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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


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Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
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Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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