# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Celestial predictions. was:[NAV-L] Old style lunar**

**From:**Frank Reed CT

**Date:**2004 Dec 12, 19:24 EST

George H, you wrote:

"That's all very well, but in practical terms, what does a mariner, given
an

on-board laptop, do to obtain positions by such methods as Frank

advocates, when at sea? First, take a mariner that's very computer-savvy,

and then take another that isn't. Just how do they go about it?"

on-board laptop, do to obtain positions by such methods as Frank

advocates, when at sea? First, take a mariner that's very computer-savvy,

and then take another that isn't. Just how do they go about it?"

How long is your trip? If I were planning to spend two months
cruising without touching an Internet-enabled port, I would simply print out the
pages. If I were advising another coder how to do it from scratch, I would first
request a consulting fee. If there's sufficient demand, I'll produce a
commercial version of my own software (but I'm skeptical that such demand
exists).

And:

"In practical terms, there's no requirement for position accuracy to be to

an arc-second."

"In practical terms, there's no requirement for position accuracy to be to

an arc-second."

I chose arcsecond accuracy simply because that's one step BETTER than that
required by any navigational calculation. Since the Nautical Almanac lists
positions to the nearest tenth of a minute, positional data accurate to the
nearest arcsecond will match the published tables except approximately one in
six times (when the rounding might shift the last digit in the wrong
direction). You will find that almost everyone who is doing these sorts of
calculations is aiming for arcsecond or better accuracy. Umland, Reis,
Wepster... they're all trying for that level of accuracy, though not always with
success.

And:

"Meeus' algorithms do all that's necessary to obtain on-board

positions to quite sufficient accuracy for any maritime application, lunar

distances included."

positions to quite sufficient accuracy for any maritime application, lunar

distances included."

I agree that the algorithmic approach is fine for standard line of position
navigation under the assumption that we're not going to worry about errors
smaller than 1 minute of arc. But I really do not think it's true that the
algorthms published by Meeus are sufficient for lunar distance calculations.
Meeus himself says that the Moon's longitude will be in error by as much as 10
seconds of arc. If you don't mind errors in your predicted lunars as large
as 0.2 minutes of arc, then yes, you could use those Meeus algorithms. No
problem. But why?? Unless you're dealing with a very old calculating device, you
only need a megabyte to store a long-term almanac that can be much
more accurate (42,000 bytes per year for the Sun, Moon, and 4 navigational
planets at arcsecond accuracy).

George scoffs:

"Frank is always quick to scoff, with words like "absurd"."

"Frank is always quick to scoff, with words like "absurd"."

No, Frank isn't always quick to scoff. Sometimes Frank is rather slow to scoff. At least that's what Frank thinks.

And George writes:

"If there's a computer on board, what's the problem in using it to make
such calculations

using the algorithms that Meeus provides? Where lies the "absurdity"? "

using the algorithms that Meeus provides? Where lies the "absurdity"? "

It all depends on your goal. Shooting lunars is a hobby for those people
who experiment with them today. If keyboarding coefficients out of a book
by Meeus is ALSO one of your hobbies, then of course, do whatever makes you
happy.

And George scoffs:

"At sea, we can do without such "tiny factors as the
gravitational

perturbations induced by the largest asteroids." Is Frank REALLY prosing

that as an argument for switching to a precomputed ephemeris? If so, how

much difference can those perturbations make? Come off it, Frank."

perturbations induced by the largest asteroids." Is Frank REALLY prosing

that as an argument for switching to a precomputed ephemeris? If so, how

much difference can those perturbations make? Come off it, Frank."

I'm sure you meant to say 'Frank should come off it', right? And
of course, no, I was not proposing that. The point is simply that the problem
has been completely calculated. Why do you have such profound antipathy for a
database?!

And:

"My own Basic programs run on a programmable pocket calculator, with a

memory of only 16 kilobytes all told, into which is fitted the programs,

stored astronomical data, and the harmonic terms of the perturbations. It

works with a cut-down set of harmonic terms, as given by Meeus in his

earlier paperback "Astronomical formulae for calculators". My program can

calculate positions of the four planets, 60 stars, Sun and Moon, over ±400

years. Results come mostly within 0.1 arc-min of Almanac predictions,

occasionally 0.2'."

"My own Basic programs run on a programmable pocket calculator, with a

memory of only 16 kilobytes all told, into which is fitted the programs,

stored astronomical data, and the harmonic terms of the perturbations. It

works with a cut-down set of harmonic terms, as given by Meeus in his

earlier paperback "Astronomical formulae for calculators". My program can

calculate positions of the four planets, 60 stars, Sun and Moon, over ±400

years. Results come mostly within 0.1 arc-min of Almanac predictions,

occasionally 0.2'."

How have you determined that?

"The worst-cases seem to be in predictions for Saturn,

which I have discovered on occasion to differ by 0.5' from the almanac, and

no doubt bigger discrepancies than that exist here and there. I haven't

made any systematic search. Nevertheless, it's quite good enough for

"ordinary" astro-navigation"

which I have discovered on occasion to differ by 0.5' from the almanac, and

no doubt bigger discrepancies than that exist here and there. I haven't

made any systematic search. Nevertheless, it's quite good enough for

"ordinary" astro-navigation"

Indeed it is. And for devices with very small amounts of memory, the
algorithmic approach still has some value. But these days even cell phones come
with lots of built-in memory. When memory is expensive and calculating time is
unimportant, it's appropriate to write code based on long algorithms. When
memory is cheap and calculating time is relevant, it's better to pre-calculate
everything and look up the results in a database.

And:

"In his later hardback, "Astronomical Algorithms" (1998), Meeus
quadruples

the number of such perturbation terms; far too much detail for me to pack

into my pocket calculator (though with double the memory, I could). This takes the magnitude of the smallest terms down by a factor of 100 or so, increasing the accuracy of the predictions by a similar factor. That would allow predictions that were more than sufficiently accurate for lunars."

the number of such perturbation terms; far too much detail for me to pack

into my pocket calculator (though with double the memory, I could). This takes the magnitude of the smallest terms down by a factor of 100 or so, increasing the accuracy of the predictions by a similar factor. That would allow predictions that were more than sufficiently accurate for lunars."

You should double-check the chapter on the Moon's position in that book.
The code is only slightly improved over the earlier publication. And the
accuracy of the planet positions are not necessarily as good as you think.
Read the section on p.220 of AA.

And wrote:

"If I were brave enough to take a laptop aboard my little boat (which I'm

not) and could guarantee sufficient Amps (which I can't), then I would

implement the Meeus algorithmic software with his full set of

perturbations."

"If I were brave enough to take a laptop aboard my little boat (which I'm

not) and could guarantee sufficient Amps (which I can't), then I would

implement the Meeus algorithmic software with his full set of

perturbations."

Why? Seriously. What difference does it make what's going on inside the
software?

Frank R

[ ] Mystic, Connecticut

[X] Chicago, Illinois

[ ] Mystic, Connecticut

[X] Chicago, Illinois