Measure the Earth's Circumference yourself

For those of you who want to do this experiment yourself, here is a step by step guide.

1. Find a willing partner on the same longitude as you. It is also very important that the place the sun is shining directly down on the earth is not between the two points you are using. If both your points are above the Tropic of Cancer or below the Tropic of Capricorn, this will not be a problem.
2. Find a spire of a known height, such as a flagpole, at each location. The spire has to be at a location where it casts a shadow on flat ground. If no existing spire is at the location, you can create one using a meter stick.
3. At the same time, have the people at both locations measure the length of the shadow that their spire is casting. This time should be predetermined. Both spires must be casting a shadow at this time. When both people have collected the data, share the data with each other.
4. Now that you have the necessary data, you can calculate the circumference of the earth. First you need to find the difference between the angles that the sun was hitting the spires. First, divide the length of your spires shadow by the height of your spire. Then find the arctangent of this number. Repeat this process for the other spire. These two numbers are the angles that the sun is hitting the two spires. Then calculate the absolute value of the difference between the two angles. Next, divide 360 by this number. Finally, multiply this number by the distance between the two spires. When you have completed this, you have calculated the earths circumference.

The calculation of the earth's circumference

This is the video in which we calculate the earth's circumference.

Caleb collects the data required in Manlius, NY

Caleb made this video accounting for what he did today and how he used his data. We received confirmation from Ms. Garrish, at Ocracoke School, that they will provide us with the length of the shadow of their 35-foot flag pole, measured at 12:15.

(Ken is making this post, so it will probably be removed tomorrow. Nice work, though, Caleb!)

introductions

Everything's in motion

We are all working really vigorously on this project, so far we have everything planned out and contacting Ocracoke. We have a video in the works and will be completed shortly and will hopefully be posted today. (I like to write things that are short and sweet)

~Q.J

We kicked out Ken!

It's true - Ken's officially been kicked out from Project Eratosthenes. Well, not entirely, but the idea from this point forward is that Caleb, Quinten, and myself will become the main contributors to this project. As of right now, Caleb's doing all the hard work - content, diagrams, mathematical analysis, data collection, etc. I'll be in charge of historical research on the work of Eratosthenes, as well as attempts made by various others trying to determine the circumference of the Earth, both successful and failed; I'll also be behind any graphics, coding, communication, and (probably) most of the blog posts you'll see here. Quinten gets to post videos, create animations in Flash for your viewing pleasure, stay on top of all the information that Caleb and I gather, keep in touch with/organize things with our buddies in North Carolina, and, you know, hold everything together. No big deal.

The minute I miss a deadline he's going to kill me.

Since nobody's following us at the moment, please expect numerous updates every day, because we all tend to think of important things long after a post has been made. Plus we don't have to worry about spamming anyone just yet.

- Lexi

Ocracoke School contacted!

At the end of the day on February 28, 2011, Ken contacted a science teacher at Ocracoke School, a small K-12 school on a block schedule.  Ken spoke with Jennifer Garrish and asked if she and her students might be interested in helping to conduct this experiment.  She graciously agreed!  Caleb is getting the ball rolling on creating the information that will be sent to Ms. Garrish so that we can calculate the circumference of the Earth using Eratosthenes's method, but on a non-solstice day.  The ball is rolling...

Caleb thinks there is a way!

After discussing Eratosthenes's method with Caleb on Monday, February 28, 2011, he was inspired to meet the challenge of calculating the circumference of the Earth on a non-solstice day from LaFayette, NY.   Following some critical thinking, drawing, and globe-pondering, Caleb decided that this challenge is indeed possible!  Most critical, he noted, is that we gather simultaneous data from a distant place along our same longitude.  While looking at a map of the United States at our school, he noticed that Ocracoke Island, North Carolina, is located nearly exactly along the same longitude as LaFayette.  After some internet research, we saw that there is a school located in what is perhaps the most ideal spot on the island.  How exciting!  Let's try and make the necessary connections so that we can conduct this experiment.

So, how can we experimentally find the circumference of Earth using Eratosthenes's method?

Eratosthenes measured the circumference of Earth on a solstice, so that the rays of the sun were directly overhead at Syene.  Can we use a similar method to experimentally calculate the circumference of Earth from LaFayette on a day that is not a solstice day?

Computer animation showing how Eratosthenes measured the circumference of Earth.

Carl Sagan introduces Eratosthenes and briefly describes the mathematics behind how Eratosthenes found the circumference of Earth