DIURNAL MOTION OF THE SUN AS OBSERVED WITH A GNOMON

Victoria Kramer

Summarized below is a Long Term project developed for monitoring the diurnal motion of the sun. This project was prepared using the outline for long term projects developed by the Earth Science Project (ESP) team assembled through the department of geosciences at the State University of New York (SUNY) Stony Brook, during the summer of 1997.

1. Hypothesis/problem statement

Why is it easier for people living in the northern hemisphere to tan in the summer than winter? Does the altitude of the sun have an impact on this phenomenon? How much does the sun move across the sky throughout the seasons?

2. Materials needed

• stick or post (fence post, basketball post)

• meter stick

• materials to measure the shadow of the gnomon (i.e. meter stick, tape measure, pens, markers, chalk, paper).

• compass to measure north

• sunny day

• table of solar altitude vs. the ratio of gnomon length to shadow length.

3. Data to be collected

• date and time measurements are made

• length of shadow

• length of gnomon

• altitude of the sun

4. Procedure

Obtain a straight stick or rod, or use a fence post or basketball post as a gnomon. If a stick or rod are used, secure them into a wooden block base as illustrated below. An alternative to making a gnomon is using a flag pole, fence post or the post on a basketball court. Using one of these objects would incorporate a sense of consistency in the placement of the gnomon.

On a day that is clear enough to see shadows, find a location outside where you can set up and observe your gnomon. Measure the length of the gnomon from groundsurface to the point above the ground surface and note this height in your field notebook. At a frequency of approximately every 30 minutes, day beginning at sunrise and continuing through sunset, note the length of the shadow the gnomon casts on the ground. Make these observations on ten different days throughout the course of 3 months. An alternative would be to make these measurements at the same time of day over the course of weeks, months and/or season to season. If this is done, the observations can be made at 5-minute intervals for a period of 20 to 30 minutes, but the observations must be done at the same time of day, and a minimum of 20 observations throughout the course of five months should be made.

If a stationary object is used in place of the hand made gnomon, use a piece of chalk to mark the location of the shadow at specific times during the day, month or season. Note these observations in a dedicated field notebook.

Over the course of the investigation, note the length and location of the shadow(s) the gnomon makes. Mark the point on the paper or ground surface where the end of the shadow falls, and write the time next to the mark. Remember to note the date and time of each measurement.

After making all your observations measure the length of the shadow. For each measurement, determine the altitude of the sun as follows: First compute the ratio Length of Stick/Length of Shadow. Then use the following table (Table 4-3-1 pg. 33 of the Robbins lab manual) to find the angle that corresponds to each ratio.

Table of Solar Altitude versus the Ratio of Gnomon Length to Shadow Length

Prepare a table with the following headings: date, time, length of gnomon, length of shadow, ratio, angle.

Throughout the course of your data collection process, review the data being gathered and note the changes in shadow length, ratio and angle of the sun at specific time intervals.

5. Presentation of Findings and Data Analysis

Information that might be in this report would include:

• A data table that would include the time measurements were made, the length of the shadow, the ratio of the shadow length to the gnomon, the altitude of the sun, and the azimuth of the sun.

• A photograph of your gnomon, and your shadow measurements made over the course of data collection (the student must be in the photograph)

• A bar graph illustrating shadow lengths observed throughout the observing period.

• A line graph illustrating shadow length at a specific time of day throughout the period of observation.

Data analysis would include the following observations.

• On what date did you observe the sun at the highest altitude?

• How did the altitude of the sun change from one observation to the next?

• Did the altitude of the sun increase or decrease throughout the day, month year?

• How does the altitude of the sun change with the length of shadow observed?

• During what time of year is the sun highest in the sky?

6. Summary and Conclusions

The summary and conclusions section of the written or oral report prepared by the students will include brief concise statements about the data collected. The statements should answer the questions developed in the data analysis section and also address the projects hypothesis or problem statement. Conclusions about the data can be made based on outside research conducted by the students or others

7. What have you learned, what might you do differently?

• Once the project is completed, the students are required to objectively evaluate the work they have done by asking themselves the following questions:

• Did the data collected answer their hypothesis/problem statement of the project?

• What does the data show?

• By comparing the information presented in their proposal with their completed project were there any surprises or additions in the process?

• If given the opportunity to repeat the project, what would you do differently?

• What did you learn?

8. Bibliography/References cited

Should include the students text and at least two additional reference sources.

Robbins, R., Jefferys, W. and Shawl, S. Discovering Astronomy Activities Manual and Kit, Third edition, John Wiley & Sons, Inc. 1995.

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