An East-West Line '

This all started several years ago. Since my property is on a curvy road and there is really no flat area on it, I wanted to have an idea of where, exactly, were north south east and west. At first, I thought, I would observe the sunset on the equinox. I don't really have a clear view to the east, so it would have to be sunset. I reasoned that during the equinox, the sun has to set exactly in the west. Well, remember, the equinox is when the night hours and day hours are exactly equal. Twelve hours each. It is the day when the sun's path crosses into winter or into summer. Although the earth still tilts at 23.5°, the axis of the earth is perpendicular to a line from the earth to the sun on those two days each year. Roughly March 22nd, and September 22. Just as you may recall from childhood while riding in the car and looking at the sky,remember wondering why the moon, stars or sun follow us along while closer objects race by? The sun is so far away that it follows you along even when walking just a few feet. So, it was important to note where the sun set on the opposite valley --AND where I was standing at the time.

Sunset on the equinox

So my line seemed a bit askew and I wondered if my method was good. Being sort of oblivious to the north star, and astronomy in general, I was figuring my line should be close enough. In fact, I suffered under the misconception that the sun would vary between 23.5° to the north or south of due west. Even further, I had no idea that the sun didn't just plop straight down.

In my observance, I realized, the sun does not just drop straight down the horizon, unless you are standing on the equator. I should have gotten a hint about this when I was up in Alaska and I kept heading for home when I thought the sun was about to set, only to find that an hour later the sun was still the same height above the horizon, just above a different mountain. It moved sideways.

Here in the mid section of the northern hemisphere, the sun sets at an angle of 41° from 90° , or 49° from the horizon(tal). Furthermore, and this shocks me to be so mentally lazy, the sun varies left and right of due west by some function ( and not just linearly) of the time of year and your latitude. Think about it, in the land of the midnight sun, the sun sets much further north than due west plus 23.5°

I happened to be looking for this function and found two: The angle, left or right, of due west that the sun will set or rise, in the extreme, that is, on the solstices, is described by "A". ...where A= arcsin(sin (23.5) / cos(L)) where L is the locations angle of latitude.

For our neck of the woods, it would be L=41 degrees north and angle works out to 32 deg. 8 min.

I noted two locations where the sun set across the valley. I used the videocamera to document the event. A few years later, I put some posts in the ground and defined a north-south line from my east west line. To do this, I got ahold of a transit level just like the one my dad used when I was a kid. A Keuffel and Esser ( K&E). What a fine device. I wanted the one my dad used, but my brother somehow got ahold of it and when he died, my nephew would not part with it. Well, I found one in better condition on ebay for around $200.

Before using my lines, I thought I better try one more method for ensuring that my line was correct. What follows is another litany of misconceptions of the motion of the earth and stars. I thought to myself, gee, the sun must shine from due south at noon every day, right? I would just check it and, most certainly I would just be a matter of observing the shadow of a perfectly vertical line at exactly noon.

So, I thought, I will just run out there and have a look. I began to doubt this idea when the shadows of street signs and lamp posts were clearly not lining up with the streets at 12:00pm. Daylight Savings!!!! Duh! Ok, I headed out to watch the shadow line up with my line --right at 1:00p.m.

Yeah. Mm-huh?

It turned out that my line was not anywhere near the shadow of a plumb bob string at 1:00pm. At about 1:11 the suns shadow cast down my line. Okay, something is screwball here. How can the sun be that far off from itself? How could I be eleven or twelve minutes off... Let's see, how far is that in angle?

If the earth turns around once in 24 hours, each hour is a 15° arc. Therefore, my 12 minute would be about a fifth of an hour, or a 3 degrees. Over the course of an 820 foot line, 43 feet! Way too much error. As my physics prof told me, when I later asked him about this, "What's the use of having a physics degree if you're going to be off by that much?".

Well, obviously an obsession is growing here. One thing I learned in physics is that when a problem goes on for too long, it's time to consult an authority.

Most people these days might ask, 'Hey, why not use a GPS unit?'. Well, I ended up using the GPS to get an idea of how close I was, but the accuracy of the GPS devices are good enough to get you to the grocery store, not to see how many inches you are from the center of your parking space. I can tell from satellite photos where to plant my line, roughly. I just wanted to see how accurate I could get.

An East-West Line '

Enter: The "Sun Transit" On the way home that day it dawned on me. First, you have to have an accurate clock. Secondly, you have to know where, within your time zone, you are making the observation. In my case it was 6° West of a multiple of 15°, therefore, I thought, the sun will shine from the south at exactly 24 minutes past the hour. The earth sweeps by in its revolving across time zones like the hour hand on a clock. It is not quantized into hours, minutes or seconds. For me to use this method, I must note the exact time and also, I found out, the variance due to the elliptical nature of the earths path around the sun. The sun transit. As it turns out, the sun shines from due south at a specific time each day called "Sun Transit". This time is about when you might expect it, but can vary by several minutes from your "noon". In my case, due to my position in the time zone and daylight savings time, my "noon" happened at 1:24pm. According to the transit ( which can be found at this website: ) The sun shone from due south at 1:17 on that day. Here's a website that, at the time of this writing, can calculate the solar transit for any location and any date: http://aa.usno.navy.mil/data/docs/mrst.php

Well, that makes me a little less off. Instead of 12 minute off, I was 5 minutes off. 5/60 of hour is an error of about 1/12 of 15° or, 1.25° Hooray! Well, how close is that? Still 18 feet at the end of a 830 foot line! I decided to go out, line up the sun at exactly sun transit for that day, use the transit-level and plot a north south line, then turn it 90° and get my east-west. At exatly 1:12, I noted the position of the sun and lined up the telescope of the transit-level using the projection of the sun onto the palm of my hand. You can even see the crosshairs!

Okay, now I was pretty close, but it occurred to me while I was taking the reading. 1:12 pm. Hmm. Do they mean the beginning of 1:12 pm or the end of 1:12 pm? It turns out, the sun's apparent path in the sky is about 1/4 of a degree during that minute. This represents an error of about 3.6 feet in a line 830 feet long. I knew I could get closer.

By looking up the time of sun transit for several days, I found that it happens in each minute for three or four days. On the day I was observing, it had JUST changed from 1:13pm to 1:12 pm. Therefore, I should have waited until the very end of 1:12 to adjust my transit-level. I was about one minute off.

How can I get my clock accurate enough to make these readings? Aha! The GPS device just happens to use very accurate timing to determine its position. I checked its display with the Grenwich Mean Time website and my computers clock was within 2 seconds... the GPS unit was dead on.

The next day I set out to make my final measurement. I moved my flag about 2 feet and 6 inches up the hill from a reference point 435 feet away. The northmost point, I moved about 4 feet. That's it. I am done now.

How close to my original line using the setting sun on equinox? 1.25 degrees. Why the difference? The hill across the valley obscures my view of the distant horizon. In the few minutes the sun is still technically ahead of sunset, it has already sunken below my view. How many minutes? I would say, about five.

CLoSE ENouGH!!!

How High the Sun!

Today, December 15th, is is a rousing 2 degrees outdoors, but the sun is shining brightly. Solar transit occurs at 12:20 (for this location) and at that time, I am measuring the angle of the sunshine off the horizon. I really love this old transit level, a Keuffel & Esser, just like my dad used to use.

At the exact time, 12:20:45pm , I measure the height of the sun off the horizon to be 25 degrees, 15 minutes. Okay? For that matter, I also note that my instrument is pointed at 4 degrees 30 minutes. Time to see if my house is actually situated ( oriented ) due north/south.

This is where most people will difinitely say I have WAY too much time on my hands. Anyway, the house does point north south, to within my degree of error in measurement. Quite close, in fact. Of course, in the city, everything lines up with the street grid.

One would figure, the height of the sun, here at 41 deg. 16 min. 00.01 seconds to be, at the height of the day, 90 degrees, minus 41:16:00.01, minus 23.5 degrees on the winter solstice.

And what would that be... 90 - 41.2668 - 23.5 = 25.233 degrees.

Well, I am off by at least 2/100 of a degree.