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Re: Sextant Accuracy and anomalous dip.
From: George Huxtable
Date: 2003 Mar 18, 17:17 +0000
From: George Huxtable
Date: 2003 Mar 18, 17:17 +0000
Gary Harkins said- >In a message dated 3/17/2003 2:45:15 PM Eastern Standard Time, >george@HUXTABLE.U-NET.COM 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. ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================