NavList:

Bob B., you wrote:
"A Lunar skeptic mentioned John Karl's book, "Celestial Navigation in the age of GPS". Chapter 8 devoted to Lunars. Specifically the Lunar skeptic quoted Karl as saying Lunars gives 2 minute UTC certainty. I read the chapter, and on page 96 he lists the following problems and their accuracy cost and then converts the 2 minutes UTC certainty to Longitude certainty 30'."

A lunar skeptic? Who? As for John Karl's book, I met John and talked about lunars with him way back in June 2006 at the NavList gathering that I had organized in Mystic (this was also when Luis Soltero did a presentation on his StarPilot app, which Paul Hirose mentioned). John Karl's book was just being finalized, at that time, under the patronage of the late Ken Gebhart, owner and founder of Celestaire. John Karl was a former physics professor who unfortunately viewed celestial navigation as a set of problems in applied mathematics. He had relatively little experience in actual sextant use or observation or lunars, and he had little knowledge of lunars generally except as applied mathematics. He had tried lunars only a handful of times with his own sextant, and he had never looked at any of the primary historical sources on lunars --the logbooks and original notes from navigators from the era.

How accurate are lunars, Bob? You attended my lunars workshop. It was perhaps a mistake on your part to attend that workshop first, but some people do get a kick out of eating dessert before dinner! :) In any case, what you learned in my workshop is that the fundamental accuracy of lunars can be summarized by remembering that the Moon moves among the stars (relative to the background celestial objects from which we measure lunars, in other words) at an average rate of 13° per day. That's close enough to 12° per day for estimation purposes, and we can reduce that by "dividing both sides" progressively:
  12° → 1day
  1°  →  2 hours (after dividing both sides by 12)
  1'  → 2 minutes (1 minute of arc of lunar distance corresponds to two minutes of time)
  0.1' → 12 seconds

So an error of 1 minute of arc in lunar distance observations would necessarily lead to two minutes of error in absolute time (Greenwich Apparent Time in the early decades of lunars, GMT in later decades, or UT in the modern era). But that's just a conversion factor. Quoting a conversion factor tells you nothing about the practical accuracy of lunars. It's only telling you that they require quality sextants for good results. Regrettably, many twentieth century sources will assert that "as every experienced marine navigator worth his salt knows, getting sextant observations as good as one minute of arc is the limit". Claims like this are often phrased in this fashion to appeal to the 'old salt'. The problem with this claim is that it is comparing apples to oranges. The observation of celestial altitudes at sea is fundamentally limited by the sea horizon due to anomalous dip, caused by unusual refraction, and also due to the well-known, but almost universally ignored, uncertainty of height of eye. But the sea horizon has no relevance to lunars. With a bit of care and a well-adjusted sextant, lunar distance observations accurate to a couple of tenths of a minute of arc are achievable on a regular basis. By averaging four, that accuracy typically doubles.

You wrote (quoting?):
"(1). NA is in accurate for coordinates of the moon = .3' "

This should be considered either "hopelessly vague and therefore always true" or "simply false". Why 'vague'? Because the "Nautical Almanac" is not a single entity. It is a family of products produced by different authorities with different goals for over two centuries. The quality of the Moon's position has varied over the centuries, especially before 1820 or so, but it has been essentially perfect for over 150 years. Why the alternative: 'simply false'? If the "NA" is interpreted to mean the modern Nautical Almanac, then the position of the Moon is typically accurate to 0.0', occasionally 0.1', while lunar distances calculated from almanac data for the Moon and another body can be off by 0.1' or occasionally 0.2'. Is that a concern? It would be a small concern if this was 1995 or 1955. But as far as modern lunars are concerned, so what? We are not dependent on the Nautical Almanac and have full access to considerably more accurate astronomical data. For example, the lunar distance tables on my website are exact to 0.0' (with rounding differences in a small percentage as large as 0.1'). But even if we restrict ourselves to the printed data in the modern Nautical Almanac, the difference would be mostly a matter of nitpicking.

You added (quoting?):
"oblateness of earth can account to .2' error."

That is irrelevant and misleading. The correction for the oblateness of the Earth, if applied, is a "clearing correction" --fundamentally it is an adjustment of the Moon's parallax. It has nothing to do with the accuracy of the true, geocentric coordinates of the Moon as published in almanacs. Also, the oblateness correction, if applied, rarely exceeds 0.1' of arc and then only in high latitudes (where accuracy in lunars or other sources of GMT are less relevant since longitude accuracy is less critical to miles on the ground in a position fix up there where the lines of longitude converge).

You added (quoting?):
"Perfectly adjusted sextants have .15 to .33' of arc error depending on quality of sextant."

That's not navigation. That's not science. It's an opionated declaration pretending to be knowledge. How good is your own sextant? Test it and find out.

And then the coup de grace:
"(2). sights at sea are expected to be within 1' to 3' depending on conditions and observer's skill."

And there we have it! That's the big, dumb mistake that gets repeated over and over. As "any old salt knows", if we can't get our latitude at Noon to better than +/- one minute of arc (and even that's "on a good day"), then how the hell could anyone measure a lunar to a tenth of a minute?! But the sea horizon is directly responsible for the limiting uncertainty of standard celestial altitude observations. That tells us nothing about lunars. With lunars that uncertainty is completely removed. Measuring angles from the Moon's limb is a process permitting much higher accuracy in observations.

And you threw this in:
"And then Karl considers earth rotates 1' in 4 sec, the 120 sec uncertainty in UT makes Longitude certainty to be 30'!"

True, true. But er... quoting John Karl on the rotation of the Earth is like quoting him on "2+2=4". :) Let's count that as "common knowledge". But just once more: the Earth turns by 1° of longitude in every four minutes of time. That's all you need to convert time differences to longitude changes. The only other detail that comes up eventually in celestial navigation is that this is the "mean Sun" rate, and the "sidereal rate" is just a tiny bit faster (not relevant here! I mention this only for "completeness").

[Slocum and van der Werf in another post...]

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA