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Re: The flat earth notion
From: Trevor Kenchington
Date: 2003 Nov 5, 09:16 -0400
From: Trevor Kenchington
Date: 2003 Nov 5, 09:16 -0400
Herbert Prinz wrote: > On a spheroidal earth, if you proceed on a rhumb line with constant speed, you > will arrive at a pole after a finite time. You won't be able to stop your vessel > at this very moment, because of your inertia . This raises the puzzling > question: Where will you be a second after you will have passed through the > pole? Neither Dutton nor Bowditch has the answer. I think that Herbert is quite wrong. Following a rhumb line on a spheroidal Earth results in a path which follows a loxodrome. A loxodrome only reaches either pole after _infinite_ time, gradually spiralling in towards the pole but never quite getting there. Hence, you cannot pass through, or even reach, a pole while on a rhumb line, though you could get very, very close if you were really determined to try. There are four exceptions to this. A rhumb line course of 090 or 270 will carry you around a parallel of latitude and will never approach either pole. I guess that that is a special case of a loxodrome, taking an infinite time to even approach either pole. In contrast, a rhumb line of 000 or 180 will carry you directly to the pole. When you get there, however, you cannot pass through the pole while remaining on the same rhumb line: At the South Pole, all possible headings are 000 and a course of 180 is undefined, vice versa in the north. Trevor Kenchington -- Trevor J. Kenchington PhD Gadus@iStar.ca Gadus Associates, Office(902) 889-9250 R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251 Nova Scotia B0J 2L0, CANADA Home (902) 889-3555 Science Serving the Fisheries http://home.istar.ca/~gadus