NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Moon altitude correction question
From: Stan K
Date: 2013 Aug 17, 18:50 -0400
From: Stan K
Date: 2013 Aug 17, 18:50 -0400
Frank,
I not only remember this, but I had the old emails in front of me while I was thinking about it. Your code always seemed OK, being within 0.1' of both the upper an lower table values, at least for every case I tested, which is exactly what you said to expect. Are you saying that if you apply (refraction and) parallax to the apparent altitude, and use this partially corrected apparent altitude as the argument for the augmentation calculation, then the augmentation cancels out? The examples in the Almanac do the SD correction after the parallax, but they are separate, independent calculation. The SD calculation could just as well have come first. The parallax does not come into play in the SD calculation (SD = 0.2724HP), and the parallax calculation uses the apparent altitude before any corrections are applied.
I'm feeling pretty dense right now. I'll have to give it some more thought. But the question is not about your code. It is about why augmentation is not mentioned in the Nautical Almanac examples. Please help reduce my density :-(
Stan
I not only remember this, but I had the old emails in front of me while I was thinking about it. Your code always seemed OK, being within 0.1' of both the upper an lower table values, at least for every case I tested, which is exactly what you said to expect. Are you saying that if you apply (refraction and) parallax to the apparent altitude, and use this partially corrected apparent altitude as the argument for the augmentation calculation, then the augmentation cancels out? The examples in the Almanac do the SD correction after the parallax, but they are separate, independent calculation. The SD calculation could just as well have come first. The parallax does not come into play in the SD calculation (SD = 0.2724HP), and the parallax calculation uses the apparent altitude before any corrections are applied.
I'm feeling pretty dense right now. I'll have to give it some more thought. But the question is not about your code. It is about why augmentation is not mentioned in the Nautical Almanac examples. Please help reduce my density :-(
Stan
-----Original Message-----
From: Frank Reed <FrankReed@HistoricalAtlas.com>
To: slk1000 <slk1000@aol.com>
Sent: Sat, Aug 17, 2013 2:19 pm
Subject: [NavList] Re: Moon altitude correction question
I haven't tested this today, but it worked seven years ago! :)
----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------
From: Frank Reed <FrankReed@HistoricalAtlas.com>
To: slk1000 <slk1000@aol.com>
Sent: Sat, Aug 17, 2013 2:19 pm
Subject: [NavList] Re: Moon altitude correction question
Stan, you wrote:
"What am I doing wrong here? I must be overlooking something."
"What am I doing wrong here? I must be overlooking something."
Long, long ago, some EIGHT-SEVEN lunations ago... we went over this very issue in NavList messages --and by "we", I mean literally "you and I"! In any case, the reason that the augmentation is not explicit is because it cancels out in this correction if you do it in the right order. As I wrote in July 2006, "If you do the SD correction after the parallax, the augmentation cancels out." Here's some "basic" code to reproduce the tables in the back of the Nautical Almanac:
begin
'Get actual HP for this case:
input(HP)
'Get observed altitude, h1, for this case:
input(h1)
'Get actual HP for this case:
input(HP)
'Get observed altitude, h1, for this case:
input(h1)
'Define kk=180/pi for angular conversions:
kk = 180/3.141593
'Define Moon's mean HP for these tables:
HP0 = 57.7
kk = 180/3.141593
'Define Moon's mean HP for these tables:
HP0 = 57.7
'SDcon is the ratio of the Moon's mean SD to HP0. A ratio of 0.2724 would
'perhaps be more accurate but this value matches the tables:
SDcon = 0.2711
'perhaps be more accurate but this value matches the tables:
SDcon = 0.2711
'SD0 is the semi-diameter at the mean Horizontal Parallax, HP0:
SD0 = SDcon*HP0
SD0 = SDcon*HP0
'Correct for refraction.
'refr0 is a function to calculate refraction (in minutes of arc)
'or take it from pre-defined tables ("stars and planets" values in NA):
h2 = h1 - refr0(h1/kk)/60
'refr0 is a function to calculate refraction (in minutes of arc)
'or take it from pre-defined tables ("stars and planets" values in NA):
h2 = h1 - refr0(h1/kk)/60
'Add in parallax in altitude and mean semi-diameter:
h3 = h2 + HP0 * cos(h2/kk)/60 + SD0/60
h3 = h2 + HP0 * cos(h2/kk)/60 + SD0/60
'The Lower Table uses the average altitude from the upper column:
havg = 2.5 + 5*int(h1/5) '"int" here is equivalent to "floor" function
havg = 2.5 + 5*int(h1/5) '"int" here is equivalent to "floor" function
'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.
dHP = (HP - HP0)/60
dSD = SDcon*dHP
h4 = h3 + dHP*cos(havg/kk)
h4LL = h4 + dSD
h4UL = h4 - dSD
'its parallax for the difference between the actual HP and the mean
'Horizontal Parallax, HP0.
dHP = (HP - HP0)/60
dSD = SDcon*dHP
h4 = h3 + dHP*cos(havg/kk)
h4LL = h4 + dSD
h4UL = h4 - dSD
'To keep the Lower Table corrections always positive, add
'5 minutes of arc to the LL correction and 35 to the UL correction.
'To compensate, subtract 5 minutes of arc from the Upper Table.
'Also subtract twice the mean semi-diameter for the UL.
UTcorr = 60*(h3 - h1) - 5
LTcorrLL = 60*(h4LL - h3) + 5
LTcorrUL = 60*(h4UL - h3) - 2*SD0 + 35
'5 minutes of arc to the LL correction and 35 to the UL correction.
'To compensate, subtract 5 minutes of arc from the Upper Table.
'Also subtract twice the mean semi-diameter for the UL.
UTcorr = 60*(h3 - h1) - 5
LTcorrLL = 60*(h4LL - h3) + 5
LTcorrUL = 60*(h4UL - h3) - 2*SD0 + 35
output(UTcorr, LTcorrLL, LTcorrUL)
end
end
I haven't tested this today, but it worked seven years ago! :)
-FER
----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------
