Geology Through Literature - Vanity Fair

The next up on my Geology Through Literature thread is Vanity Fair by William Thackeray. Vanity Fair was written in 1848 and follows a group of wealthy urbanites throughout the time period of Napoleon's reemergence from Elba and his eventual defeat at Waterloo. You can get my complete thoughts on the book/story over at my other blog - The Remnant, but for here I will just go into the geological or basic scientific aspects that are brought up in the story.

Chapter XXV

There was only one instance of geology brought up in the story but it was one I had not thought about before.

"Who'd think the moon was two hundred and thirty-six thousand eight hundred and forty-seven miles off?"

This made me question when we actually figured out the distance between the Earth and the Moon. This story was written in 1848 and that seems very early compared to our modern day scientific techniques.

According to Nasa, the Earth is an average of 238,855 miles away, not that far off of the 236,847 miles quoted in the novel. And actually the distance between the Earth and Moon changes depending on the orbit. It goes from 225,623 miles up to 252,088 miles away (Space.com). So in reality, the novels distance quote was spot on. 

The distance from the Earth to the Moon was determined way earlier than the 1800's. In 270 BC, Aristarchus derived the Moon's distances using a lunar eclipse. The Greeks had already known the Earth was a sphere and that the Moon orbited the Earth (since it was assumed everything orbited the Earth at that time). He used this information, along with the duration of one lunar orbit (~a month) and the time it takes to fully cross through the Earth's shadow during an eclipse to determine that the Moon is about 60 Earth's away from the Earth. Without the actual Earth radius though, this couldn't be more refined, until Eratosthenes determine the Earth's circumference a couple of decades later (as discussed earlier). 

More detail on the mathematics of Aristarchus' calculations can be found on Nasa's website: 

http://www-istp.gsfc.nasa.gov/stargaze/Shipprc2.htm

Another method was developed by Hipparchus to measure the distance between the Earth and the Moon using a total eclispe of the sun. You can read about his methods here:

http://www-istp.gsfc.nasa.gov/stargaze/Shipparc.htm

References

http://spaceplace.nasa.gov/moon-distance/en/

http://www.space.com/18145-how-far-is-the-moon.html

http://www-istp.gsfc.nasa.gov/stargaze/Shipprc2.htm

http://www-istp.gsfc.nasa.gov/stargaze/Shipparc.htm

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.

Calling for Researchers - Measure your Earth the Oldschool Way

This is a call for people to get out there and try some science the way it was done in the olden days before Columbus screwed us all up (BTW: Side note - Columbus thought he was in India because he had the size of the Earth wrong by about half even though someone calculated it out long before he was born). In my previous post (My failures in science part 3 - Measuring the Earth) I gave an in depth review of my attempts at measuring the Earth last Summer Solstice as well as the history of Eratosthenes who actually did calculate it out. Well the time has come around again for the next Summer Solstice (June 21st) and I will be trying it again (more like on the 20th and the 22nd).

 And I call on you all to try it too. 

I will reiterate the story a little here.~2200 years ago a man named Eratosthenes measured the size of the Earth by using shadows in Egypt. It turns out he was only off by less than 10%. I tried the same thing and was off by 60%. I feel I have to do better than someone 2,200 years ago, so I am trying it again.

It doesn't matter if you are wrong or don't have fancy equipment all you need is a stick and a ruler to measure the length of a shadow and a car to get some distance between your measurements. You can use Google Earth to measure the distance between the points as well. The more accurate you are the closer you can come to an actual value (theoretically).

If you have a blog, post about your attempts and link to it in the comments section. If you don't have a blog feel free to write about your attempt in the comments.

This is fun (I swear) and it is calling back to the basics of science.

My failures in science part 3 - Measuring the earth

The most recent of my science failures involves me trying to measure the size of the Earth in the method of Eratosthenes. If you don't know his tale, basically it was this: ~2200 years ago a man named Eratosthenes lived in Egypt. He noticed that the shadows were different lengths based on his location at the same time of day at the same time of year (the summer solstice). He saw that at noon in one location (Alexandria) there was no shadow and at the same time and date at another location further south (Syene) there was a shadow. This indicated that not only was the Earth round, but he could calculate the size of it. Since he knew the distance between the two locations he used the angular difference to calculate the circumference of the Earth.

Eratosthenes found out that the difference in his angles was 7.2 degs and the distance was 5040 stades. So the size of the Earth was:

  Circumference = 5040 * 360/7.2 = ~250,000 stades

The length of a stade is debated but let's say it was 176.4 meters. So he calculated out that the size of the Earth was 44,100 km. The actual polar circumference of the Earth is 40,008 km, a difference of only ~9%. I state polar because Eratosthenes measured locations north and south of each other, hence he would get the polar circumference.

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This is where I come in. I wanted to measure the size of the Earth this way as well. I realized several things quickly:

1. I needed two locations north and south of each other because the angle of the sun would be the same along lines of latitude.

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

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.

4. I needed two locations that fell along the same longitude so that I could calculate a direct polar circumference.

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1. Well, I started out. First thing is I constructed a measuring device.

And this is where my problems start. The board was warped. I thought this might have been a good thing since I could then level out uneven terrain easier. But it made the board much more unstable. I used the newspaper to level out the board as best as I could.

2. Calculating out the time was pretty easy. I found out when the sunrise and sunset were and figured out halfway between them. It tuns out it was about 1:30 pm. 


3. The way Eratosthenes calculated out the circumference is that one of his locations had no shadow, so I wasn't entirely sure it would work for me where I had two shadows and I was subtracting the angular difference between the two. (A vs B for Eratosthenes, B vs C for me). But I think there should be no real difference.

4. I also figured I couldn't measure the two different locations on the same day so I did one the day before the summer solstice (June 20th, 2012) and one the day after (June 22nd, 2012). That way any differences would average out. I picked my first location as outside my geology building. The second location I drove south for an hour or so and when the time got near to high noon I drove towards the same longitude. The second problem I ran into was I didn't realize that the lake south of Salt Lake City (Utah Lake) was directly south of the city, not off to the west like I imagined. I had to take a measurement as close to the edge of the lake as I could get since I obviously couldn't drive to the center of the city.

5. So I went out and measured the shadow at the almost correct time.

I marked them on the board and you can see I had some error based on wobble of the board. A little wobble means that the shadow doesn't go directly down the board as I liked, so it took a little work to get everything lined up.

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With the measurements all done, I now had to calculate out the answer. First I measured the distance in Google Earth. I made a new GPS point based on what would have been directly south of the first location and measured the distance between those two.

A recreation of my notes

The board height was 752 mm, the same at both locations. It was the shadows that changed slightly between sites. With the changes in shadow lengths, I was able to calculate out the angles.

As you can see in the image about, I got 16,314 km as the polar circumference of the Earth. I was only off by about 60%. Damn.

Now where did I fail and how do I fix it:

1. The system that I had built was clearly unstable. Making a newer and better one would surely fix the problems. I was going to add the legs that you can unscrew making it easier to level out and keep it leveled out.

2. Measuring from 2 locations which were clearly not directly north and south of each other added unneeded errors. Figuring out locations ahead of time should fix this. Also maybe some locations further apart.

3. I ran into slight problems besides getting to the localities in that I couldn't measure the angles at precisely the high noon mark. Getting to a site earlier and setting up will fix this hopefully.

4. I don't think there was anything wrong with my math but I could double check that that was all done correctly.

So this year we are going to make another attempt at it and hopefully get better results.


References:
http://www.eg.bucknell.edu/physics/astronomy/astr101/specials/eratosthenes.html
http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=646&bodyId=1079