Tuesday, October 23, 2007

The Equation of Time

This is really about the different ways of representing "the equation", but first a little preamble. (or you could Google "equation of time" and view all 94,700 results :wink:)

Watches are, of course, mainly instruments to measure the passage of "time". However, "time" in that context is a man-made concept and is dependent on the machinations of atomic clocks and such-like. Furthermore, the division of the planet into time zones, although good for commerce and the punctuality of trains, has also helped to divorce us even further from the reality of the time by which humanity once lived i.e. solar time; for example - when it is noon at Greenwich (by "noon" I mean when the Sun is at it's highest, not 12 o/clock), the Sun over Rockall Island still has yet to climb quite a bit, even though it's in the same time zone. This also explains why using your watch to find North can send you wandering up to 15 degs off, and that's not including the 6 deg penalty for forgetting to correct for Summer Time (who, me?).

Anyway, the "equation of time" represents the imperfect motion of our planet around the Sun. The equation itself is horrendous, don't even bother to look at it. Generally, we tend to use the term to mean it's result for any given day of the year. Lindbergh used such a result on his epic flight to Paris. The equation of time is also of significance to garden gnomes, strangely enough. "What's the time, Grumpy?" - "Bloody 'ell have I got to climb up the sundial again??". You see, if you set a sundial to your watch on Feb 14th to please SWMBO, I guarantee it will be a half-hour fast when you next look at it on Nov 5 between fireworks.

So, without further ado, here are several ways from worst to best to represent this "equation of time" . . . ta daaa . . !!

The most seriously boring way is a table:

Part of a Sun Data table . . .
Col. 1: Date
Col. 2: Equation of Time. Number of minutes and seconds the Sun is off compared with an accurate clock which shows local mean time.
Col. 3: fast or slow (Sun).
Col. 4: Declination of the Sun in degrees and minutes. When negative, the Sun is south of the celestial equator; when positive, north. Values are averaged over the 4 year leap year cycle.


A little better - a graph

I prefer, at the very least, a visual approach. Here's the equation plotted out on bog-roll. You'll notice that clocks do agree with the Sun four times a year but it's not really obvious why in this graph form.

equation of time in graph form

Better yet

If the graph is plotted against the angle of the Sun instead of against the time of year, the effect of our wobbly orbit, etc becomes immediately apparent.

The figure below is called an "analemma" (no jokes, please).

graphic figure of eqn of time

and there's an even prettier one on our family globe, I didn't even know what it was until yesterday:

However it does look like the folks below knew all about it. It's a Jaeger-LeCoultre Gyrotourbillon (photo by Ron DeCorte, taken from Timezone.com). The cam rotates just once per year, as you should expect by now ;-) - if anyone knows what the months cam does, please leave a comment to this post.

jeager le coultre eqn of time cam

However I like this one the best. Straight from nature - a time-lapsed sequence of the Sun at 8:30 AM for a year, by Dennis di Cicco

time lapse of Sun at 8:80 am for one year

Here's quite a good site on the subject analemma.com.


Dave Sweeting said...

I think the Month cam mentioned on the a Jaeger-LeCoultre Gyrotourbillon is for a perpetual calendar. It is clear that the distance from the centre of the cam to the diameter for any given month relates to days in the month, with the closest being February (28/29 days), and April, Jun, September all next closest (30 day months). All of the initialled months are 31-day months, as this is where there is most material to label.
It would seem clear that the position of the cam follower forces the month to change over at 28, 30 or 31 as a result

Anonymous said...

The month cam on the geared device you have pictured appears to relate to moons position could be the depth of phase at the start of each month. What is the device go to? Is it a clock or watch portion? M@

Ted Cossins said...

Thanks for commenting, M@. The device is from a Jaeger-LeCoultre Gyrotourbillon wristwatch, as far as I know.