a Microsoft Word document and can be downloaded as either a Word 6.0 version document
В (Links to an external site.)
or an Office 97 verision document
В (Links to an external site.)
.
- b) short wooden pencil (with eraser)
- c) metric rule
- d) protractor
- e) glue
- f) cardboard
- g) large piece of blank white paper
Construction of shadow stick board and gnomon
Attach the shadow stick dial to a large piece of white paper and attach these to a piece of cardboard. Be sure that the paper does not wrinkle. Glue or tape may be used. The gnomon will be constructed out of a short wooden pencil. Use a wooden pencil that is at least 5 cm in length (including the metal eraser jacket). Cut off any remaining eraser such that it is flush with the metal jacket. This will be the base of the gnomon. Sharpen the pencil until the overall length of the pencil is 4 cm. Glue the pencil to the center circle of the shadow stick dial or use a thumbtack. Push the thumbtack thru the center of the dial diagram, then place the pencil on the thumbtack.
Print off two copies of the shadow dial. One is to be used to construct your shadow stick board, the other is to be turned in with this assignment. Transfer all of the data from your shadow stick board to the second copy of the shadow dial. Do not turn in your shadow stick board.
Note: In the following exercises it is important that the shadow stick board be level and the gnomon is vertical. It is also very important that the shadow board is not moved during observations.
Collection of Data
Set up your shadow board in a location that will receive sun throughout the day, and on a day that will not have too much cloud cover. Align the 0В° such that it points roughly north. It does not have to be exact as you will determine a true north-south line. At intervals during the day, mark the location of the tip of the shadow. You should record a point at least once every 30 minutes. More observations can be made, although more than four time in an hour is not necessary. If possible begin your observations at sunrise and continue them until sunset. In any case, it is important that you begin your observations at least two hours before noon and continue as late as possible. At each point that is marked, write the local time. Once all the observations are complete lightly trace a line connecting all of the points, making sure that you can still see all of the data points along your line.
Recording the Data
On the table below, record the following information for each data point. The time that the point was marked on the dial. The length of the shadow should be measured from the center of the dial. All measurements are to be made in millimeters. The Ratio is simply the length of the stick (measure the length of your pencil from base to tip) divided by the length of the shadow. The Altitude is calculated using the Ratio. Take the arctangent of the Ratio to get the Altitude. On most scientific calculators this is the tan-1 button. The resulting number will be in degrees of arc. For example, if the Shadow Length is 20 mm, and the pencil 40 mm, the Ratio is 40 mm divided by 20 mm, which equals 2. The arctangent of 2 (tan-1 2) is equal to 63.5 degrees. The final column is the Azimuth. In order to complete this column, the north-south line must first be determined.
Time
Shadow
Ratio
Altitude
Azimuth
Determination of North-South Line
The north-south line can be found using one of two methods. The easiest is to determine where the shadow’s length was the shortest. You may not have observed this point, but the line that you sketched through the data points can be used to determine this point. Draw a line through the center of the shadow dial and the point on the line representing the shortest shadow length. This line will be pointing north. Remember that the Sun is to the south and the shadow points to the north.
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The other method is to determine when the shadow point crosses one of the concentric rings on the shadow dial. Mark that location and then trace that ring until it intersects the shadow line again. Measure the number of degrees between these two points. By bisecting this angle, you can determine the north-south line.
Once the North-South line has been found it is a simple matter to determine the azimuth of the sun at each of the recorded data points. The azimuth is the angle that is measured clockwise from the north point on the horizon to the point on the horizon over which the Sun is located. Since the Sun’s shadow points in the opposite direction from the Sun’s location, the azimuth of the Sun on the shadow dial is measured clockwise from the south line of your north-south line.
Determination of Local Noon
Local noon occurs when the Sun reaches its highest altitude. This also corresponds to the shortest shadow length. You may not have recorded a data point at this time but by using your data you should be able to closely approximate at what time local noon occurs.
Estimated Time of Local Noon: __________
Does Local Noon occur at 12:00 p.m. local time? If not, explain any differences between the time that local noon occurred and noon on the clock.
Determination of Latitude
At the time of the equinox, the latitude can be calculated using the formula:
90В° – altitude of the Sun at local noon = Latitude
Altitude is defined as the number of degrees measured along a perpendicular from the horizon to an object in the sky. During other times of the year the noon altitude of the Sun (H) must be added to the declination of the Sun (Оґ).
Latitude = 90В° – H Оґ
The altitude of the Sun at Local Noon is determined from the data collected. The declination of the Sun (Оґ) must be obtained from the tables in Section C of The Astronomical Almanac [current year]. This table lists the date and Apparent Declination. Declination is either positive or negative depending on the time of year.
Latitude = _________________
Equinox and Solstice
Determine the exact time (month/day, hh/mm) and Apparent Declination of the Sun during the following events in [current year] by using the information found in The Astronomical Almanac [current year].
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month/day hh/mm Оґ (ddВ°mm’ss”)
Vernal Equinox
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Summer Solstice
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Autumnal Equinox
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Winter Solstice
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Your Birthday
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Determination of Sunrise and Sunset
Using The Astronomical Almanac, available in the BHC Learning Resource Center’s Reference section, determine the local time for Sunrise and Sunset. Use the tables for Sunrise and Sunset in Section A. This table will give times for sunrise and sunset for different latitudes along the Meridian of Greenwich (0В° Longitude). The Quad Cities is located at approximately 90В° W Longitude. One hour of time is equal to 15В° of longitude.
How many hours difference is there between Greenwich, England and the Quad Cities? _______
What is the time of sunrise for the day of your observations? ____________
What is the time of sunset for the day of your observations? ____________
What other source of information lists the daily sunrise and sunset times?
Spacing Double
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