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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: That magic number: 3438
From: David Pike
Date: 2016 Nov 4, 16:51 -0700

Robin you wrote:

David,  You wrote: Which I suppose is because in this case 3438 is being used as a constant and is effectively dimensionless.

It's really just that the ratio (length of ship/distance to ship) doesn't depend on the units. As Frank noted the appearance of 3438 in the formula is "thanks to the way the nautical mile is defined",

On reflection, I don’t think the definition of the length of a nautical mile comes into it in this example.  3438 is simply the constant needed to convert radians to minutes of arc.  Length of vessel divided by distance away comes out in radians.  I.e. length of the tiny part of the circumference of the small circle centred at the observer that the ship sits on divided by the radius of the circle, and
2pi radians = 360x60 minutes of arc, so 1 radian = 360x60/2pi minutes of arc = 3438minutes of arc. DaveP

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