A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2010 May 13, 23:37 -0700
As George has noted, Paul is apparently ready to move on from this lunar observation. In this post, I am addressing some of my comments and questions to Paul personally because they are his observations, after all. But this post, like any NavList post, is for everybody who's interested, and Paul, if you don't want to discuss this one further, that's ok!
So here are my thoughts...
There are quite a few software products which have added a minimal feature for clearing lunars in the past few years. Some are excellent, but many of these have errors or inconveniences. Those problems, coupled with the general lack of familiarity with the process among beginning lunarians can lead to a lot of frustrations. Do we blame the software tools? Do we blame a beginner's errors? Do we blame the process of lunars generally? Usually for a beginner, it's a complex interaction of all three things.
Paul Jackson, you initially provided some good basic information on this observation, but the numbers didn't add up, so we had to guess where things might have gone astray. First things first, what was the time? Andres has suggested that you might have made a one day error in the Greenwich date. To resolve this, I have a question for you, Paul: when you made your very first post on this under the subject "Help with Lunar distance" four days ago, did you make that post NavList about ONE hour after you took that lunar sight? Or was it about TWENTY-FIVE hours after you took the sight? The time of your post as listed on the message boards was about 19:23 GMT on May 9, so I have been assuming that you did NOT in fact make any error in the date and that you posted your message about an hour after the sights.
Next, the altitudes clearly didn't make any sense, no matter how you slice it, and many people noticed that right away. For future reference for the rest of you engaged in lunarian reverse-engineering, when you see wildly out-of-line altitudes connected with a lunar observation, you can usually assume that they are calculated altitudes and this is the result of some sort of "operator error" with software or tables. That was always a risk with lunars. Calculating altitudes is just another opportunity to screw things up. Historically, navigators observed the altitudes with lunar observations, not because observed altitudes are necessarily intrinsically better (though you could argue that, too) but primarily to save the very large extra work of calculating the altitudes and to avoid the very real risk of making mistakes in such a calculation. But if you do calculate altitudes, always peform a "sanity check". Even a quick observation of an altitude made with no horizon visible will at least get you in the right ballpark.
We now have to pursue this story on a few different tracks. We have TWO related but independent lunar observations that we can work with for different purposes:
1) We have the measured distance taken by Paul from a KNOWN location at a KNOWN Greenwich Time. For this we will have to calculate fresh altitudes, and then we can see what it tells us about the actual lunar observation.
2) We have the same observed distance paired with some altitudes (the ones he entered, around 21 and 22 degrees) which we know are incorrect for Paul's location but they WOULD be correct at some other location(s) and therefore we can look at those for further information on the software that Paul used when he was trying to clear his lunar since he has posted the output of that software from those inputs.
Case (1): The easiest way to do this is to use my online lunars calculator. Paul, if you want to experiment with lunars, of course, there are plenty of ways you can clear lunars (you mentioned Bruce Stark's tables) but if you want some quick results to see how your observations are coming along, you should really try out my online calculator. Over two hundred people (as counted by IP addresses) have used it to clear over two thousand lunars in the past six years so it has been battle-tested. To try it, go here:
and click on "Clear a Lunar Online". Next you enter your observational data in the form. Enter your best estimate of your latitude and longitude, IC, temperature and pressure if unusual, and height of eye if you've observed altitudes from a sea horizon. Select the body you observed. Then enter the altitudes if you observed them, OR, as in this case, since we don't have believable observed altitudes, just leave those boxes blank and the software will calculate the correct altitudes. Next enter the Greenwich date and time (be SURE you've got the right date, and double-check that you have real Greenwich Mean Time (UT)), and then enter the observed lunar distance. Select whether it was a "Near" or "Far" lunar (--and are you sure?). There are also two options which you can select/de-select for experimentation, but in general, for best results, leave those option boxes unchecked. Now click "Calculate".
For your location, Paul, and the observed LD at that GMT, the software calculates the altitudes and tells us that the Moon was around 34 degrees high and Jupiter around 40 degrees. Now tell me something, isn't that more consistent with what you saw in the sky? Your calculated altitudes had both objects at nearly the same altitude. But if you remember the general appeatance of the sky when you made the observation, wasn't it the case that Jupiter was well above the Moon? Or not? This calculational results page also tells us that there is an error in your lunar of 23.1'. That's very large --bigger than the semi-diameter of the Moon. That's so large in fact that it tells us something has gone badly wrong. A "usual suspect" here is the choice of Near versus Far limb. So let's change that and re-calculate. Use your browser back button to go back to the form for data entry and switch from "Near" to "Far". Then hit "Calculate" again. The error is now -9.5'. This is also very large but better. Again, something has gone very wrong. I believe Robin Stuart guessed correctly what you did wrong here. Based on the appearance of the Moon in the sky and its orientation, it would not have been possible to do a Near limb lunar here. The limb of the Moon closest to Jupiter was not illuminated (except by faint earthshine, usually too indistinct for these observations). You should have brought Jupiter to the far limb of the Moon, rather close to the Moon's lower "horn" (near the Moon's physical north pole). But it has been my experience that beginners sometimes make the mistake of thinking that "Near limb" means placing the other celestial body on the exact center, as nearly as they can tell, of the Moon's illuminated limb. I think that's what Robin was guessing, and it's my best guess, too. Did you, in fact, place the image of Jupiter right smack on the center of the Moon's illuminated limb so that it appeared on the edge of the Moon just about half-way between the "horns" of the crescent moon? If so, that would nicely explain the error in this observation since that spot would be ROUGHLY 23' from the near limb and 9' from the far limb.
Case (2): Now we ignore the actual location of the observer, and use the entered altitudes and the ouput from Omar Reis's "Navigator" software which Paul posted to try to determine what exactly that software is doing and find out if there might be some problem with it. Scanning down the output from the Navigator software, I immediately notice some very familiar letters: A, B, and Q. It turns out --and this is news to me-- that Omar Reis used my "Easy Lunars" posts from NavList from the Spring of 2004 (which are also listed on my web site) as the basis for his calculations! This is fine if he did it right, except that this series method should NOT be used when the distances are less than 10 degrees (like this case) or the altitudes are below 15 degrees. I stated these limits on the process when it was first posted, but that's in the nature of the subject. Thinsg get lost in the re-telling. I should add that the error incurred by using this method outside the limits is not at all large. In this case, the exact solution differs by only 0.3 minutes of arc from the "Easy Lunars" A,B,Q solution. But there is a more serious problem. If you work through the numbers, it turns out that Omar made a mistake when implementing this calculation. A and B, the "corner cosines" or "projection factors" are supposed to be calculated using the observed altitudes of the bodies' centers, the so-called "pre-cleared" altitudes. Instead, he is using the completely cleared altitudes. In effect, this takes out the refraction and parallax twice, once directly and once indirectly. This results in a substantial error of about 5 minutes of arc in the cleared distance in this case. That's a true software error.
There's also the problem which has been emphasized in a number of posts regarding the Moon's motion relative to Jupiter. This only affects the calculation of GMT from the sight and does not reflect on the accuracy of the clearing process or the observations themselves. If you're interested in experimenting with lunars to see how good you are at taking the sights, you don't need to worry about this issue. Sights with the Moon off to one side are just as good as those when the Moon is directly aligned with the other body. But note that this is not an issue specific to Jupiter. It applies to all of the "other bodies" in lunar sights, and the Sun only gets off the hook because we can never see the Moon when it is very close to the Sun. If you want to decide whether the other body is appropriate for getting GMT (which is NOT the only approach to this question) then draw a line extending the equator of the Moon across the sky ahead and behind it. This line will generally be perpendicular to the "horns" of the Moon. Draw a ray from the center of the Moon extending to the other body. If the angle between that ray and the extended equator of the Moon is less than 45 degrees, then the loss in accuracy is probably not worth noticing. If the angle is as much as 60 degrees or greater, you can expect significant reductions in accuracy in the resulting GMT. You can still use sights out-of-line like this for practice and to test your lunarian talents (and for anything else you can think of to do with lunar distance angles), but you should state your results as an angular error in that case rather than an error in GMT.
And one more issue with Jupiter which hasn't come up. Jupiter's angular diameter is about 0.6' of arc. That's big as far as lunars are concerned, and you can see it as a tiny disk through a moderately powerful sextant telescope. That disk has to be placed on the limb of the Moon so that it is split along the limb in order to be consistent with most software for clearing lunars (and to be consistent with historical practice). If you don't get that right, you could get another error of up to 0.3'. And consider that another reminder that you should use the highest power telescope you have available on your sextant when shooting lunars.
So let's total everything up. We've got a large error because the wrong altitudes were used. That's the biggest problem by far with Paul Jackson's results. We have to throw those altitudes out and either observe them with the lunar itself or calculate them correctly using some software or tables we trust and using that software or those tables correctly. This was the biggest problem here and the error that results from this mistake is over 30' of arc. Next, it appears likely that Paul measured an angle to the Moon's leading limb which is not the same thing as a "Near Limb" observation. And indeed a Near Limb observation was effectively impossible at this Greenwich Time. This led to an error of +23' or -9' depending on how you look at it. Finally, the software that he used to clear the sights also has some errors: it shouldn't have used this A,B,Q series method for such a short distance, or at least it should have warned that this was "not recommended", though the error from that is only 0.3' and also there is a serious error in the way the method has been implemented in the "Navigator" software resulting in an error of about 5'.
Advice for anyone trying out lunars for the first time:
Use the Sun as the other body, try Jupiter, Saturn, Venus (Jeremy has convinced me that at least some people get excellent results with Venus lunars) and maybe some of the standard lunars stars, too, like Spica and Antares, but don't worry too much about which "other body" you use. Be sure to use the highest power telescope accompanying your sextant. Be sure to adjust everything properly and get a really good index correction above all else. Find ways to steady your hands; try holding the frame with both hands. If you find yourself in a ridiculous posture with the sextant upside down and sideways, straining your hands, then just wait a few hours or try again another day. That would have been consistent with historical practice, too. And although those geometries where the Moon is nestled up close to a bright planet are visually appealing, there are some good technical reasons why you should avoid them for lunars, and there's also the historical fact that MOST lunars were taken at much larger angular distances. Also, experiment with swinging stars along the limb of the Moon. You've got it right when the star or planet (or the limb of the Sun) just barely nicks the limb of the Moon as you rock the sextant past. Don't try to place a star on some specific spot on the Moon's face, like the center of the disk, or the center of the illuminated limb, or one of the horns. Those simply don't give useful results. When you clear your lunars, start with some convenient software that you KNOW from your own experience or recommendations from NavList has been properly validated. You can always branch out later and learn tabular methods like the historical methods in Bowditch, Norie, and others, or perhaps a more modern tabular method like Stark's tables. But save that for LATER. The great advantage for a beginning lunarian today is the opportunity to clear large numbers of sights with almost no effort. You can separate the process of learning the physical and observational aspects of the method from the separate issues of working up the sights.
By the way, Paul, as I noted at the top, you don't need to reply to any of my specific questions here if you're done with this sight. I am addressing this to you BECAUSE they are your observations, but the comments I'm making here are for the assembled navigators of NavList generally. :)
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