Dear Roger, I do enjoy your thought-provoking messages!
I have been thinking over your comments on the globe dial: I call sundials like this "Terminator" sundials as they tell time by the terminator line between the sunny and dark sides. So far, so good. An eloquent description of how these dials work. You continue: It is not a sharp line like a shadow This is what set me thinking... In general, a shadow is not any sort of line, sharp or otherwise. On a plane surface shadows are two dimensional. Maybe you meant: It is not a sharp line like the edge of a shadow This can't be right either because the edge of a shadow, the penumbra, is precisely the part which prevents it from being sharp! The terminator is just a posh word for the penumbral region at the margin of the shadow on the globe. You can ponder whether the penumbral region of this shadow is more or less sharp than the shadow of, say, a vertical stick. The truth is that it is both more sharp and less sharp! Here's why... The penumbral region of the shadow of a vertical stick increases linearly as you get further from the base of the stick. The penumbral region of the shadow of on a globe has uniform width all the way round. Imagine a bug crawling over the surface of the globe and crossing the terminator at right-angles... The bug goes from full shadow to full illumination by the sun by crawling an angular distance of about half a degree On a 10 foot diameter globe this is about half an inch. The penumbra of the shadow of a vertical stick increases from zero width indefinitely. It will be half an inch across at about 5 feet from the base if the sun is low. If the Earth didn't have an atmosphere, its own terminator would again be about half a degree across. In the Tropics, when the sun sets normal to the horizon, it would take about two minutes to go from being just wholly visible to being just fully below the horizon. The atmosphere stretches this a bit because refraction increases rapidly as solar altitude heads towards zero. The atmosphere has a small effect on the terminator on a globe but it also has a small effect on the shadow of a stick. You can ignore this effect. You continue... Orientation is important. Not on a globe it isn't. Globes tend to look the same whichever way you orientate them :-) Very best wishes Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
