NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Latitude by Lunar Distance
From: George Huxtable
Date: 2006 Oct 14, 22:09 +0100
From: George Huxtable
Date: 2006 Oct 14, 22:09 +0100
I had charged Frank Reed with "over-egging the pudding", in claiming an accuracy of 6 miles either way in position-finding by his proposed method. His response was hardly a diplomatic one, for a list-owner addressing a contributor, no matter how irritating that contributor may be. It has given rise to a chuckle or two, here in Southmoor. Frank sneered at my use of an Ebbco sextant, which was hardly relevant to the question in hand. I consider that to be an appropriate instrument for navigating my small boat, though that does not imply that I am unaccustomed to other sextant types. I have no illusions about its imprecision, and would not dream of using it to measure a lunar. And he ended with- | A general comment: | George, we all know that you have severe 'allergic reactions' to new | ways of looking at celestial navigation. Basically, every time I've | brought up something new on this list in the past three years, you have | sunk into a state of denial, usually launched by a post saying that I | am not answering your questions the way you want them answered. I question the "usually" here, but if I that has involved a request for rigour in list discussions, I make no apology for it. Anyway, my back is broad. It's not the first time Frank has had a go at me, and with luck, if I continue in the same vein, perhaps it won't be the last. ====================== Now, back to the matter in question, the precision of Frank's proposed method of position-finding without a horizon, which he claimed to be within 6 miles. Let's return, first, to the precision in measuring a lunar distance, the angle between Moon limb and star, for which he claims 0.1'; better, at a guess, than has ever been claimed by any navigator in the history of navigation. This involves a subtraction of index error from observed angle. To get the result to 0.1', what accuracy is required for those two separate observations, and what accuracy does he achieve? Where does irradiation, at the Moon's limb, come into this, in determining those two quantities: does he claim immunity from its affects, or that somehow it doesn't apply? Let's investigate an error-budget in the overall determination. That was one reason why I have asked for an explanation of the procedure, with relevant numbers, because Frank hasn't stated where his celestial predictions are to come from. Is his observer, from his jungle clearing, privileged to obtain JPL predictions, beamed to him from a satellite or a convenient mobile-phone antenna? Or will he have a laptop with him, programmed up with JPL (or similar) algorithms? Or will he rely, like the rest of us do, on the Nautical Almanac, as I am going to assume from now on. Using the almanac, how do you find what the predicted angle should be, between Moon and star, at a particular moment of GMT? You will have to look up many quanties in the almanac, each one stated to the nearest 0.1', a potential error of +/- 0.5'. First, to find the star position, you need- 1. star dec 2. star HA 3. GHA Aries to nearest hour-point. 4. Aries change, for part-hour and for the Moon- 5. dec to nearest hour-point 6. d correction to dec for part-hour 7. GHA to nearest hour-point 8. GHA change for part-hour 9. v correction to GHA for part-hour these allow the lunar distance to be calculated, for a mythical observer at the centre of the Earth. 9. Moon semidiameter must be allowed for The following terms vary with the altitudes of the bodies- 10. HP cos alt (Moon parallax) 11. star refraction 12. temp and pressure correction to star refraction. 13. Moon refraction. 14. Temp and pressure correction to Moon refraction. Depending on the details of the geometry, it's possible for any one of those 14 terms to affect the result by up to .05', one way or another, simply because of the way they are tabulated in the Nautical Almanac. Of course, most are KNOWN to a much higher accuracy, but not from that Almanac. It is, of course, true that all 14 are highly unlikely to all add up in the same direction, to their full extent. They are also highly unlikely to cancel out to zero. Without making a full statistical analysis, it seems reasonable, to me, for the standard deviation of the resulting scatter to be taken as root-14 x the spread of each component, or 3.7 x .05', or 0.19'. If anyone can suggest a fairer way to combine those errors, I hope they will. So, just the uncertainty in taking numbers from the Almanac, on its own, has already contributed 11 miles (rms) either way to the scatter in the result, even before any observation errors have been accounted for. Above, we were analysing the error involved in one Moon-star position line. There will be a similar error in the other position line. So much for Frank's overall uncertainty of 6 miles. Does that explain why I was keen to get a full explanation of the procedure, with numerical examples? 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. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---