Here is a copy of the letter I sent to Rory, who contacted me through my
web page (http://www.uwrf.edu/sundial/), before the letter from Jack Aubert
was posted.
Cheers,
John
Rory,
I am sorry to have taken so long to reply but I have a couple of deadlines
to make.
Your question is an interesting one and I think if you study the large
photo of the Swensen Sundial you can see the answer.
>
>Many years ago a golf-playing uncle in Los Angeles asked me why it was
>that the shortest day of the year was the winter solstice, but the sun
>actually set earliest on about Dec. 13 (he had noticed that he could get
>in an extra hole of golf on Dec. 21 -- I'm not making this up.)
>
>After a lot of research (there was no Web then!) I realized the answer
>had to do with the equation of time, the difference between solar and
>sideral days, and mean solar time (and no doubt you know more about this
>than I do.)
>
Yes you are correct. The annalema shapes arise because of the equation of
time, shifting the correct positions of the hour markers.
Now on my dial sun rise/sun set can be represented by a horizontal line
through the base of the lower gnomon. In other words the tip of the shadows
can never be higher than that point. Now I didn't cut the annalemas off
there or put a horizontal line (we already have the lines of the mortar in
the bricks) as I thought it would spoil the looks of the whole dial. There
are some anchient dials in existence that have so many lines on them that
the meaning of some of them have been lost!
Anyway imagine a horizontal line through the bottom of the gnomon. Look at
where that line intersects an analema, say the 5 pm or right-mostone. It is
somewhere between the two upper daylines for the Gold or spring side but it
is between 2nd and 3rd day lines for the Fall side. This is because in the
late Fall the Sun sets before 5pm and the shadow never reaches that part of
the analemma. Because of the rapid curve of the annalemas near the top of
the dial the time of sun set varies rapidly becoming later as we pass the
Winter Solstice.
This explains the change in sunset and that the earliest sunset is not at
the winter solstice.
>So I told my uncle this, and the family got down to accomplishing other
>life-tasks. Unfortunately, I recently realized that this explanation
>must be false. This came about by looking more closely at an analemma on
>a globe. If I am not mistaken, the analemma describes not only the
>difference between mean and clock-time (due to the eccentricity of the
>earth's orbit being non-zero) but also the (I guess arbitrary) dates on
>which our clock is "set." I.e. when the official timekeepers say that
>the annual clock is zeroed. And here, I was shocked to see a) that this
>date seems to be the winter solstice; and b) that I had never noticed
>this before!
>
No its a difference and when averaged over the whole year it must come out
to zero.
Also its not just the eccentricity of the orbit with the Earth being
closest to the Sun on Jan 4th. but the larger effect (+-10 mins to +-
8mins.) is due to the 23.5 degree tilt of the Earth's Axis. The
eccentricity effect is zero Jan 4th and 6months later. The tilt effect is
zero Dec 21st. and every 3 months after.
>You see, I always knew that the earth was moving fastest around
>Christmas time (near perihelion) and so I figured it made sense that the
>clock was furthest "out of whack" around this time. And sure enough,
>consulting either an almanac or a St. Joseph's Aspirin calendar, one can
>see that the sun indeed sets earliest on Dec. 13, not Dec. 21. BUT HOW
>IS THIS POSSIBLE, IF THE CLOCK IS "ZEROED" ON THE SOLSTICE? Shouldn't
>the equation of time being equal to zero on Dec. 21 mean that the sun
>should set the earliest on that date, too?
>
The equation of time which is the combination of the two effects is actualy
zero close to the 25th. but this is not arbitary.
I hope this helps but I realise this is complicated and drawing diagrams
would help.
All the best
John S.
