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

**Re: Daytime Venus Lunar**

**From:**Paul Hirose

**Date:**2012 Aug 15, 23:08 -0700

Antoine Couëtte wrote: > Further to results last obtained on Greg's second Lunar dated Aug 14th, 2012, (i.e. the one with Lunar Distance = 2°05'8 See hereunder), I need to take back some comments on the comparison made yesterday between own results and Frank's calculator results obtained on this specific Lunar > > > With NO phase correction, if I enter my value of 2°05'980 into Frank's Calculator, I am getting a grade of Error in Lunar 0', Error in Longitude 0°01'5. My program allows only the center, near limb, or far limb of the target body to be observed. It expects that the user will observe a limb instead of the center if the target planet appears non-circular. In fact, it analyzes the illumination angles and recommends the correct limbs for altitude and lunar distance. That's very nice when the choice is not obvious. But as we shall see, the program needs help if the observer prefers to shoot the center of light. In this run I use the far limb in order to get the semidiameter of Venus. (If the center of Venus is selected, semidiameter is not needed and not displayed.) Then I will adjust the computed lunar distance to the center of Venus, and to the center of light. time: 2012-08-13 13:43:56.000 UTC 2012-08-13 13:45:03.184 TT (Gregorian) JD 2456152.5 0.572954 (TT) 66.777 seconds delta T estimated position: +34°10.400' -119°13.800' north lat, east lon 2 meters above ellipsoid atmosphere: 19° C (66° F) at observer 1012.5 mb (29.90" Hg) altimeter setting 1012.3 mb (29.89" Hg) pressure at observer Moon to Venus separation angle: 2°21.135' computed, center to center, unrefracted 0.069' refraction 2°21.066' center to center, refracted 15.174' Moon near limb refracted semidiameter 0.200' target far limb refracted semidiameter 2°06.092' Moon near limb to Venus far limb 2°05.800' observed angle - 0°00.292' observed - computed unrefacted separation angle rate: -19.3" per minute (topocentric) 79% of total angular velocity geocentric coordinates (true equator and equinox, DE421 ephemeris, IAU 2006 precession, 2000A nutation): 6h11m27.228s +20°49'04.1" Moon RA and dec. 14.998' apparent semidiameter 6h23m24.748s +19°55'58.0" Venus RA and dec. 0.201' semidiameter 3h16m36.972s local apparent sidereal time geocentric separation angle and rate: 2°56.337' center to center -27.77" per minute 84% of total angular velocity illumination conditions: 75.6° 4.5° Sun unrefracted az, el 149.9° zenith angle, Moon to Sun 131.8° Moon phase angle 150.0° zenith angle, Venus to Sun 91.0° Venus phase angle zenith angles: 165.5° Moon to Venus 346.1° Venus to Moon recommended limbs: Use Moon lower limb. Use Venus lower limb. Use Moon near limb. Use Venus far limb. My programe says (observed - computed) lunar distance = -.292'. But remember, that assumes an observation of the far limb of Venus. Refracted semidiameter = .200', so, if we assume an observation of the center of Venus, (observed - computed) = -.292 + .200 = -.092'. In reality, the center of light was observed, so the -.092' error requires a phase correction. > With Phase correction, if I enter my value of 2°05'896 into Frank's Calculator, I am getting a grade of Error in Lunar 0', error in Longitude 0°00'5. I have never applied correction for phase angle, and did not find much information or formulas. A 1976 paper by Safronov begins with some classic formulas, then presents a new model - which is too elaborate for me. http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1978SvA....22...78S&db_key=AST&page_ind=0&data_type=GIF&type=SCREEN_VIEW&classic=YES In the Explanatory Supplement to the Astronomical Almanac is a polynomial for Mercury and Venus phase corrections. It was derived during the creation of the DE200 ephemeris. Rewritten for phase angle in degrees (vs. quadrants) and better computational efficiency, it is: -.03 + (4.33e-3 + (5.80e-5 - 3.57e-7 * i) * i) * i That is the correction in semidiameters. E.g., at 45° phase angle, the center of light is .25 semidiameters from the center of the body. At phase angle 0 (fully illuminated) the correction is an obviously wrong -.03, but the small error is trivial since Mercury and Venus are not observable at phase angles near 0 or 180. The 91.0° Venus phase angle and that formula give a correction of .575 * .200' = .115'. My program says the far limb of Venus is the correct one for a limb shot. Therefore, the correction is away from the Moon - but not directly away! As already noted: 150.0° zenith angle, Venus to Sun 346.1° zenith angle, Venus to Moon Zenith angle is the "azimuth" from one body to another on the celestial sphere. The zenith is "north". E.g. if the Moon is exactly above Venus, the zenith angle from Venus to the Moon is zero. The angle increases counterclockwise. This is actually the same sense as azimuth, though it seems backward because you're looking out from inside the celestial sphere. In this case, the direction of the Sun from Venus, with respect to the direction of the Moon, is 150.0 - 346.1 = 163.9°. The correction to the observed lunar distance is the cosine of that angle, times the .115' phase correction computed above. So add the -.111' to the observed lunar distance (center of light) to get the estimated center of Venus observation. Recall that I found the observed - computed lunar distance = -.092', if computed for the center of Venus. If computed for the center of light, that becomes -.203'. That assumes the correction affects only the distance, not the angles. But they do change, especially that close to the Moon. Unfortunately, I don't have time to do a better job. I can only hope that the small semidiameter of Venus prevents any serious error. Also, as Safronov says in his paper, there's significant disagreement among the standard formulas. One last thought: as dear old George used to say, a single observation says little about accuracy. You could have been lucky, or unlucky. Even a run of several observations could have systematic errors in common. -- I filter out messages with attachments or HTML.