Dear Mr. King, I have really enjoyed this problem. In one sense it is simple because it not about hours, but about events.
In a recent post you said: From: "Frank King" Subject: Re: simultaneous sunset > > One of the many nice features of this puzzle is that there > is no need to know the time of sunset (or sunrise) and, in > consequence, you can lay any understanding of hour-angles > on one side. > But I am having a problem understanding something. Are you saying below that ANY two locations MUST have a moment of mutual sunrise/sunset? Or are you saying, for any location there exists a second location at EVERY longitude that will have one mutual moment sunrise/sunset? I can understand the second statement, but not the first. At first glance I rejected the second statement, but clearly it must be true if the sun covers half the Earth every instant. For example, if I calculate the solar declination for the two latitudes of 42°N and 10°N and 90° difference of longitude -- I get a declination of -47°. Certainly this is outside the range of -23.5° to +23.5° for our current situation on Earth. This would be two locations that never share a sunrise/sunset event. Yet 42°N and -64.7S and 90° longitude difference share a common event on winter solstice. Location 2 is determined given location 1, difference in longitude and solstice solar declination of 23.5° . Warren > I have a comment on one of Warren's notes: > >> two locations with too great of a difference of >> longitude, would be too far apart to ever have >> the same moment of sunset. > > This is not quite the whole story... > > The great circle which separates light from dark > necessarily encompasses EVERY longitude, so there > will be points almost 180 degrees apart which > have the same moment of sunset. > > Half the points on this circle will correspond to > sunset and half to sunrise. The most northerly > and most southerly points will, respectively, be > points where sunset is immediately followed by > sunrise and sunrise is immediately followed by > sunset. > > My formula doesn't distinguish between sunrise and > sunset and the leading minus sign could equally be > a plus sign: > > tan(dec) = [-]sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2) > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
