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Re: First Moon-Star Lunar
From: Sean C
Date: 2017 Dec 29, 13:17 -0800
The first formula (the only one used for the star) is the refraction calculation. In the almanac it is given as:The second formula is the parallax in altitude calculation. It is given as:
PA = HP ∙ cos(H); where (again) H is the apparent altitude and HP is the horizontal parallax
[I just noticed that I mis-typed this as "HP ∙ sin(H)" in my original message. Cosine is the correct function.] The N.A. also gives a correction for oblateness which can be added to the value of PA:
OB = -0.0032° ∙ sin²(Lat) ∙ cos(H) + 0.0032° ∙ sin(2 ∙ Lat) ∙ cos(Z) ∙ sin(H)
It also states that "At mid latitudes and for altitudes of the Moon below 60° a simple approximation to OB is:
OB = -0.0017° ∙ cos(H)
There are several other useful formulae in this section, such as dip, DR and fix calculations. If you don't have access to a N.A., just let me know and I can detail those equations for you as well, if you like. Also, let me know if any of the above is unclear or if you have any other questions.
Regards,
From: Sean C
Date: 2017 Dec 29, 13:17 -0800
Ed,
You asked about how I was calculating the "dh" values.
These are formulae from the "Sight Reduction Procedures" section of the Nautical Almanac. (Pp. 277 - 285 in my 2016 commercial edition.) This section details how to calculate various values directly using a calculator or computer program.R = -0.0167° / tan(H + 7.32 / (H + 4.32)); where H is the apparent altitude
This formula assumes a standard pressure and temperature of 1010 mb / 10 °C. If the pressure and temperature are known, one can correct for them as well by multiplying the refraction value by "ƒ". The formula for "ƒ" is:
ƒ = 0.28 ∙ P / (T + 273); where P = pressure in mb, and T = temperature in °C
So, for example: if the pressure and temperature during your lunar had been 30 °C / 990 mb, the result would be:
0.28 ∙ 990 / (30+273) = 0.915
-0°1.4' ∙ 0.915 = -0°1.3'
PA = HP ∙ cos(H); where (again) H is the apparent altitude and HP is the horizontal parallax
[I just noticed that I mis-typed this as "HP ∙ sin(H)" in my original message. Cosine is the correct function.] The N.A. also gives a correction for oblateness which can be added to the value of PA:
OB = -0.0032° ∙ sin²(Lat) ∙ cos(H) + 0.0032° ∙ sin(2 ∙ Lat) ∙ cos(Z) ∙ sin(H)
It also states that "At mid latitudes and for altitudes of the Moon below 60° a simple approximation to OB is:
OB = -0.0017° ∙ cos(H)
Sean C.
