# Is the Earth Flat? Test It for Yourself

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Is the Earth flat? You may THINK you know the answer. But, with rapper B.o.B saying "flat!" and physicist Neil deGrasse Tyson saying "round!" how can you really know?

Here at the highly empirical (and underground) headquarters of RealClearScience, we don't want you to take anything on faith, only on evidence. Here's how you can test whether or not the Earth is flat for yourself.

Materials:

Commitments:
You
A friend 500+ miles away
Less than 10 minutes
A piece of flat ground outside

Each of you will need:
A phone
A ruler of exactly the same length*
A tape measure
Strong tape
A Protractor

*This includes any small areas between the ends of the ruler and where the numbers start! If your ruler has these, do yourself a favor and saw them off-- who wants to deal with that?

Procedure:

You're going to need one friend who lives at least a few hundred miles from you. The further away they are, the better it will work. You're also going to need a day with enough sunlight to cast clear shadows at both of your locations. On such a day, here's what to do:

1. Find a time that both of you can go outside for ten minutes. Then, pick a precise time, down to the minute, to make a measurement. On your phone, go to the official US atomic clock time, listed at time.gov to make sure your time is accurate.

2. Ten minutes before that time, both of you need to go outside and set up the experiment as follows:

Find a level spot. The easiest way is to choose a paved sidewalk and then see if your roll of tape will roll in any direction. If it doesn't, the ground is level. Otherwise, you can use a level.

Here's the only tricky part: Set your protractor upright on the ground. Now, take your ruler, stand it upright on the ground, and tape it to the protractor at a right angle so that the side of the ruler goes through the center point and exactly the 90-degree line at the top:

Now, turn your contraption so that the flat of the ruler faces into the sun.

At the exact time specified, measure the distance from the base of the ruler to the end of its shadow. Measure this shadow length very carefully and record the number.

Data & Calculation:

Find the difference between the two measurements (subtract). If you measured 150 mm and they measured 162 mm, you have 12 mm.

Result:

If the Earth is indeed flat, the difference in shadow lengths should be this number:

0

If your number is not 0, the Earth is not flat.

Analysis:

This result applies, via something called the small-angle approximation, so long as you believe that the sun is 93 million miles from the earth. It even works if you believe that the sun is as close as a few million miles away. At these distances, all rays from the sun hit the earth at so close to parallel angles that you can't measure the difference with this simple experiment. Shadows of identical objects cast by light rays coming from the same direction can only have different lengths if the objects casting them are rotated at some angle with respect to one another. Since both of your rulers were set level to the local flat surface of the earth, the surface itself must be angled, curving between the rulers.

If you got zero, you have a novel scientific finding, and you'll need to repeat it very carefully and calculate and propagate your experimental uncertainties to make sure. Then email me.

Extra Credit: How Big Around is the Earth?

If the Earth is indeed round you can calculate its diameter, accurate to within a percent or two, with one modification to this experiment. (More precisely you can calculate its radius of curvature. To ascertain that the Earth is roughly completely round, you need to repeat this measurement repeatedly across all time-zones and find the radius of curvature to be the same everywhere.)

It's a hard modification though. You must take your measurement at a precise time and only at one line of longitude. The time must correspond to when the sun is at perfect zenith overhead at local noon at a spot that must be in the tropics. The location is constrained to directly north or south of that tropical zenith spot.

Ancient Greek mathematician Eratosthenes did just this around 250 BC and got a reasonably accurate result.

Conclusion:

You don't have to take scientific facts on face value. You can always test them and see for yourself.

(Top Image: AP)

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