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

My Failures in Science - Part 2: Transit of Venus

In a continuation of my previous post (Part 1) I will talk about my attempt at picturing the Transit of Venus which took place shortly after the solar eclipse.

Part 2: Transit of Venus

June 5th, 2012, a little over 2 weeks after the solar eclipse, Venus passed in front of the sun during what is called the Transit of Venus.

Lessons Learned from the Solar Eclipse:

1. I did learn at least one of my lessons from last time. I went out to get the pretty cheap glasses ($1) to watch the Transit.

2. Camera's were a plenty and iPod was fully charged.

The Transit:

The failure of capturing the solar eclipse drove me to do better this time. The problem though, was that the Transit provided a much smaller target to photograph. Luckily though we had a much sunnier day and was able to see the sun for most of the period of transit.

View of the sun from the car at the lake.

We were even able to see the Transit really well with the glasses.

My wife using the paper eclipse glasses.

The only problem though was trying to capture the transit on film. We had heard that trying to take a picture with our camera could fry the lens (or something like that). So I didn't want to that directly. Especially since I only had my wife's camera and she would probably be pissed if I broke it. I figured I could try to photograph it with my iPod Touch.

View of the Transit through the glasses as photographed by my iPod Touch. The sun is partially eclipsed by some clouds.

Another photo of the Transit as photographed with my iPod Touch pressed up against the glasses after the clouds had passed.

 The problem with this though, was that the resolution of the iPod was way too low. I'm pretty sure the size of Venus was smaller than an individual pixel in the above images.

Well we headed back to the house since we didn't know of anyway to capture it well. But I wasn't giving up. The next thing I tried was to use my Aluminum Foil pinhole projection from the Solar Eclipse (pictured in the previous post).

Pinhole projection attempt.

That didn't work. Not sure if Venus was just too small to be projected in such a manner or it wasn't working at all.

The next and last attempt was to try and take a picture with our DSLR through the glasses and hope it didn't damage anything. The first picture I took was just trying it out without a filter and since I didn't have an extreme zoom I felt I wouldn't have any problem damaging the camera.

Picture of the sun without a filter. Running out of time as the sun sets behind the house and the clouds.

After taking several photos I think I might have captured it but I still can't be sure. I don't remember where Venus was at the time so I can't be sure that the darker pixel represent it and aren't just darker pixels.

View of the Transit taken with a DSLR through cheap eclipse glasses. Venus is possibly near the right edge of the sun.

Another picture of the sun zoomed in a bit. I don't think that Venus is visible in this one.

So although I had better equipment, I still wasn't adequately prepared.

Next time, though, as mentioned in the last post, I will be better prepared. Perhaps obtaining an eclipse lens would be the best bet. But I will also try out the ideas that were mentioned in the comments to get a range of results.

My Failures in Science - Part 1: The Solar Eclipse

The wonderful thing about science is that you can often learn just as much, if not more, when mistakes are made than when everything goes according to plan. It is the errors that show us that something wasn't accounted for and those discoveries can be the really interesting things.

To discuss some of my scientific mishaps, I felt like a good way was to create a series of blogs. These are mostly from some of my more random adventures in scientific enlightenment but I feel they are fun.

Part 1 - The Solar Eclipses

On May 20th, 2012 there was a solar eclipse. It was toted as one of the best chances in my lifetime to view a solar eclipse. According to the map below I wasn't in the ideal of locations (in Salt Lake City) but I was in a good location to at least get a partial eclipse.

The problem was that we didn't have any equipment for viewing a solar eclipse. I didn't have the glasses (the store was all sold out) and we couldn't afford anything more specialized for the camera. We also happened to wait until the last minute so that didn't help matters either. This meant I had to make something or go without witnessing it.

I ended up trying to make a "Pinhole projector" but I didn't have the time or materials to do it properly. What I came up with was my "Aluminum foil board".

My homemade eclipse tools

I took a piece of cardboard, cut a square hole in it. Then covered the hole with aluminum foil. The aluminum foil was then pierced with a pin (later to be "adjusted"). A wooden board was also painted white for a projection surface.

Aluminum foil projection board

 We had a problem though. For the majority of the solar eclipse we had cloud cover. In an environment where we have little to no precipitation for the entire year (SLC gets ~15 in/yr), we ended up having cloud cover the one time I need it to be sunny. 

View of the "Solar Eclipse" through the clouds

  My wife though had the idea to head on down to the park anyway and see if we can see anything (we don't have a good view of the setting sun from our house but the park down the street has some amazing views). So we walk on down (~20 minute walk) at around 7pm. Peak time was around 7:30pm, with the eclipse ending at 8:30pm. The sun started to peek out around the clouds at 7:30. The problem was that the clouds still interfered with my system so I couldn't tell if it was working until the sun was fully out. When it finally came out I was able to project an image on the board by adjusting the distance between the projection surface and the pinhole. Unfortunately, though, the pinhole seemed to be too small for anything worthwhile to be visible on the projection. So taking a key I widened the hole into a now "no-longer pinhole" projection system. 

Zoom up of "pinhole"

This seemed to work rather well. You can see the result with the partial eclipse being projected onto the board in the picture below, which is even visible in the low res photo taken. Although the projections on the board ended up being very, very faint. In all of the examples of pinhole projection systems it seemed like the projection should be as clear as a strong shadow. Something must have been constructed wrong.

My wife pointing out the eclipse to my daughter.

One of the problems with this event, you will notice, is that there are very few pictures taken. The reasons for that:

No Photos Reason 1 - We forgot our DSLR camera at the house after we went for the walk to the park. There was not enough time to go back and get it before sunset/the end of the solar eclipse.

No Photos Reason 2 - My iPod Touch was our backup. It was not charged sufficiently and died immediately after the second photo. Pictures of the equipment were taken at a later date. The only photos taken at the eclipse was of the cloudy day and my wife and child looking at the board.

After the iPod died we were actually loaned disposable glasses from a family sitting near us so at least we were able to see the eclipse, if not document it.

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So now we come to why this was a failure of science on my part.

1. I should have started prepping for this way ahead of time. Purchased glasses or something. A camera lens designed for an eclipse would have been awesome but probably cost prohibitive.

2. Cameras need to be brought and charged and backed up. Make sure you have them. It is hard to take pictures without cameras.

3. When making you own equipment. Follow the directions. This is the problem of the fuzzy projection. I believe if there was a tube involved to direct the projection it would have worked better. But I'm not 100% certain. Maybe next time.

4. Improvisation with the equipment most likely won't make things better. Although my pinhole started to work after I "fixed" it, it may have just been my imagination the whole time.