Measure the angular height of the sun using shadows. This information will be graphed and compared to other locations in the state or world. By measuring the angle of the sun, you will be able to determine how the angle changes due to latitude, longitude and the time of the year.
What is, or will be, the greatest angular height of the sun on this date?
Is the sun ever over your head during the day? If so, at what time?
How can the angular height of the sun be used to determine your approximate latitude?
Why is there a variation in the rate of change between another community and yours?
During the time measurements were taken, what was the rate of change in degrees per minute?
Will the measured angle be greater, smaller, or the same at a more northern latitude?
Will the measured angle be greater, smaller, or the same at a different longitude?
Will the measured angle be greater, smaller, or the same at a more southern latitude?
You will determine the angular height of the sun by measuring the angle of the string with the ground.
You will calculate the tangent of theta by measuring the height of a pole and the length of its shadow.
You will determine the influence of latitude, longitude, and time of year by comparing data from other sites.
Student data:
Angle measurements and shadow length measurments obtained by students are needed.
Record your results in the appropriate boxes below.
Complete attached form.
U.S. Naval Observatory
Altitude (angular height) and azimuth data for the Sun or Moon can be obtained for your town, for any day of the year at this site. You choose the dates for which you want data (such as, first day of summer, winter, fall, and spring) and select your location
Locate a pole or post that casts a shadow all day. The shadow that is cast by the pole must be on solid ground or cement, not on the grass.
Place one end of a string on the top of the post and the other end of the string at the end of the shadow as indicated in the diagram below.
Use the protractor to measure the angle that the string makes with the ground and record this on the data table. Note: If the "zero degree" mark of the protractor is not flush with the ground, you will have to add approximately 4 degrees to your angle measurement.
Measure the length of the shadow, from the bottom of the post to the end of the shadow. Record this on the data table.
Double check the angle measure by using the "parallax" (or tangent) formula. The tangent of the measured angle should be approximately equal to the height of the pole divided by the length of the shadow. Record the result on the data table as the calculated angle.
Repeat the procedure every 5 minutes for the time period indicated by your teacher up to 60 minutes. Use a hardcopy of the attached file to record your data.
Use the above data to graph the results. NOTE: Refer to the Aurora tool "Modifying Aurora Forms" in order to generate related bar graphs.
Answer the "Engaging Questions" found in the Teacher's section of this lesson.
To ensure that accurate data are obtained, students must use care when measuring angles. Explain and demonstrate how to measure the angles. Meter sticks and string were used by some students and work well if the meter stick is perpendicular to the ground. We found that chain link fence posts work the best, if they are perpendicular to the ground. Make sure the protractor has no space between the "0" angle and the bottom edge of the protractor. Make sure there is no grass underneath the protractor.
When selecting a pole to use, be sure that the pole is as straight up and down as it can be ( the pole should be perpendicular with the ground). When measuring the angle, be sure that the protractor is on the ground and not just sitting on top of the grass. Check to be sure that the 90 degree mark on the protractor is directly above the point where the string is on the ground, at the end of the shadow. The angle measurement and shadow length should be taken within a reasonable amount of time of each other, due to the fact that the shadow length is continuously changing.
You can assist your daughter or son simply by helping him or her notice how high the sun is in the sky during the day and by encouraging her or him to notice from which direction the sun rises and sets every day. He or she will be surprised to learn that the sun does not always rise straight east or set straight west; it varies during the year!
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