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, and, therefore, 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, as measured over the poles.

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, and, therefore, 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, as measured over the poles.

Overview

The Earth is in constant motion. Each day marks one complete rotation of the Earth. Each year marks one orbit around the Sun. The first motion is obvious, as we easily observe the change from day to night and the movement of the stars, Moon, and Sun in the sky. The second one, however, requires a much longer period to observe and can be made visible only measuring over a long time. The students will discover the change in seasons as they measure the length of their shadow and compare it three or four months later.

(This activity assumes a location in the Northern Hemisphere. Results will be reversed in the Southern Hemisphere.)

TOTAL TIME A long term project where there will be three months between observations. Each observation will require less than 5 minutes for measurements, but time to get students outside and organized will vary.
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, either 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:
    • The date
    • The time of day
    • 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. Collect their observations.
  3. After three months, have the students re-measure the same object's shadows at the same time that they made their first observations. Remember to account for the daylight savings time change if necessary.
analemma

Discussion

If the activity was begun out at the start of the school year, the shadows will be longer when measured three months later. If the activity 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 (not the distance between the Earth and the Sun) is also responsible for the seasonal changes in our weather. As the Earth moves around the Sun, it changes from being tilted towards the Sun to being tilted away, and then back again. Shadows will be shorted when tilted towards the Sun and longer when tilted away.

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 slightly inclined relative to the orbit around the Sun, and the path around the Sun is elliptical.

Therefore, the Sun's apparent motion in the sky 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 appears 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.
  • Listen to a NOAA Weather Radio, check weather.gov, or listen or watch your local radio or television stations for updated weather or preparation 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. Winter weather can vary across short distances, especially in mountainous areas. 
  • Move animals to sheltered areas. Have a water supply available and ensure it does not freeze. 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.

What to Do Before a Heat Wave

  • Make sure your summer wardrobe includes light colored, light weight, loose fitting clothes and wide brimmed, light colored hats.
  • Have sunscreen and sunglasses.
  • Avoid getting a sunburn because it will limit your body’s ability to stay cool.
  • Reschedule outdoor events for either the coolest part of the day or another day.

What to Do During a Heat Wave

  • Never play in a car and do not leave children, pets, or other dependents in a closed vehicle, even for a few minutes. Temperatures inside a closed vehicle can become deadly within minutes. Between 1998 and 2022, an average of 38 children a year have died of heatstroke in a car, and these deaths can occur year round. Keep cars locked, even in your own driveway!
  • Avoid strenuous activities, especially during the hottest parts of the day.
  • Reduce body temperature by taking a cool shower or bath, or putting hands/feet in cool water. 
  • Stay hydrated – Drink plenty of water.
  • Help your pets keep cool. It will feel as hot for them as it will for you. 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.)

Visit Weather.gov/heat or Heat.gov for more information on National Weather Service heat-related watches, warnings, or advisories, as well as more safety tips and information.

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, and, therefore, 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, as measured over the poles.