NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Photo sextant sights
From: George Huxtable
Date: 2008 Jul 30, 17:00 +0100
From: George Huxtable
Date: 2008 Jul 30, 17:00 +0100
Wolfgang K�berer is right to question that example of an intended lunar distance measurement by camera, in Navigator's Newsletter 99. Andres Ruiz has provided the relevant link in- http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=31;t=000040 Wolfgang wrote- "Yesterday I received "The Navigator's Newsletter" issue 97 - 99. The last issue contains an article by David Burch (from his book "Emergency navigation") about "Photo sextant sights". As this had been discussed on the list not too long ago I read the article right away. It relates the example of a "Photo sextant sight" taken in Florida at 27deg 12,2 min N, 80 deg 13,4 min W. ... The article sums up: "had we not known time or longitude, we would have found our longitude this way to within 53 min ". This would mean a possible error of about 47 miles - which is probably acceptable. Then I did a quick "Sumner": I varied the input to see what happens to the result. On the assumption that there is no error in latitude (having bent my sextant only after taking the height of Polaris or a star on the meridian) and that my time is correct, I varied my assumed longitude and got a perplexing result: Using Frank's program and assuming I am about 150 miles out in the Atlantic (= assumed longitude 77deg 10 min W) I got the following result: "Error in Lunar: 0 min Approximate Error in Longitude: 0 deg 00.4 min" which - following David Burch � I interpret as saying I am almost at my assumed position. As the "Photo Sextant Sight" supposedly was taken 3 degrees further west something doesn't fit. What did I get wrong? It's not the input, I checked it several times." ============================ I haven't checked out those details, but suspect that Wolfgang did nothing wrong. It's simply that this was a completely inappropriate geometry for measuring a lunar distance, as a glance at the photo will show. Look at the way the gibbous Moon is illuminated. Draw a diameter across the Moon, which divides it so that the lighting on each side of that diameter is symmetrical. That line (which is at right-angles to the line joining the Moon's rather-blunt "horns") shows the direction from which light is falling on the Moon from the Sun. That direction is the great-circle joining the Moon to the Sun.. Very closely, it's also the direction in which the Moon is moving against the star background, because the Moon never strays more than 5� from the plane of the ecliptic. And that motion, in that direction, is what a lunar distance is attempting to measure. So always, a lunar distance is the spacing measured between the Moon and another body that is on, or near, that line of symmetry. Now look at the spacing between the Moon and Jupiter, that's being measured in the photo in an attempt to determine the Moon's position along its track. You can see that it's nowhere near that optimum direction; in fact, it's not far short of being at right-angles to it. The Moon isn't travelling towards or away from Jupiter, it's simply going past it. And so the measured spacing is almost completely insensitive, as a measure of longitude. Frank's lunar calculater estimates the error in longitude simply by multiplying the error in lunar distance by a factor of 30, taking a typical value for Moon's motion, but, crucially, assumes that the measured distance is always in or near the correct direction. In the example shown, the misalignment is so great that the error could easily be 5 or 10 times greater than that. A Moon-Jupiter lunar is usually highly recommended, because Jupiter is always close to the ecliptic in its path, so what has gone wrong in this case? It seems to be a consequence of trying to use a camera, rather than a proper angle-instrument, to make the measurement. To keep distortions low in the camera optics, it's desirable to keep subtended angles small. But in traditional lunar-distance measurement, the measured angles are kept to 25� or more, so the two bodies are well spaced around the ecliptic, and smaller angles than that wouldn't even be shown in the lunar tables. You would never even consider measuring with a sextant lunar distances of 5� and-a-bit, as was being attempted here. And so the bodies were not at all spread around the ecliptic; instead, it was damn-near a conjunction between the Moon and Jupiter, exactly the wrong moment to try a lunar distance. I'm a bit sad that this example has now shown up in Navigator's Newsletter, because its editor, David Burch, asked my opinion about it, and I explained, back in late 2006, the drawbacks of that particular camera-shot. There are other drawbacks in making celestial observations by camera rather than by instrument, but that will do to be going on with. George. contact George Huxtable at george@huxtable.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---