Learning Lesson: The Shadow Knows II

Overview

Sometimes a claim is made that Christopher Columbus sailed west to prove the world was round and not flat, but that wasn't the case at all. Even in ancient times sailors knew that the Earth was round and ancient scientists not only suspected it was a sphere, but even estimated its size. Measuring the length of a shadow and knowing the distance from the equator, the students will determine the circumference of the earth.

TOTAL TIME 20 minutes
SUPPLIES Meter/yard stick or long dowel; Masking tape; String (at least twice as long as the stick); Protractor; Globe or world atlas
PRINTED/AV MATERIAL None
TEACHER
PREPARATION
This experiment can only be done at solar noon twice a year; at the spring and autumnal equinox. These are the two times the sun is directly over the equator. You can do this experiment one or two days before or after the equinox to work around cloudy days.
SAFETY FOCUS Winter or Summer safety rules.

Procedure

This experiment needs to be conducted at solar noon on March 20 or September 22 (plus or minus two days if necessary to work around the weather).

  1. Tape the string on the very end of the stick.
  2. Place the stick vertically into level ground. (Make sure the stick is in a true vertical position.)
  3. Determine "solar noon" (highest point in sky sun reaches on a given day) for your location from the NOAA Solar Calculator.
  4. At "solar noon" extend the sting at an angle where it does not make a shadow on the ground. Tape it to the ground. Be careful to not pull the stick out of its true vertical position.
  5. Using the protractor, measure the angle between the ground and string.
  6. Using the globe or atlas, determine the distance your location is from the equator. A quick way to learn your location's latitude is to use the National Weather Service weather forecast-at-a-glance page.
    • Go to weather.gov.
    • On the large map, click on the your location. (It takes you to the local NWS Forecast Office).
    • On that locate office page click your location again. (This provide you with your local forecast.)
    • On the forecast page there is another map with a green rectangle showing the actual forecast point you selected. You can fine tune your forecast point by scrolling and zooming that map if desired.
    • Below that map is some information about that forecast point including the latitude and longitude. To obtain you distance from the equator, take your latitude and multiply by 111.111 for distance in kilometers. For distance in miles, take the value in kilometers and multiply by 0.6214.
  7. Use the following formula to determine the circumference of the earth:

Discussion

When conducted on either spring and autumnal equinox the measured angle should be the same as (if measured precisely) or very close to your locations' latitude. This is because on these two days the sun is exactly overhead at the equator at solar noon.

To solve for the circumference, multiply the distance from the equator times 360 and divide by the measured angle. The circumference around the poles is 24,860 miles (40,009 kilometers). The students answers will be similar depending upon the accuracy of the measurements, time of the measurements, and if the stick used in casting the shadow was truly vertical.

The actual circumference around the equator is slightly larger, 24,902.4 miles (40,076.5 kilometers) than over the poles. This ever so slight buldge is due to the earth's rotational speed and the fact that the earth's core is liquid and not solid.

Live weatherwise

If the students complete the lesson in the fall, then teach them the following winter safety rules.

  • The best way to stay safe in a snowstorm is to stay inside. Long periods of exposure to severe cold increases the risk of frostbite or hypothermia. Also, it is easy to become disoriented in blowing snow.
  • If you go outside to play after a snowstorm, dress in many layers and wear a hat and mittens. Many layers of thin clothing are warmer than single layers of thick clothing. One of the best ways to stay warm is to wear a hat; most body heat is lost through the top of the head. Keep hands and feet warm too. Mittens are warmer than gloves. Covering the mouth with a scarf protects lungs from extremely cold air.
  • Come inside often for warm-up breaks. Long periods of exposure to severe cold increases the risk of frostbite or hypothermia.
  • If you start to shiver a lot or get very tired, or if your nose, fingers, toes, or earlobes start to feel numb or turn very pale, come inside right away and tell an adult. These are signs of hypothermia and frostbite. If you experience these symptoms, you will need immediate attention to prevent further risk.

If the students complete the lesson in the spring, then teach them the following summer-time safety rules.

  • Avoid the Heat. Stay out of the heat and indoors as much as possible. Spend time in an air conditioned space. Only two hours a day in an air-conditioned space can significantly reduce the risk of heat-related illness. Shopping Malls offer relief if your home is not air-conditioned. If air conditioning is not available, stay on the lowest floor out of the sunshine. Remember, electric fans do not cool, they just blow hot air around.
  • Dress for the Heat. Wear loose-fitting clothes that cover as much skin as possible. Lightweight, light-colored clothing reflects heat and sunlight and helps maintain normal body temperature. Protect face and head by wearing a wide-brimmed hat. Avoid too much sunshine. Sunburn slows the skin's ability to cool itself. Use a sun screen lotion with a high SPF (sun protection factor) rating.
  • Drink FOR the Heat. Drink plenty of water and natural juices, even if you don't feel thirsty. Even under moderately strenuous outdoor activity, the rate your body can absorb fluids is less than the rate it loses water due to perspiration. However, if you have epilepsy or heart, kidney, or liver disease; are on fluid-restrictive diets; or have a problem with fluid retention, you should consult a doctor before increasing liquid intake.
  • Eat for the Heat. Eat small meals more often. Avoid foods that are high in protein because they increase metabolic heat. Avoid using salt tablets, unless directed to do so by a physician.
  • Living in the Heat. Slow down. Reduce, eliminate, or reschedule strenuous activities such as running, biking and lawn care work when it heats up. The best times for such activities are during early morning and late evening hours. Take cool baths or showers and use cool, wet towels.

Fast Facts

In 1492, Christopher Columbus sailed west from Spain trying to reach India, from which all sorts of valuable spices could be brought.

Everyone knew India was east of Spain, but the way east was blocked by the Turks and Arabs which meant a long journey around Africa. Columbus reasoned he could also reach India by sailing westward, and he proposed to do so, by crossing the ocean west of Spain.

The story is told that many people opposed the idea from what they knew about the size of the Earth, they felt the distance was too great.

Columbus countered with a different, smaller, but wrong, estimate of the size of the Earth. Only at the last moment did Isabella and Ferdinand, queen and king of Spain, changed their minds and support him on his journey.