From: Antoine Couëtte
Date: 2018 Sep 23, 10:22 -0700
RE : Venus-phase-correction-Bernecky-sep-2018-g42825
What a small world !
Thank you very much for your detailed and very impressive work.
I just submitted to NavList a reply to Paul Hirose - just published as: Unexpected-USNO-height-correction-precepts-Couëtte-sep-2018-g42827 - and in which I mentioned :
I am using our most regretted George Huxtable's recommended formula published in NavList  on Sep 18th, 2010.
Let SD be the angular semi-diameter seen from Earth center, "φ" the phase angle, then the phase correction "λ" is computed as follows :
λ = [ 8 / (3π) ] * sin² (φ/2) * SD
1.b - Numerical Application
As per your request here-under, I am giving here-after extra digits to 0.01' to be sure that round off errors do not "contaminate" this numerical example, although extra-digits are not really necessary in this specific example.
- Venus semi-diameter : 0.42'
As a numerical application, with φ = 139° as stated in your second post referenced here-under, then λ = [ 8 / 9.425... ] * sin² (139°/2) * 0.42' = 0.31' .
You had the kindness of using my Venus Example of March 18, 1977 and you found : δ GHA= +0.265' and δ DEC = -0.185'
My own results are extremely close from yours with : δ GHA= +0.263' and δ DEC = -0.184' which boil down into δ Height = +0.31' in this specific example as mentioned here-above.
Looks like your own computation results fully confirm the results published by George Huxtable. Excellent ! :-)
Nice work and well done !
Very Best Regards,
Antoine M. "Kermit" Couëtte