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    Re: How many ways to define a day?
    From: Frank Reed
    Date: 2021 Jun 22, 10:43 -0700

    Matus, almost a week ago, you wrote:
    "Thank you Frank, this was a super nice puzzle."

    Great. I'm glad you enjoyed it. Of course, I built it from your analysis of that earlier case, so really it's your invention. :) By the way, I apologize for my late reply to your message.

    You continued:
    "My answer is: Cape Canaveral, FL The resulting position lies between 28°10' N and 28°27' N, and between 80°30' W and 81°00' W. This rectangle contains Cape Canaveral the city (but not really the space centre), and that's the only interesting location in that region. My conclusion is that you entered "Cape Canaveral" into the search bar and the website gave you the city rather than the launch pad. "

    You're spot on! And yes, that's very close to what happened :). I decided first to move to Florida for "geographic variety" from the last case. Originally I considered using Disney World but then though Pad 39A/B at KSC might be more entertaining, more "resonant". As you suggest, the weather site wanted to give me a slightly different location, and at that point I decided it was more "nautical" since the location is close to Port Canaveral, which is a large cruise ship port.

    You added near the end:
    "By the way, I have to attribute the "lunar distance" idea to my girlfriend, who came up with it. She didn't even seem to need time to think when I told her I was struggling with the longitude; she suggested right away to look at the difference between the Moon and the Sun. Annoying. :)"

    That's great. Yes, there's a key concept here: the Moon's position doesn't repeat (this Wednesday won't match next Wednesday or a month from now either), and the Moon is different for every observer on Earth. If I start out at 28° N in Florida half an hour after sunset, the sky has a certain appearance. If I jump to the coast of China, near Taizhou, on that same date also half an hour after sunset, the sky will look almost exactly the same, really indistinguishable without careful measurement. The one big exception is the Moon. The evening sky is the same in every longitude, for a given latitude, except for the Moon.

    So that worked great! I really had no expectations going in how well you would be able to determine the position. I'm happy to see it analyzed. :) One uncertainty in this is that we have not assessed the astronomical calculations behind that weather website (wunderground.com). A few spot checks suggest that basic data on sunset, sunrise, twilight, etc. are done right, but at least one number (which doesn't impact your analysis) is quite poor: the fraction illumination of the Moon. I checked in a few times over a couple of days, and I believed t's calculated only once daily for 0h UT for the entire local calendar day. But most users of this weather website are in the US, and 0h is currently between 5:00pm and 8:00pm zone on the previous date time in the continental US. That means that the illumination of the Moon is between 0.25 and 1.25 days behind schedule. For the Moon, that's a lot, and it leads to a curious disconnect between the listed phases of the Moon, which are given correctly to the nearest date, and the calculated illumination of the Moon. Note that it's not necessary to calculate an exact value at every refresh of the website. If the percent-illumination of the Moon is known at 0h UT for every day of the month (which, of course, can be tabulated easily well in advance), then simple linear interpolation yields the value to the required precision at any specific UT, fast and efficient.

    While you're visiting that website, wunderground.com, take a look at their symbols for "First Qtr" and "Last Qtr". The former is drawn about 33% filled in, and the latter about 52% filled. I suspect that the artist tasked with this project was uncertain about the meaning of "quarter" phases of the Moon. And yeah, that is some screwy, annoying vintage terminology! The "quarter" phase moons are actually "half" full (quarter of a month, half illuminated).

    Frank Reed
    Clockwork Mapping / ReedNavigation.com
    Conanicut Island USA

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