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Fred,

I'm sorry if my wording made you think I was riding a high horse. It
wasn't my intention to do anything of the kind. You just keep asking
variants of the same question and, having starting by trying to answer
the first one, I have continued (at some cost in time and trouble) to
try answering the rest, since nobody better informed seems willing to
step into the breach in my stead.

This time, you wrote:

> The ship is sailing away. The farther away it gets, the lower the image
> sinks.  First the ship is hull up, then only the sails or mast shows,
> then only the tops of the sails, finally nothing.  By simple geometry,
> the curvature of the earth is blocking a view of the ship: the earth is
> between you and the ship.


That is true, of course, and would be so in the absence of anything that
curved the rays of light, i.e.: straight lines drawn between the ship
and your eye would produce that sequence of observations -- as I am sure
you understand full well.


> Now, as the image is sinking, my understanding is that the real ship is
> normally lower than it appears, just as the setting sun is already
> below the horizon at sunset.


No. The comparison with the Sun is mistaken.

The light from the Sun which reaches your eye passes (for many millions
of miles) through the vacuum of space. It then encounters the thin air
of the outer atmosphere, passing gradually into denser air, until it
reaches the still-denser air near the surface, where it enters your eye.
It is that passage through progressively denser air which causes the
refraction and hence causes the visible image of the setting Sun to have
a higher altitude than the the true position of the Sun has.

Light from a ship just over the horizon, in contrast, travels to your
eye through the dense air near the surface for its entire path. Thus, it
will not generally experience any significant amount of refraction in
either direction. Your perceived image of the ship should coincide very
closely with the true position of the ship.

The exceptions come when there is intense layering of air close to the
surface instead of uniform density, such that the light rays are bent.
If there is warm air over colder water, the mastheads of the ship will
appear higher above the horizon than they should. If there is cold air
over warmer water, her mastheads will appear lower than they should.
Both happen.

However, water is not subject to the intense heating and cooling that
land surfaces can be, so the gradients in air temperatures immediately
above the sea are very rarely really intense. Meanwhile, ship's masts
are not all that high (unlike Kieran's desert mountains). The latter is
important because the light from the horizon will be curved just as the
light from the ship is curved -- both will appear to move up or down
relative to the horizontal plane but they will move almost the same
amount. So the apparent height of the mastheads is usually close to the
true height. Not always but usually.


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

   

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