NavList:

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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