Lesson 1 Activity 1: Tools of the Ancients

A. How Columbus Determined His Latitude

Time

Materials for each group of four students

• Drafting triangle or ruler
• Protractor
• String (12 inches long)
• Tape
• Paper clip
• Quarter
• Notebook and pencil

Procedures

1. Make an instrument to observe the height of the Sun above the horizon, as follows:
   

   1. Tape a protractor to the side of a triangle, aligning one outside edge of the triangle with the zero point and 90-degree mark on the protractor, as shown in illustration A.

   2. Clip the paper clip onto the quarter and tie the paper clip to the end of the string.

   3. Tape the string to the protractor so that it hangs freely from the zero point, as shown in illustration B.

   4. Align the pencil with the zero point and 90-degree mark on the protractor and tape it in place, as shown in illustration B.

2. Take observations when the Sun is highest in the sky, which is generally within a half hour of noon. The analemma (illustration D) shows the variation between solar noon and noon according to standard time on the clock. If you are in a time zone observing daylight Savings time, the Sun will be highest an hour later.
   

3. To take a reading on the Sun with this instrument, do not look directly at the sun; observe the shadow of the instrument. Stand on pavement or another smooth surface(not grass). One student holds the instrument a few feet above the ground so that the pencil points directly at the Sun and the string hangs freely next to the protractor.

   Looking at the shadow on the pavement, the student moves the instrument until its shadow appears as a line (from the triangle and protractor) with a dot (from the pencil), as shown in illustration C. The other students take turns reading the angle between the string and the 90-degree mark on the protractor, and recording this angle in their notebooks. The readings will probably differ, so the group compares them and settles on the best value. It may be best to discard the highest and lowest readings and average the other values.

4. To determine the latitude, adjust this number, representing the angle, to correct for the tilt of the Earth's axis. The adjustment changes with the seasons. Use the analemma (illustration D) to determine the correction needed. For observation in the Northern Hemisphere, the Sun appears lowest in the sky in late December; at this time, add 23.5 degrees to the reading; at the summer solstice in June subtract 23.5 degrees from the reading. Intermediate adjustments for readings between these dates can be estimated from the analemma.

Extension

1. Construct a scale model of the solar system showing relative sizes of` planets and distances from the Sun.

2. Discuss what might have happened had Columbus used Eratosthenes' measurement of the Earth's circumference.

3. Look more closely at the analemma. Why does the length of the day vary?

B. Local time and "Grinnage time"

Time

Nine 10-minute observations, mostly concentrated around noon.

15-30 minutes discussion after observations are made.

Materials for each group of four students

• One pole about 3 feet long to hammer into the ground or a free-standing pole with a pointed top (you can use an old antenna or a gate post with a pointed top)
• A "do not disturb" sign to mark the experiment area
• String about 15 inches long with a weight at one end
• Nine 1- by 2 inch pieces of scrap paper labeled with the observation times
• Nine stubby pencils
• Protractor
• Measuring stick or tape
• Notebook and pencil

Materials in the classroom

• Blackboard on which to draw a scale model of your sundial

Procedures

1. Working as a class, choose a flat spot where the Sun will not be blocked during your observation period. Beware of shadows from trees and buildings.

2. Set up the pole, being careful to make it vertical; using the string with the weight on the end as a plumb bob, check to be sure the pole is vertical. The pole should be placed firmly enough to remain in position throughout the day. Measure the height of the pole and record the measurement in the notebook.

3. Label the scraps of paper with the times you will take observations, such as at 10, 11, 11:20, 11:40, 12, 12:20, 12:40, 1, 2. Plan observations to be as symmetrical as possible around local noon. Note that during daylight savings time, local noon is delayed one hour. Find your location on a map that shows time zones; the closer to a time zone boundary, the greater the difference between local noon and noon according to the clock.

4. Divide the class into groups of three to take observations. A pair of students marks the position of the end of the pole's shadow.

   One student (the observer) pokes a pencil stub (point down) through the piece of paper labeled with the time and holds it on the ground such that the point of the pole's shadow falls on the hole where the pencil goes through the paper. The second student (the recorder) verifies the position, and the observer pushes the pencil in the ground.

   The third student (the measurer) then measures the length of the shadow from the base of the pole to the pencil; the recorder records this in the notebook with the time. The measurer then uses the protractor to measure the angle between the shadow and its previously observed position, which the observer marks by stretching the string from pole to respective pencil; the recorder writes this value in the notebook.

   Be careful during observations not to move the pole. Observations and measurements should be made quickly but carefully; 3 minutes should be enough time.

5. Back indoors, record the various measurements on the blackboard on a scale drawing of the sundial.

6. After your last observation of the day, ask the class to determine the time when the Sun was at its highest. This is local noon.

7. Discuss the difference between local noon as measured by the sundial and as indicated by the clock.

Extension

1. Notice that the sundial becomes a compass at local noon --that is, the shadow at local noon points to the Geographic north pole. Using a compass, find the difference between geographic north and magnetic north. Experiment with the magnetic compass and map use. Discuss orienteering. (Information is available in such publications as the Boy Scout Handbook and the USGS leaflet "Finding Your Way With Map and Compass.")

2. Using geometry, calculate the width (in degrees) of a time zone. With this information calculate your longitude by comparing your time with time in Greenwich, England.

Glossary