A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunar mechanics and Double Alts.
From: George Huxtable
Date: 2003 Apr 29, 13:33 +0100
From: George Huxtable
Date: 2003 Apr 29, 13:33 +0100
1. Congratulations to Doug Royer for his well-spent Saturday taking on-land sextant observations. He got far more out of it than I expected, and far more than most of us would have got, I think. This is where his experience at sea and his regular sextant practice have paid off. 2. However, it leaves a few questions outstanding. Doug refers to "Moon's upper horn-Enif" etc. While the horn of a crescent Moon might appear to provide a nice well-defined point to measure to, there's no simple way that I know of to correct a lunar distance measured to a horn, to compare with a lunar distance to the centre of the disc (which is the distance one can deduce from the Almanac). I think measurements to a horn are a waste. 3. Following from that, I'm unsure what Doug refers to as Moon's disk in his "Moon's disk - Mars combination". A lunar distance is always measured to the "Moon's limb", so that the dot of Mars (for example) just brushes the outer, sharper edge of the apparent Moon as the sextant is tilted. This may be the Moon's nearer limb or the further limb to Mars (or other object), depending on how the Moon is being lit by the Sun at that time. So it will be greater or less than the distance to the Moon's centre, accordingly, by a Moon semidiameter. Attempts to estimate the unseen centre of the Moon's disc, and measure to that point, won't be accurate enough for a lunar distance. I don't know if that was what Doug was doing when he referred to measurement to the "Moon's disk": if it was, I am warning against it. Mars itself will (depending on its semidiameter) sometimes show in a 6x telescope as a visible crescent (I think) rather than a point, and when this happens with a planet it's best to allow the Moon's edge to bisect the light from that part-disc. A modern almanac is adjusted to give the position of the centre-of-light, not the centre of the planet. It's a tiny effect, though. 4. Doug measured "0703 and 0849zt Moon-Sun". Where I live, it was 100% cloud that day. It would be interesting to know if Doug could readily find the pale Moon in the daytime sky. Did it help, that he had been watching it since before dawn and had a good idea where to find the Moon with respect to the Sun? Was the Sun at 0703 at a usable altitude (more than 10 degrees, say) so that its refraction correction could be relied on? No doubt by 0849 it was well up. Did he look out next day, Sunday, and (if the weather remained clear), could he see the Moon at all? Clear mountain air may have helped him: here, even when there's no real cloud, the skies are seldom crystal-clear. 5. Glad that he found a good reflector material. I don't know what dark Karo syrup is. The main reason for choosing a dark liquid is to prevent a view of the bottom of the tin from confusing the reflected image. 6. Doug uses the term "Double Altitudes" to describe altitudes measured in a reflector. This can be a bit confusing in the context, as "double altitudes" is a recognised procedure for obtaining latitude and local time from two altitudes of the same body, usually the Sun, measured (usually but not necessarily) before and after meridian transit, and well-separated in time. For what Doug was doing, I suggest the term "reflected altitudes" would be better. 7. He says he got good reflections even on Sirius at twilight. Of course, with a reflector, star altitudes can be measured at any time of night, with a really black sky, because there's no need for twilight to see a horizon. Could Doug see fainter stars, such as Polaris, in a reflector at night, well enough for measuring? 8. Doug said- >A good >many people responded that they calculate the alt. of each body.Is this or >actually takeing the Double Alts.the preferred way?If one doesn't really >know precisely where one is wouldn't measureing the alts. give you a better >end result of the Lunar than calculateing the alts.?Is calculateing the >alts. a step saver or am I just not seeing something? I need guidance on >this matter. To do the whole job properly, a measurement of the altitudes is called for. Otherwise, if you calculate the altitudes from a clock time, then you are assuming what you are trying to obtain: it's a circular procedure. Doing it that way, using GMT from a watch, and known longitude, allows you to predict what the lunar distance should be, so it allows you to check how accurately you are measuring it, but that's about all. Not very satisfying, really. Perhaps Arthur Pearson takes a rather different view. With at least one altitude observation (a "time-sight", away from the meridian) and a known latitude, you have enough data to work out local apparent time. From that, you can obtain calculated altitudes from the Almanac, and use that information to correct your lunar, and obtain GMT and hence your longitude. See "About Lunars, Part 4a" for details. I think measuring the observed altitudes of the two bodies was far more satisfying and was considered the right way to do the job by the mariners of the lunar era, even though it restricted star and planet lunars, at sea, to dawn and dusk twilights. 9. Doug ended- >From reading the stories about the L + C exp.,they measured the >alts. instead of calculateing them.Does calculateing the alts. give you a >better time factor to work with? For those unacquainted with the history of the exploration of the American continent, L & C refers to the explorers Lewis and Clark. Lewis and Clark neither measured the altitudes of the bodies involved, nor did they calculate them. They simply noted the measured lunar distance to a body, and noted the corresponding watch-time, and left it at that, hoping that others would do the calculations on their return (which didn't happen, until very recently). They were familiar with the techniques of using a liquid reflector to measure altitudes (using a water surface, Bruce Stark tells me): that was how they obtained their latitudes. But even their latitudes were sometimes way out from the today's presumed positions of their camps. See Richard.S.Preston, "The Accuracy of the Astronomical Observations of Lewis and Clark", table, pages 185-186, to be found at www.aps-pub.com/proceedings/jun00/Preston.pdf . If their latitudes could be 25 arc-minutes out, what value can be placed on their lunar observations? I no longer put a high value on the astronomical expertise of Lewis and Clark. George Huxtable. ================================================================ contact George Huxtable by email at firstname.lastname@example.org, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================