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Re: Modern Lunars
From: Paul Hirose
Date: 2016 Sep 20, 16:08 -0700
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 your document. Although the program displays sidereal time, it actually uses the "new paradigm" introduced in 2000, with the Celestial Intermediate Origin instead of the equinox, and Earth rotation angle instead of sidereal 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.