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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Modern Lunars
From: Paul Hirose
Date: 2016 Sep 20, 16:08 -0700

```On 2016-09-20 7:43, Antoine Couëtte wrote:
> Re: LUNAR #2 (re: http://fer3.com/arc/m2.aspx/Modern-Lunars-Couëtte-sep-2016-g36570)
> One thing puzzles me ... the difference between our Azimuts:
> For the Moon, you get  85.4227° , while I get: *Moon Z = 85.42280° including
a Parallax in Azimut equal to dZ = -14.59022” , which - without the parralax
in Azumuth - would put the Moon at 85.4268 °*
> For the Sun, you get 85.4223°, while I get: *Sun Z = 85.42227°, including a
parallax in Azimut equal to dZ = - 0.02538”*
> Maybe a difference in Aries GHA ? I am computing it at ARIES GHA = 107.057
931 8 °, but I am ignoring some higher order cross-terms of the "Equation des
Equinoxes".

Below is the complete output of my program for the time and place in

Although the program displays sidereal time, it actually uses the "new
paradigm" introduced in 2000, with the Celestial Intermediate Origin
time. The result should be virtually identical with either method.

Altitude and lunar distance rates ignore refraction, and so in this
extreme case are not accurate. However, the solution still converges to
.00001° in 10 iterations.

initial time:
1855-09-07T08:04:52.320 UT1
1855-09-07T08:05:00.000 TT (Gregorian)
2398833.5 + 0.336806 = TT Julian date
+0m07.680s delta T
+0.00000° +0.00000° polar motion x, y

initial coordinates:
+30.11083°  -30.00000° north lat, east lon
-30.03209° ephemeris east lon
0.0 meters (0 feet) above ellipsoid
+0.00000° +0.00000° deflection of vertical xi, eta

23.9 C (75.0 F) at observer
985.4 mb (29.10″ Hg) altimeter setting
985.4 mb (29.10″ Hg) station pressure
50.0% relative humidity
0.0002 water vapor partial pressure fraction
1.0002616 index of refraction at 550 nm

Moon:
0.00000° dip
48.87353° apparent lower limb altitude
0.01306° refraction
-0.24932° unrefracted semidiameter
49.10980° unrefracted altitude of center
49.10989° predicted altitude
-0.00009° intercept
85.42269° predicted azimuth

altitude partial derivatives:
0.080° per ° N latitude
0.862° per ° E longitude
0.208° per minute time

Sun:
0.00000° dip
4.49557° apparent lower limb altitude
0.16522° refraction
-0.26465° unrefracted semidiameter
4.59500° unrefracted altitude of center
4.59376° predicted altitude
0.00123° intercept
85.42225° predicted azimuth

altitude partial derivatives:
0.080° per ° N latitude
0.862° per ° E longitude
0.216° per minute time

predicted Moon to Sun angle:
44.51613° center to center, unrefracted
0.14519° refraction
44.37094° center to center, refracted
0.24921° Moon near limb refracted SD
0.25805° Sun near limb refracted SD

43.86275° observed angle
43.86369° computed Moon to Sun
-0.00093° observed - computed

separation angle partial derivatives:
+0.000960° per ° N latitude
+0.010420° per ° E longitude
-0.005044° per minute time
78% of total angular velocity

DE406 ephemeris
149597870.691 km per au

BCRS position (km) and velocity (km/day).
Moon:
1.451103229e+008 -3.292822757e+007 -1.421809283e+007
5.026452032e+005 2.244336976e+006 9.749565176e+005
Sun:
-9.706259896e+005 -9.457987890e+004 -1.279692556e+004
-2.457214254e+002 -9.827485677e+002 -4.192286425e+002

GCRS to celestial intermediate matrix
(IAU 2006-2000B precession-nutation)
0.9999014 -0.0000010 0.0140430
-0.0000016 1.0000000 0.0001888
-0.0140430 -0.0001888 0.9999014

108.90837° Earth rotation angle
7.137195h Greenwich apparent sidereal time
5.137195h local apparent sidereal time

23.45805° mean obliquity
-0.00255° +0.00217° nutation in longitude, obliquity

polar motion matrix:
1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000

Moon apparent geocentric place:
-2.0877426e+005 3.0144303e+005 1.6977604e+005 GCRS
4.0410580e+005 geometric distance (km)
8.169499h +25.29193° equinox RA, dec
8.292861h intermediate RA
237.45752° SHA
0.24634° semidiameter
0.90436° horizontal parallax
119.22732°  +5.07609° ecliptic true lon, lat
119.22987° mean lon

Sun apparent geocentric place:
-1.4628618e+008 3.3148350e+007 1.4380829e+007 GCRS
1.5068267e+008 geometric distance (km)
11.024173h  +6.25884° equinox RA, dec
11.147536h intermediate RA
194.63740° SHA
0.26465° semidiameter
0.00243° horizontal parallax
164.10755°  +0.00026° ecliptic true lon, lat
164.11011° mean lon

geocentric separation angle:
45.10541° center to center
-0.007558° per minute
85% of total angular velocity

illumination conditions:
85.4° 4.6° Sun unrefracted az, el
180.0° Moon to Sun position angle (0 = zenith)
135.4° Moon phase angle (0 = full, 180 = new)

position angles:
180.0° Moon to Sun
360.0° Sun to Moon

recommended limbs:
Use Moon lower limb.
Use Moon near limb.

```
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