GMT by Lunar Altitude computationsNote this is not a routine moon sight, but a special technique that illustrates the power of the StarPilot, especially its zoom plot function. StarPilot includes a sophisticated analysis of Lunar Distances as a means of determining GMT from the moon. It is a versatile technique that will work in nearly any sky with a moon in it, but it requires not only highly accurate sights, but sights of a special nature — namely, a diagonal sextant measurement of the distance between moon and another body along the moon's path across the sky. There is another way to find GMT from the moon that is not as often applicable, but when it is, it is easier to complete in that no special types of sights are required — although high accuracy is still crucial. This method is often called GMT by "Lunar altitudes" as opposed to GMT by "Lunar distances." To our knowledge, the first person to describe this technique in modern times was John Letcher (author of a wonderful, though sadly obscure, celestial nav book, but more famous for his also pioneering work on self-steering equipment). Sometime later, but independently, the technique was also described by Francis Chichester. The prerequisite for the technique is a moon bearing near due east or due west at twilight. We also assume we have a watch that is running properly, but it has an unknown error in it. Our task is to use celestial measurements to determine the watch error of this watch — it can be minutes, hours, or days, but let's assume we know the day. See the StarPilot Emergency Nav notes on how to determine the day by just looking at the sky. The simple principle of this technique is this: if we take 3 simultaneous sights, 1 each of two bodies that intersect in a good angle for a fix, and a third sight of a moon lying near due east or west, then the longitude difference between the 2-body fix and the moon's LOP is a measure of our watch error. In other words, if the watch were exactly right and we took 3 precise sights, then all 3 lines would intersect in the same place which was our true position. If the watch is wrong, the moon line will defer from the intersection of the other two, and the amount it is off is related to the watch error. Note that the latitude of the 2-body fix will be our correct latitude, even though the watch time was in error.
Example: For this example, we will also assume that you have read through the other parts of the StarPilot description so you know more or less how it works... in other words, we will not review all the input steps here. After taking the 6 sights listed at the end of this exercise, we plot out the results to establish what we would have obtained had we taken all 3 sights simultaneously. Naturally this cannot be done simultaneously, but if we take the series of sights 1-2-3 then 1-2-3 again, we can graph the results and interpolate a set of simultaneous values. This is a normal technique often done at sea to minimize running fix corrections. We take the moon, and two nice bright planets.
ZD=+8, WE = ? (but enter as 0 sec), HE = 9ft, IC = 0, DR = 47° 45' N, 123° 05'W, date = Jan 19, 2000, our speed = 0.
WT body Hs LOP 17:50:00 Mars 25° 04.9' a = 18.2' T 223.5°
Now we start to zoom in by moving the cursor to the center of the LOPs as shown below top left and then press Enter and update the DR to that position and replot with a scale of 3 to get the picture next to it.
We need to know now how far east the moon line is of the planet fix, so set the cursor on the planet fix (below left) and press Enter to get the Lat-Lon of that location (bottom right). From this we see that our proper latitude is 47° 39.1 N and the longitude of this intersection is 123° 35.1' W (not our correct longitude yet since we don't know the time yet).
Now move the cursor to the moon line (below left) at the same Lat and press Enter to get that data as shown below right. This longitude is 123° 31.8' W, which is 3.3' east of the planet fix. Our next step is to guess from this how much the watch is fast and then adjust it by that amount and do the sight reductions again. Each time we do an iteration like that we should get closer, and when all 3 lines coincide we can assume we have the right time. Note the obvious, however, that we are assuming all sights are precisely accurate. Even a small sight error will cause a relatively large time error. And the analysis here is a bit more complicated than normal time evaluation. For example, if we do a 3-star fix that makes a nice tight triangle but unknown to us our time if off by 1 minute, the lat will be right, but the longitude will be off by 15' -- too far west if the watch is fast, and too far east if the watch is slow. But this analysis does not help us find our watch error from the moon sight. Here we must consider that the moon is moving relative to the stars at the rate of about 360° every 30 days or 12°/day or 12x60'/24x60 min = 1'per 2 min of time. So our 3.3' discrepancy would correspond to a time error of about 6.6 minutes. Hence our first guess is that we are 6m 36s fast.
Now we redo the sight reductions at the new time of 17:50:00 - 00:06:36 = 17:43:24 WT on Jan 19, 2000. Note our DR has been stored in roughly the middle of the lines (47.39, -13.329) but it does not matter where this is for the sight reductions. WT body Hs LOP 17:43:24 Mars 25° 04.9' a = 43.9' A 221.5°
Our time correction was clearly too big, we have overshot the mark. Now lets see how many minutes too far we have gone. As before, set cursor on the fix and read the longitude, and then set cursor on the moon line at the same latitude to read it.
The difference is 0.9', or using our previous estimate, 0.9 x 2 = 1.8 min = 1m 48s. This would imply that our time error was not 6m 36s fast, but 6m 36s - 1m 48s = 4m 48s fast. BUT, we know from the first iteration that 2m per 1' is too big a rate. We wanted to move 3.3 and we moved 3.3 + 0.9 = 4.2. In other words, we should reduce our rate by 3.3/4.2 = 0.79. So, 1.8m x 0.79 = 1.4m = 1m 24s, and our better guess is 6m 36s - 1m 24s = 5m 12s. So once again, redo the sights with a new time: 17:50:00 - 00:05:12 = 17:44:48.
WT body Hs LOP 17:44:48 Mars 25° 04.9' a = 09.5' T 223.4°
Now, again, move the cursor to the center of the fix, update DR, and replot with a scale of 10. Now we are essentially done, the fix is very good now — note from the right-side screen that the range DR to fix is 1.78 miles, so this is a very tight triangle and we have found that our watch error was 5m 12s fast. The true error was 5m exactly, so this turned out well. The main constraint on this method is it requires a moon lying near east or west at twilight. This one off by 9° worked fine. Practice with various conditions to see what the limits are. The virtue of this method is it takes only standard sights, no special sextant handling and no special computations. We just iterate the time till we get the lines to coincide.
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