NavList:

Frank wrote:

> Note: in the lower table, find the
> Lower Limb  correction for HP=57.7 ...it's 5.0 all the way across. Makes
> sense.

Don't know if things have changed since 2004, but the two closest entries
are now 57.6' and 57.9' (LL entries are 4.9' and 5.3' respectively). Maybe
they've re-done the entire table since then?

> I  have a request: could someone please check the value for the Moon's
> altitude  correction for 0 degrees altitude from a post-2004 Nautical
> Almanac (I don't  have one).

Assuming you want just the basic altitude correction (and not parallax), the
2006 Nautical Almanac (Commercial Edition) shows a correction of 0 degrees
34.5' for 0 degrees 00 minutes of altitude.

I'll need an exact figure for HP if you want that correction, I'm not going
to type the entire column into this e-mail....  ;-)

--
GregR
Certified Sextant Geek


----- Original Message -----
From: <FrankReedCT@aol.com>
To: <NavList@fer3.com>
Sent: Monday, July 24, 2006 4:19 PM
Subject: [NavList 897] Nautical Almanac Moon Correction Tables


>
> A few weeks ago, Stan asked how the Moon  altitude correction tables in
the
> back of the Nautical Almanac were constructed.  There's no mystery about
> calculating the total correction. The only tricky part  was understanding
how the
> upper and lower tables are separately created. I  thought some of the rest
of
> the group might be interested in this.
>
> The  upper table is constructed using a mean value of the Moon's HP of
57.7
> minutes  of arc. The lower part then gives the increment in the correction
for
> the  difference between the actual HP and that mean value. In order to
keep
> the  corrections additive, 5 minutes of arc are added to the correction
for the
> Lower  Limb and 35 to the correction for the Upper Limb. In trade, 5
minutes
> of arc are  subtracted from the upper table. Note: in the lower table,
find the
> Lower Limb  correction for HP=57.7 ...it's 5.0 all the way across. Makes
> sense.
>
> I  have a request: could someone please check the value for the Moon's
> altitude  correction for 0 degrees altitude from a post-2004 Nautical
Almanac (I
> don't  have one). I'm curious whether they remembered to update that table
to
> keep it  consistent with the minor revision of the refraction tables for
the Sun
> and  stars. From a pre-2004 Nautical Almanac, the corrections are 33.8
from
> the Upper  Table and 0.3/0.9 (LL/UL) from the Lower Table. This has no
> significance for  practical navigation. I'm just curious.
>
> And here is some Basic code that  will generate the values in the table to
> 0.1 minutes of arc accuracy. If you see  any problems with it or know of
any
> simplifications in the calculational steps,  I would be interested to hear
about
> them.
> >>>>>>
>
> kk  = 180 / 3.141593
>
> 'The mean value of the Moon's Horizontal  Parallax:
> HP0 = 57.7
> 'The ratio of SD to HP. 0.2724 would probably be more  accurate but 0.2711
> 'reproduces the values in the almanac tables.
> SDcon =  .2711
> INPUT "HP:", HP
>
> FOR h1 = 0 TO 89 STEP  1
> PRINT h1
>
> 'The observed altitude, h1,  determines the refraction
> h2 = h1 - refr0(h1 / kk) /  60
>
> 'The semi-diameter is proportional to HP0. Augmentation  is
> 'proportional to sine altitude:
> SD = SDcon *  HP0 * (1 + .016 * SIN(h1 / kk)) / 60
>
> 'Add the semi-diameter  to the LL sight, subtract for UL:
> h2LL = h2 + SD
> h2UL = h2 - SD
>
> 'After clearing refraction and semi-diameter,  correct for the
> 'parallax at the mean value HP0.
> h3LL = h2LL + HP0 * COS(h2LL / kk) / 60
> h3UL = h2UL + HP0 *  COS(h2UL / kk) / 60
>
> 'The Upper Table correction is  essentially the difference between
> 'h3 for LL and the observed  altitude h1.
> h3 = h3LL
>
> 'The Lower Table uses  the average altitude from the upper column:
> havg = 2.5 + 5 *  INT(h1 / 5)
>
> 'h4 (LL/UL) is the increment in the Moon's  semi-diameter and
> 'its parallax for the difference between the  actual HP and the mean
> 'Horizontal Parallax,  HP0.
> SD = SDcon * (1 + .016 * SIN(havg / kk))
> dHP = (HP - HP0) / 60
> h4LL = h3LL + SD * dHP + dHP * COS(havg /  kk)
> h4UL = h3UL - SD * dHP + dHP * COS(havg /  kk)
>
>
> 'To keep the Lower Table corrections always  positive, add
> '5 minutes to the LL correction and 35 to the UL  correction.
> 'To compensate, subtract 5 minutes from the Upper  Table.
> UTcorr = 60 * (h3 - h1) - 5
> LTcorrLL = 60  * (h4LL - h3) + 5
> LTcorrUL = 60 * (h4UL - h3) +  35
>
> 'output the results:
> PRINT "Upper Table  Correction:    ";
> PRINT USING "###.##";  UTcorr
> PRINT "Lower Table LL Correction: ";
> PRINT USING "###.##"; LTcorrLL
> PRINT "Lower Table UL Correction:  ";
> PRINT USING "###.##"; LTcorrUL
> IF LEN(INKEY$)  THEN EXIT FOR
> SLEEP
> NEXT
>
> END
>
> FUNCTION refr0  (objectalt)
> 'refraction for a given observed altitude
> altdeg = objectalt *  kk
>
> IF altdeg < 15 THEN
> IF ABS(altdeg - INT(altdeg))  > .001 THEN
> PRINT "No refraction  data."
> END
> END  IF
> 'these refraction values are taken directly from the Nautical  Almanac:
> SELECT CASE  INT(altdeg)
> CASE  0
> totalref =  34.5
> CASE  1
> totalref =  24.3
> CASE  2
> totalref =  18.3
> CASE  3
> totalref =  14.4
> CASE  4
> totalref =  11.8
> CASE  5
> totalref =  9.9
> CASE  6
> totalref =  8.5
> CASE  7
> totalref =  7.4
> CASE  8
> totalref =  6.6
> CASE  9
> totalref =  5.9
> CASE  10
> totalref =  5.3
> CASE  11
> totalref =  4.85
> CASE  12
> totalref =  4.45
> CASE  13
> totalref =  4.1
> CASE  14
> totalref =  3.8
> CASE  15
> totalref =  3.6
> END SELECT
> ELSE
> tanz = 1 /  TAN(objectalt)
> totalref = .9716 * tanz - .00111 * tanz ^  3
> END IF
>
> 'returned in minutes of arc
> refr0 = totalref
>
> END  FUNCTION
>
> <<<<<<
>
>
> -FER
> 42.0N 87.7W, or  41.4N 72.1W.
> www.HistoricalAtlas.com/lunars
>
>
> >


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