# Determining Time From First Principles - Update 1

2024-03-15 - [52] 12:31

In my journal post "Winter Nights New Year Oath - Determining Time From First Principles" from back at the end of October, I wrote about making 4 pledges involving figuring out what time it was from first principles rather than relying on clocks.

Winter Nights New Year Oath - Determining Time From First Principles

Those pledges were:

- Determine Solar Noon (High Noon) from my location using physical objects I can create
- Determine where the night sky from my location rotates from
- Figure out how to determine when the Solstices are by the height of the Sun in the sky
- Attempt to figure out Solar Midnight after determining a Solar Noon

Well, it's been about 6 months since then, so I figured I'd write an update on how these pledges have been going.

## Pledge 1: Determine Solar Noon (High Noon) from my location using physical objects I can create

To determine Solar Noon, all you need is a straight stick, a flat level surface, and direct sunlight. Place the stick perfectly staight up in the flat level surface (for instance a piece of land that's quite level). The Sun will cast a shadow on that stick. At Solar Noon, when the Sun is exactly South of your location (North if you're in the Southern Hemisphere), the shadow will be the shortest it will get throughout the day. This is because Solar Noon is the point in the day where the Sun is highest in the sky.

The equation to determine the length of the shadow cast by the stick is as follows:

    shadow-length = stick-length / tan(sun-angle)

shadow-length is the length of the shadow cast by the stick from the Sun. stick-length is the length of the stick. sun-angle is the angle of the Sun above the horizon. tan is the tangent function. As sun-angle gets larger, shadow-length gets smaller. For instance, if sun-angle was 30 degrees and stick-length was 12 inches, shadow-length would be about 20.78 inches, but if sun-angle was 15 degrees instead, shadow-length would be about 44.78 inches.

I consider this pledge to be fulfilled.

## Pledge 2: Determine where the night sky from my location rotates from

I had to eyeball this, even though I already knew that Polaris barely moves in the night sky. Every night, I would see Cassiopeia and the Big Dipper rotate around Polaris. The further away from North I was looking, the faster everything seemed to be moving in the sky during any particular night. Eventually I came to the conclusion on my own that everything rotated around a point near Polaris. I could be more exact if I set up a thin rigid sight that I could look through to test how much Polaris generally moved.

While I could (and probably will) do a bit more work to determine how stationary Polaris is, I consider this pledge to be fulfilled.

## Pledge 3: Figure out how to determine when the Solstices are by the height of the Sun in the sky

This ended up being a little easier than I expected. The Solstices can be determined by measuring the length of a shadow cast by an upright pole/stick on Solar Noons. On the Winter Solstice, the shadow cast at Solar Noon will be longer than the shadow cast on Solar Noons surrounding that day. On the Summer Solstice, the shadow cast at Solar Noon will be shorter than the shadow cast on Solar Noons surrounding that day. It'll generally appear in both Solstices that the shadow length is the same as the Solar Noons before and after, so it's just a matter of taking the middle day for that clump of days that appear to be the same length.

I consider this pledge to be fulfilled.

## Pledge 4: Attempt to figure out Solar Midnight after determining a Solar Noon

When I made this pledge, I thought at best I could only maybe figure out a complicated way of determining Solar Midnight using some form of time keeping like burning candles after Solar Noon hits, but wouldn't be able to verify anything by the end of the year. I was surprisingly wrong. A while back ago, I read somewhere that you could use the calendar day and the location of the Big Dipper to determine Solar Midnight. Eventually I started experimenting and noticed that the star "Caph" of the constellation Cassiopeia very neatly aligned itself to the starts of seasons. The following method only works in the Northern Hemisphere.

As seen in the image, Cassiopeia and the Big Dipper rotate around Polaris and that circle of rotation can be split up into 24 sections. At the Spring Equinox, Caph will be directly below Polaris at Solar Midnight. If Caph is below the horizon, you can find the side of the Big Dipper and just add (go counterclockwise) 11 hours. As the tropical year progresses, the point of Solar Midnight shifts along the wheel counterclockwise at a rate of 1 hour counterclockwise about every 15.2 days or 2 hours counterclockwise per zodiac sign. Solar Midnight will shift 6 hours counterclockwise every tropical season.

Knowing my longitude and the amount of minutes Real Solar Time is from the Mean Solar Time, I can pretty consistently determine the clock time in my town within an error rate of about 15-20 minutes as long as the sky is clear. Out of all of the pledges, this was the one I thought I would get the least far on, which is why I worded the pledge with "Attempt to figure out". It turns out fulfilling this pledge has been the most useful for me in my day to day life, so much so that I plan on getting a tattoo of that star time chart I posted in this section on my right hand and the equation of time chart on my right arm. I consider this pledge definitely fulfilled.

## Ending Thoughts

4 out of 4 pledges fulfilled, although I do want to work a little bit more on pledge 3 to absolutely convince myself that Polaris barely moves in the night sky. I did not expect pledge 4 to work out as completely as it did and to be as useful as it was. I think I may try to work out determining the equinoxes without having to take the amount of days between the solstices and dividing by 2, but we'll see if I can come up with something.

I might do another update on these pledges later this year, but considering I fulfilled all 4 pledges, I might not. Figured I'd put "Update 1" in the title just in case I do a second update.

## Contact/Reply

If you would like to reply to this post, feel free to send me an email.

Email: vi@vigrey.com [Email]
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