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Subject: Re: Sextant Accuracy and anomalous dip.
From: George Huxtable (george@XXX.XXX)
Date: Tue Mar 18 2003 - 12:17:52 EST
Gary Harkins said-
>In a message dated 3/17/2003 2:45:15 PM Eastern Standard Time,
>george@XXX.XXX writes:
>
>> My general objective is to get these observations as accurate as
>> possible, say to within 0.1 or 0.2 miles. I'm not sure why I have this
>> objective, but it persists.
That message didn't come from George Huxtable, but from Fred Hebard.
Gary went on to say-
>Is your house at sea level? If not you will have error caused by your
>elevation. Usually these can be ignored at moderate elevations, but in your
>case, attempting to get ultimate accuracy, they may be a factor. The error
>will be greater when the sight is a smaller Hs.
In response to a question from Peter Fogg, asking if he was referring to
dip, the answer was-
>No.
>
>Imagine yourself on top of a mountain taking a sight. Imagine that the sight
>measures 45 degrees using a bubble horizon or artificial horizon. At sea
>level and the same geographic location (if that were possible) the sight
>would measure higher. If you measured the same 45 degrees at sea level you
>would have to be further away from the sun's GP. I hope that's clear, it's
>easier to show using a sketch.
The effects Gary refers to (caused by parallax) are completely negligible.
The worst-case would be that of the Moon, because it's by far the closest
to us in the sky. Almanacs provide the direction of the Moon in Dec and GHA
as seen by an imaginary observer at the centre of a transparent Earth. It
has to be so, because the compiler of the almanac has no idea where on the
surface of the Earth his customers are going to be. When observing the
Moon, it's essential to correct its almanac positions to correspond with
the geometry from the viewpoint of a real observer, wherever he happens to
be on the surface. This is the correction for parallax.
The worst-case is when observing an object near the horizon, and this
maximum value is called the Horizontal Parallax or HP. The HP of the Moon
varies slightly in its out-of-circle orbit, but is always somewhere near 1
degree, and depresses the Moon, toward the horizon, by that amount. That is
the parallax caused by the displacement of our imaginary observer from the
centre of the Earth to a real position on its surface, a shift equal to the
radius of the Earth or about 4000 land-miles. An elevated observer would
change that parallax only in (inverse) proportion to the change in his
distance from the Earth's centre.
The effect Gary is referring to would require his house to be at an
altitude of about 1/60 of 4000, or 66 land miles above the Earth's surface,
to shift the Moon's position by an extra minute of arc. For other objects
than the Moon, the effect of parallax is even smaller, by a factor of at
least 100.
For these reasons, the variation of parallax with altitude above the
Earth's surface can be neglected by navigators, though precise mountain-top
astronomers may need to take it into account.
Peter Fogg and Fred Hebard have responded correctly to this topic, but
perhaps the rough numbers provided here will give a bit of extra insight.
George Huxtable.
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contact George Huxtable by email at george@XXX.XXX by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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