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How to read a sundial March 20, 2012

Posted by aquillam in Astronomy, MichiganAstro.
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First, a few quick notes about time. It isn’t as simple as you think.

The meridian is a line that runs north to south and passes straight overhead. The Sun is at its highest point in the sky when it crosses the meridian, so the meridian is the reference point. Using the Sun’s meridian crossings to measure time is solar time, and that’s what the sundial reads.

The Earth moves faster when it is close to the Sun and slower when it is farther away. Also, the Earth is tilted, so the Sun appears to move higher and lower in the sky, making it appear to move faster and slower. Combining this obliquity and the changing orbital speed means that the Sun doesn’t take exactly 24 hours for every meridian crossing. If you plot the variations in the time it takes the Sun to cross the meridian each day, you get something called the equation of time.

On average, the Sun takes 24 hours to go from one meridian crossing to the next. That’s tropical time. You can use the equation of time to convert solar time to tropical time. Everyone at the same longitude will have the same solar and tropical times.

Since the tropical and solar time depends on your longitude, you can have minor changes in those times simply by moving a few miles east or west. That’s fine if you’re taking you cabbages to market in a cart, but not so good if you’re trying to coordinate trains on a single east-west track that runs hundreds of miles, and it’s terrible if you’re trying to get two servers half way around the globe to agree on when data was sent. So, time zones were invented, then daylight savings time was thrown in for good measure. Also, leap years and even leap seconds are added to keep the calendar and clocks all synced reasonably to the sky. All these adjustments are done at a governmental, civil authority level, so time on your watch is called civil time.

What we really want to do is get from the solar time on the sundial to the civil time on the watch. To do that, you’re going to need the graph of the equation of time (see http://en.wikipedia.org/wiki/File:Equation_of_time.svg) and the longitude (try http://www.findlatitudeandlongitude.com/) of the sundial. You’ll also need the central longitude of your time zone. http://sundials.org/index.php/art-of-dialing/longitude-correction.

To convert from solar (sundial) time to civil time:

Get the sundial reading and add all the adjustments:
sundial time + equation of time offset + longitude adjustment + other civil adjustments

Other civil adjustments is usually daylight savings time. For most places, this means add an hour to the sundial time in summer, or don’t add anything in winter.

The longitude adjustment is the difference between the longitude of the sundial and the center of the time zone, converted to minutes. The Sun takes 24 hours to move 360º, which works out to 4 minutes/degree, so we’ll multiply the difference in longitude by 4. The Eastern time zone center is at – 75º (or 75º W), and Ann Arbor is at  – 83.74º. The difference is -75 –  – 83.74º =  + 8.74º.  4 minutes/degree * 8.74º ~ 35 minutes (round to the nearest minute.)

For a sundial in Ann Arbor, I will always add 35 minutes, and in the summer I will also add 1 hour.

The equation of time adjustment depends on what day of the year it is. For this example, I read the sundial on March 16, 2012. The day of the year was 31+29+16 = 76. Looking at the graph, 76 is about half way between 60 and 90, so that corresponds to about -10 minutes.

If the sundial read 13:38, the civil time should have been:
13:38 – 00:10 + 00:35 +01:00 = 15:03, or 3:03 PM

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