Wednesday, November 12, 2014

My Failures in Science - Measuring the Earth Part 2

In response to my failure to measure the Earth before (See post here for background and details) I again attempted to measure the Earth using the length of the shadows during the the days before and after the summer solstice. To recap here is the background:

~2200 years ago, a man named Eratosthenes made a pretty good estimation of the size of the Earth using the length of shadows during the summer solstice at two different locations.

To repeat this experiment there are some requirements:

1. I needed a measuring stick that was perpendicular to a board to measure the length of the shadow.

2. I needed two locations north and south of each other that fell along the same longitude, so that I could calculate a direct polar circumference.

3. I needed to find out when "noon" was, since daylight noon (the highest point of the sun) is not the same time as clock noon.


1. To fix some of the problems that stemmed from the last experiment I created a larger and better measuring stick.

Here is my handy assistant making calculations and measurements.

I used comments on my previous post to improve on this on. I increased the size of the vertical stick, chose a metal rod since it was not warped and not likely to become warped without noticing, and on the bottom I placed screw feet so I could adjust the levelness of the board. 

High Noon time was set for 1:29 pm on both the day before and after the summer solstice. 

From the previous post I am going to take 2 readings from two locations that are approximately along the same line of longitude. (C and B on the diagram below). From these I will calculate the difference in the angle and therefore can calculate the size of the Earth.

This time I went for a bit further and ended up at a distance of 66,758.87 m apart from each measurement. I had hoped this would help with the accuracy of the results. 

I had double checked and my math previously was correct, where:

Circumference = Arc Length * Difference in the angles/360

For this experiment:
Arc length = 66,758.87 m
Difference in the angles = 1.4149 degress

  C = 66,758.87 * 1.4149/ 360
  C = 16,985.79 km

Still I am majorly off. Only by 57% this time. A 3% improvement. Good?


Next year I will perform the experiment again. This time with a larger measuring device and more distant measuring localities.


  1. You'd need to increase your distance by more than an order of magnitude to match Eratosthenes, right? I wonder if that would result in an order of magnitude error decrease.

    You are also changing both variables (distance and stick length) with this one. While it is probably a good idea to get a bigger stick, would you consider keeping this contraption around for next solstice? It would be interesting to see whether you get the same result at a longer distance.

    1. Interesting idea. Not sure if I have the pieces of it around anymore since I ran the experiment a while ago. I will have to look and see and maybe run the experiment with both a new device and the old one.


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