A group of people are claiming that the Earth is flat.  Meanwhile, much of humanity believes the Earth is round.  Who is right, and who is wrong?

Folks: we live in the Internet age, which means we can test these ideas with an EXPERIMENT.  To participate, all you need are three one-meter measuring sticks, a sunny day, some flat ground, and an Internet connection.  I hereby declare October 24th, 2017 as the day we #MeasureEarth.

What to measure

The goal is to determine the length of shadow your stick creates when you hold it straight up on a specific date at a specific time of day.  Then compare the length of shadow you measured with what people in other parts of the world measured.

Wait, why?

Do you expect people at other latitudes to measure the same length of shadow that you measure?  Why or why not?  What do you expect if the Earth is flat?  What if the Earth is round?  Discuss with your family, friends, classroom, or in the comments section!

Things you need

Three one-meter measuring sticks, flat ground, Internet connection.  Recommended add-ons: a plumb-bob or other device to ensure your stick is vertical, a camera to take photos of your experimental setup, a social media account to post your photos with tag #MeasureEarth.

Procedure

On October. 24th at noon local time (1pm if your region is on Daylight Savings Time, noon otherwise), we #MeasureEarth!

  1. If it’s sunny, go outside to a location with flat ground.
  2. Position one measuring stick (henceforth the Shadow-casting stick) vertically.  The stick’s entire shadow must fall on the ground for the experiment to work.  Optional: use a plumb-bob or other device to keep the stick as close to truly vertical as you can.
  3. With the other measuring stick(s), measure the length of the shadow created by the Shadow-casting stick.
  4. Optional: Take photos of your setup!  Post them to social media and tag your posts with #MeasureEarth.
  5. Record the following quantities in the #MeasureEarth Google form:
    • your school/classroom/group/own name
    • your location (city and country)
    • your latitude*
    • your longitude*
    • the date of the experiment (should be Oct. 24, 2017)
    • the clock time of the experiment (e.g., 1:02pm, if that is the time on the clock)
    • the length of your Shadow-casting stick (should be 1.0 meters)
    • the length of shadow you measured
    • optional: the angle of incoming sunlight (see method of calculation below in the basic trigonometry section)
    • any comments about what happened during your experiment that might have compromised its quality.

*You can find your latitude and longitude here https://mynasadata.larc.nasa.gov/latitudelongitude-finder/ or at a number of other websites.

measureearth
This diagram shows the experimental setup, including the option to calculate the angle of incoming rays of sunlight.

Analysis

You did it!  Look through the world-wide results to compare the length of shadow you measured to what people in other parts of the world measured.  Especially focus on how the length of shadow relates to the experiment’s latitude.  Do you notice a pattern?  Describe the pattern in as much detail as you can.  If you know basic trigonometry, try the analysis in the trig. section below to see if you can get an even clearer description of the pattern.

Conclusion

How does the pattern you observed relate to the pattern you predicted depending on whether Earth is flat or round?

Middle School and up: consider trying…

Basic Trigonometry:

Calculate the length of the shadow divided by the length of the Shadow-casting stick.  This is the tangent of the angle between the incoming rays of sunlight and the vertical direction, and we call this quantity tan(θ) (pronounced “tan-theta”). Now take the arctan of tan(θ) to solve for θ, the angle of incoming rays of sunlight.  Convert your answer from radians to degrees by multiplying 180/π.

Compare your calculation of θ to what people around the world measured.  How does latitude relate to the angle θ?  Can you write down a simple equation that describes this rule?

Seasons and Times:

If you did this experiment on a different date of the year or at a different time of day, how might the relationship between latitude and θ change? [NOTE: You can test these predictions by repeating the experiment on the same date a few hours after noon, and at local noon on a date months in the future!  Feel free to record your results in the Google form if you do this.]

Circumference of Earth:

Look up the distance between two cities with similar longitudes but different latitudes.  What was the difference in θ measured in these two cities?  Use the difference in theta, dθ (pronounced “d-theta”), to estimate the circumference of Earth.  There are 360 degrees in a circle, so the circumference of Earth is the distance between the two cities times 360 divided by dθ.  Compare the circumference you calculated to what’s on the Internet: were you close?  The ancient Greek scientist Eratosthenes did a very similar experiment in the third century B.C.

circumference
This diagram illustrates how to calculate the circumference of the Earth based on the angles of incoming sunlight measured at two different latitudes (but the same longitude) and the distance between those locations.

 

High School and up: Consider trying…

Data Science: Look for other patterns in the data.  Compare the measured values of θ to the values of θ you predict in the Trigonometry section based on latitude.  What is the difference between the measured and predicted value?  Are there any locations around the world with particularly large differences between the predicted and measured values of θ?  Why is this happening?  What other patterns do you notice in the data, and why might they be there?  You can get creative about which fields of the questionnaire you investigate!