Measuring the Earth Project - General Procedure

Preparation

To do this experiment you will need some materials to measure shadows accurately. Your "gnomon" will be a meter stick that is perpendicular to the ground. For your measurements to be accurate, it is critical that the meter stick be vertical. (Note the devices used below. Wind can be a major factor. Just ask Kathleen Smith. She held a contest to see which group could come up with the sturdiest measurement station.)

Saint Andrew's Catholic School
Fort Worth, Texas

Manasquan High School
Manasquan, New Jersey

It is helpful to have a piece of paper to note where the the end of the shadow is. Also a compass will come in handy to determine in which direction the shadow falls. Since the edge of the shadow is "fuzzy" and the shadow is moving from west to east (northern hemisphere), you want to be careful in deciding where to place your mark.

Have your class work in groups of 3 or 4.

Set up your measurement station. Place paper under the station so you can mark where the shadow ends (see photos above.). Since the edge of the shadow is "fuzzy" and the shadow is moving from west to east (northern hemisphere), you will want the students to be careful in deciding where to place their mark. The students may find it interesting that the shadow points towards the north. But does it point to true or magnetic north? A compass will come in handy to determine this.

Take measurements every 2 minutes beginning at least 10 minutes before local noon which is the time that the sun is highest in the sky. (This will most likely NOT be 12 noon as indicated on your time measuring device (sometimes called a watch). Students should note that when the sun is highest in the sky the shadow length is the shortest.

After some discussion, each group reports this result to the entire class. The teacher writes each group's best value on the board. Assuming there will be different values, students will need to determine their "best" shadow length and decide which will be the class's best estimate of the shadow length at local noon time.

Make a scale drawing of your stick and shadow. Complete the triangle and measure the sun's angle with a protractor.

The students and teacher fill in the chart below.

Chart 1

Site	Location on globe - latitude	Location on globe - longitude	Shadow length	Sun angle
(Your school's name goes here)	.	.	.	.

These values are entered into the central data base for this project. (Details explained at site.) Choose shadow lengths data from other sites. Inform these sites that you using their data.

You might want to make a chart and place it next to a wall map of the world. Use the map to mark where the participating schools are located.

Chart 2

Site Location on globe -
latitude Location on globe -
longitude Shadow length Sun angle

your school . . . .

school #1 . . . .

school #2 . . . .

Etc. . . . .

After you have several schools with entries, the students pick out one of the schools to complete the chart with. Have your students extend the chart to include the central angle, circumference, and percentage error.

Chart 3

Site Location on globe -
latitude Location on globe -
longitude Shadow length Sun angle "Center of the earth" angle N/S Distance Circum-
ference % error

your school . . . . . . . .

school #2 . . . . . . . .

School #3 . . . . . . . .

Etc. . . . . . . . .

Now that you know the central angle, draw the location of your school and another school on the circumference of a large circle.

Determine how many "slices" fit into this circle.

Use the north-south distance to determine the value of the circumference. Explain why that works.

Calculate the percentage error. (Use 40,000 kilometers as your benchmark.)

Repeat the same process for a different school.

Call up the website that contains the calculations and see how well you did. Confirm your calculations with the spreadsheet values.

Create a web page describing the activity and what you and your students learned from doing this project.

Link your webpage to the Noon Day "quilt" (See details at the discussion area.)

(Optional approach: Use trigonometry to determine the sun's angle.)

Additional notes:

The distance from your school to another site is not the "as the crow flies" distance, but rather the north/south distance. As a result this can be more of a challenge. Have students use map scales to determine the distance. The least satisfactory, but very accurate method is to determine the north/south distance from the site's latitude. Though the math is good here, the need for using the actual circumference of the earth as part of the calculation is a bit of deception since you are using information that you are setting out to show. What the ancients did was hire surveyors or behamists to measure the distances needed. A modern solution would be to drive from one site to another and use the speedometer as your measuring device. Of course, the sites would have to be on the same longitudinal line. A compromise would be to have the students use scale methods for estimating the distance, then comparing them to the more accurate methods to see how they did. The compromise would be to choose the more accurate measurement for the purposes of this activity.

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