Learning Lesson: The Shadow Knows I

Fast Facts

Measuring the length of shadows actually lead to the first known measurement of the circumference of the earth. Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made an accurate estimate of the earth's circumference.

He read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well.

In Alexandria, almost due north of Syene, the sun was not directly overhead at noon on the same day because a vertical objects cast shadows. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit.

From geometry, the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria which was about 7.2°. Since this angle was 1/50 of a circle, and the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference.

His result, 250,000 stadia (28,740 miles / 45,984 kilometers), is quite close to modern measurements of 24,860 miles (40,008 kilometers) over the poles.

Overview

The Earth is in constant motion. Each day the earth makes one complete rotation. Each year, the earth makes one orbit of the sun. The first motion is obvious. The second one, however, is much harder to notice except over a much longer period and can be made visible only by some time and some measuring. The students will discover the change in seasons as they measure the length of their shadow and compare it three to four months later.

TOTAL TIME A long term project where there will be three months between observations. But for each observation there will be less than 5 minutes for measurements.
SUPPLIES Yard/meter stick or tape measure; Sheet to log measurements.
PRINTED/AV MATERIAL None
TEACHER
PREPARATION		 None
SAFETY FOCUS Winter or Summer safety rules.

Procedure

  1. On a sunny day, early in the school year or just after the winter break, take the students outside to a fixed landmark such as swings, fence, light post, or bench. Have the student record three things:
    1. The date
    2. The time of day
    3. The length of the shadows of several fixed objects
  2. Return to the classroom and ask the students if they think the shadows will become longer or shorter in three months' time. Collect their observations.
  3. After three months, have the students remeasure the same object's shadows at the same time that they made their first observations. Remember to account for the daylight savings time change.

Discussion

If the learning lesson was begun at the start of the school year, the shadows will be longer when measured three months later. If the lesson was started in January, the shadows three months later will be shorter.

The change in the shadow's length is due to the tilt of the earth's axis relative to the sun. This tilt also is responsible for the seasonal changes in our weather and not based upon the distance between the earth and the sun.

Careful measurement of the sun's elevation in the sky at the same time each day for a year reveals an interesting pattern called an analemma. An analemma is the "figure 8" pattern the sun makes in the sky over the course of one year. This figure is the result of the earth's orbit around the sun.

If the earth's orbit were circular and the equator was perfectly in line with the orbit around the sun, then the sun would appear exactly in the same location in the sky each day at noon. However, the earth's rotation is inclined slightly to the orbit around the sun and the path around the sun is elliptical.

Therefore, the sun's motion relative to the stars changes over the course of the year, sometimes appearing to move faster and sometimes appearing to move slower. This means that when the sun is photographed at noon on different dates of the year, its position is in a different location.

You may want to make an analemma at your location. Choose an open location with a tall object nearby that casts a shadow over your site. Then at the same set time (local standard time) each day, mark the location of the tip of the shadow with a drop of paint. Mark the beginning of each month as well. (Remember to ignore the daylight-saving time effect). Over the course of a year, you will have created an analemma which can also be used as a calendar.

Building a Weather-Ready Nation

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

What to Do Before a Winter Storm

  • Use a NOAA Weather Radio with a tone-alert feature to keep you informed of watches and warnings issued in your area. The tone alert feature will automatically alert you when a watch or warning is issued.
  • Contact your local emergency management office or American Red Cross for information on designated public shelters in case you lose power or heat.

What to Do During a Winter Storm WATCH

  • Listen to a NOAA Weather Radio, or local radio or television stations for updated information. Local authorities will provide you with the best information for your particular situation.
  • Be aware of changing weather conditions. Severe weather can happen quickly. Temperatures may drop rapidly, winds may increase or snow may fall at heavier rates. What is happening where you are may not agree with local forecasts.
  • Move animals to sheltered areas. Have a water supply available. Most animal deaths in winter storms are from dehydration.
  • Avoid unnecessary travel. Your safest place during a winter storm is indoors. About 70 percent of winter deaths related to ice and snow occur in automobiles.

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

  • Do not leave children in a closed vehicle, even for a few minutes. This is a "No-Brainer". Temperatures inside a closed vehicle can reach 140°F-190°F degrees within 30 minutes on a hot, sunny day. However, despite this common sense rule, deaths from heat occur almost every summer when someone leaves a child in a closed vehicle.
  • When outdoors, protect small children from the sun. Their skin is sensitive.
  • Help your pets keep their cool. It will "feel" as hot for them as it will for you. As with children, do not leave your pets in a closed vehicle. Be sure your animals have access to shade and a water bowl full of cold, clean water. Dogs don't tolerate heat well because they don't sweat. Their bodies get hot and stay hot. During summer heat, avoid outdoor games or jogging with your pet. If you would not walk across hot, sunbaked asphalt barefoot, don't make your dog walk on it either. (Dogs can also get blisters on their paws from hot pavement.)

 

Fast Facts

Measuring the length of shadows actually lead to the first known measurement of the circumference of the earth. Eratosthenes, a Greek geographer (about 276 to 194 B.C.), made an accurate estimate of the earth's circumference.

He read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well.

In Alexandria, almost due north of Syene, the sun was not directly overhead at noon on the same day because a vertical objects cast shadows. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit.

From geometry, the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria which was about 7.2°. Since this angle was 1/50 of a circle, and the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference.

His result, 250,000 stadia (28,740 miles / 45,984 kilometers), is quite close to modern measurements of 24,860 miles (40,008 kilometers) over the poles.