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.

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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?

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

2 comments:

  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.

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    Replies
    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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