When will the sun set in the middle of the channel in 2002?


Data
Latitude N43 46.787
Longitude W86 26.103
bearing down channel (from Street Atlas 9.0) 293.6
Date Day Time of sunset (EDT) Azimuth at sunset
August 4, 2002 Sunday 9:03 PM 294.5
August 5, 2002 Monday 9:02 PM 294.1
August 6, 2002 Tuesday 9:00 PM 293.6
August 7, 2002 Wednesday 8:59 PM 293.3
August 8, 2002 Thursday 8:58 PM 292.9


Astronomical data are from the US Naval Observatory


After going through all of this, I attended !0 AM coffee at the Pointe Wine and Deli. The subject came up, and Murph Schader said "Of course it's August 6. The sun always sets down the middle of the channel on that date."

Of course, the sun sets in the middle of the channel twice each year, the same number of days before the solstice and after the solstice. The early date is 5-5-2002. We had heavy cloud cover, but several astronomers gathered at the PYC, and we are sure that this is what it would have looked like.

Dick Ouweneel checked the data, and found that the sun set at 19:51 on May 5, and 20:00 on August 6. Why the difference in time? This led to an interchange between Dick Ouweneel and his friend Bill Brandenburg. Here is the exchange.



Dave,

It's relax and enjoy time.

A few days ago I finally got around to sending the "sun observation timing dilemma" to the friend who can and did get in to this. The following are his words from a just-received email. I do remember that in the analemma's figure-eight pattern, the lower portion is larger than the top portion. Hold that image.

May I introduce Bill Brandenburg. Dave, Bill, Bill, Dave.

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The Earth's orbit around the Sun is an ellipse (not a circle) and the earth's axis-of-rotation is tilted approx 23.5 degrees to the plane of that orbit. (The Earth is nearest the Sun in Jan and farthest away in Jul). And a "year" is just a bit more than 365.24 days. All of these lead to the Sun being slow, compared with the time on your accurate wrist-watch, from late Dec thru mid-Apr and mid-Jun thru late Aug, and fast from mid-Apr thru mid-Jun and late-Aug thru late-Dec. (Remember the figure 8 -- the analemma -- on world maps and globes). Although your 5/5 observation was about 46 days before the Summer Solstice, and your 8/6 one will be about 46 days after, 5/5 was when your watch was behind the Sun and 8/6 will be when the Sun is behind your watch. (Let's ignore the atmospheric refraction that causes the "apparent" time of sunset to differ slightly from the "actual" time). I haven't (probably can't anymore) "done the calculation", but interpolating an analemma (see, what else, www.analemma.com), it looks to me like the Sun was about 3 minutes ahead of your watch on 5/5, and will be maybe 5 minutes behind on 8/6; so, considering only the analemma, I'd guess that the 8/6 event might be 8 minutes later than that on 5/5. If the difference is actually only 3 minutes, there's probably something significant that I'm not considering (relativity?). Like hops in a Bell, we probably ought to nail down the projected vs actual and the reasons for the differences.

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I should add that the "Bell" which Bill referred to is Bell's beer of Kalamazoo, such as the Oberon served at the PYC. Bill and I had a recent exchange on this subject and he is responding in the above context. As I find new beers, I send Bill a geometric figure which describes the beer to Bill. It is a language that has taken many years and other units of research to develop, but the effort has been rewarding to date and will definitely be funded in the future.

Regards,

Dick Ouweneel
There is an interesting and educational applet here.