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Re: Moonrise over Connecticut, 19 October 2021
From: Antoine Couëtte
Date: 2021 Oct 29, 21:41 -0700

Frank,

Complement and results confirmation to my my last post referring to your recent reply to my previous post .

As regards the SUN and the Moon, you published :

Object       GHA        Dec         Hc       Zn

SUN        153 39.1   S10 18.4   - 0 15.2   256.4

MOON 339 48.3 N 4 02.6 + 0 38.9 85.2°

Own results are (with 1 extra non-significant digit published here on purpose in order to wipe out all round off errors in the comparison process) :

SUN        153°39.08'  S10°18.43' - 0°15.19' 256.45° and SD = 16.06'

MOON 339°48.26' N 4°02.62' + 0°38.86' 085.18° and SD = 15.03' . Hence both of us are "using" exactly the same Moon and the same Sun.

Let us travel through the classical reverse engineering process from Hc to refracted LL height for both bodies:

(1) Start from MOON Geocentric height Hc = +0°38.86' ( For SUN : Hc = -0°15.19')

(2) Compute and apply Horizontal Parallax correction as relevant for Hc : MOON PA = 0°55.09' Unrefracted Topocentric MOON Center height = -0°16.22'

(SUN PA = 0°00.15' and Unrefracted Topocentric SUN Center height = -0°15.34' )

(3) Compute Augmented Semi-Diameter : SD = 15.04' (SUN SD = 16.06')

(4) Compute Unrefracted Topocentric Moon LL height = (2) - (3) = -31.26' (SUN : (2) - (3) = -31.40')

(5) Compute inverse refraction for (4) : MOON Inv(Ref) = -33.36', here computed from -31.26'. (SUN Inv(Ref) = -33.40' here computed from -31.40').

(6) Compute Refracted Topocentric Moon LL height : (4) + (5) = 0°02.10' (SUN : (4) + (5) = 0°02.00')

(7) Compute Direct refraction (i.e the "usual one") for (6). MOON Refr = -33.36' now computed from +0°02.10'. (SUN Refr = -33.40' now computed from +0°02.00') with French Éphémérides Nautiques Values used here.

(8) Publish : Refr, SD, PA and Sum.

As a reminder, the values currently published in the USNO Web Application clone are the following ones:

For Assumed Position: Latitude N 41 18.4 Longitude W 72 30.0 Almanac Data | Altitude Corrections Object GHA Dec Hc Zn | Refr SD PA Sum o ' o ' o ' o | ' ' ' '  SUN 153 39.1 S10 18.4 - 0 15.2 256.4 | -31.0 16.1 0.1 -14.8   MOON 339 48.3 N 4 02.6 + 0 38.9 85.2 | -24.0 15.0 55.2 46.2

The values indicated here-under are therefore derived fom the French Éphémérides Nautiques refraction tables.

For Assumed Position:  Latitude    N 41 18.4                 
                                        Longitude   W 72 30.0                 
                                                                               
                        Almanac Data                |    Altitude Corrections  
 Object       GHA        Dec         Hc       Zn    |   Refr   SD    PA    Sum 
              o   '      o   '      o   '       o   |     '     '     '     '  
 SUN        153 39.1   S10 18.4   - 0 15.2   256.4  |  -33.4  16.1   0.1 -17.2  
 MOON       339 48.3   N 4 02.6   + 0 38.9    85.2  |  -33.4  15.0  55.1  36.7

Once corrected, the values in the USNO Web Application clone should show up very close from the ones listed immediately hereabove. Any difference should be explained by the slight differences in refraction values for very low altitude between the the French Éphémérides Nautiques and the Nautical Almanac.

Hoping that there are no typos here-above and hoping too that all this work this fullly clarifies the situation.

Antoine M. "Kermit" Couëttte

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