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> -----Original Message-----
> From Trevor J. Kenchington
> It was a bit off the topic of the thread but Jim included in one of his
> posts, as an explanation for Bill:
>  > 1. The Visible Horizon is the one you see with your naked eye when
> you look
>  > at the apparent bounday between the sky and sea (or earth).  A
> line from
>  > your eye to that horizon is called the Visible Horizon.
>  > 2. The Geometric Horizon is the real line between your eye and
> the actual
>  > boundary between sky and sea/earth.  Since light bends between the
> horizon
>  > and your eye, then the Visibile Horizon is rarely coincident with the
>  > Geometric Horizon.  The difference is accounted for mainly by
> terrestrial
>  > refraction.
>  > 3. The Sensible Horizon is part of the Horizon Coordinate System.  The
>  > Sensible Horizon is a line from your eye that runs out into space
> parallel
>  > to the Celestial Horizon.  The angle between the Sensible
> Horizon and the
>  > Visible Horizon is called the Dip.  The Sensible Horizon is a very
>  > non-intuitive concept for learners.

Trevor wrote in reply,

> The sensible horizon might be better understood as a plane,
> perpendicular to the direction of gravity acting on the observer and
> drawn through the observer's eye. It is parallel to the celestial
> horizon because that too is a plane perpendicular to the direction of
> gravity acting on the observer but drawn through the centre of the Earth.

I have not yet found an independant reference to this idea that the
horizontal coordinate system's horizons are perpendicular to gravity.

> The visible horizon isn't a line drawn from the observer's eye to the
> apparent sea/sky boundary. For piloting purposes, it is a circle drawn
> on the Earth which coincides with that apparent boundary but for
> celestial navigation it is another plane perpendicular to the direction
> of gravity (as are all the horizons). Specifically, the visible horizon
> is a plane drawn through the points where rays of light from the
> observer's eye which just graze the sea/sky boundary cut the celestial
> sphere. But that is a really weird concept since the celestial sphere
> doesn't actually exist.

The visible horizon can be sloppily described as "a line drawn from the
observer's eye to the apparent sea/sky boundary" for certain purposes, such
as visualizing Dip, but you are correct in pointing out that it has a more
generalizable and precise definition.  Bowditch 2002: "Visible horizon. The
line where earth and sky appear to meet, and the projection of this line
upon the celestial sphere. If there were no terrestrial refraction, VISIBLE
and GEOMETRICAL HORIZONS would coincide. Also called APPARENT HORIZON."  I
had not paid attention to the fact that the visible horizon was horizontal
to the celestial horizon.  I drew this by placing a circle representing the
earth inside a circle representing the celestial sphere, and projecting
everything to the outer sphere.  I put that new figure at
http://jimthompson.net/boating/CelestialNav/CelestNotes/Coordinates.htm#Hori
zonCoordinates,
added the actual definitions from Bowditch 2002, changed the word "line" to
"plane" in several places, and reorganized the section.

> The geometric horizon is closely similar, in concept, to the visible
> horizon. But I don't think it is right to say that the difference is a
> matter of the geometric horizon being defined by the "actual boundary
> between sky and sea". The actual boundary between sky and sea is the
> curved (and often rough) surface of the water. The geometric horizon is
> defined in terms of a cone, centred on the observer's eye and tangential
> to the water surface, in contrast to the visible horizon's definition in
> terms of curved (by refraction) light rays.

I think we said the same thing here, but in two different ways, and at two
different levels of semantic precision.  Bowditch 2002: "Geometrical
horizon. Originally, the celestial horizon; now more commonly the
intersection of the celestial sphere and an infinite number of straight
lines tangent to the earth's surface, and radiating from the eye of the
observer."

Thanks Trevor -- I always enjoy the clarity of your posts.  All that Table
15 stuff was a heck of a lot more fun than doing or family book-keeping and
preparing my talk for work next month.

Jim Thompson

   

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