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Antoine is an absolute stickler for precision, which is to be applauded. 
Here, he is investigating the details of the computed offset between the 
centre of Venus and its centre-of light, for perceived discrepancies.

However, my understanding of what Meeus states seems to differ from his. I 
wonder whether our copies correspond, about this question.

Antoine writes-
"NOTE: the "phase effect" correction values given hereabove are computed 
through assuming that the "planet center of light" is the "mid-point of its 
illuminated disk as seen from the Earth" . This computation method seems a 
customary and well accepted one (See Jean Meeus's "ASTRONOMICAL ALGORITMS", 
Chapter 40 "Illuminated Fraction of the Disk and Magnitude of a Planet").

My own copy of Meeus is 2nd edition of 1998, in which the chapter with that 
title is 41, not 40. In that chapter, I can't find the words that Antoine 
quotes. Is he, perhaps, translating for us from a French-language edition? 
Those words would be particularly sloppy, coming from Meeus, who is another 
stickler for precision and clarity, because there is in general no such 
"illuminated disk", but an illuminated crescent or other non-disk shape.

Nowhere, in that chapter or elsewhere, have I found any attempt to compute 
or estimate a "centre-of-light", though Meeus considers in some in detail 
the illuminated fraction k of the planet, and, elsewhere, of the Moon.

Presumably, in finding the centre of light, we have to assume uniform 
brightness of the illuminated fraction, between the outer semi-circle and 
the inner half-ellipse of the terminatot, and find the position of the 
"centre-of-gravity" of that area by a bit of elementary integration (which 
I haven't bothered to do). Those with a practical turn of mind could get an 
answer, perfectly good enough for our purposes, by cutting out a series of 
Moon shapes, with varying phases, from cardboard, then testing where they 
balance across a knife-edge.

That will result in a much smaller value of offset, from the planet's 
geometrical centre, than if you just look along the symmetrical bisector of 
the planet, and derive a displacement  by averaging the outer radius and 
the terminator radius, where they intersect it.

Meeus was writing for astronomers, who presumably have the sort of 
telescope that can clearly identify those two radii; and not for the likes 
of us, who in a sextant scope can only view such planets as a displaced 
blob-of-light.

Anyway, it seems likely to me that Antoine is computing that offset in a 
different way to Frank, which may be the reason for the discrepancy. If so, 
it seems to me to be Frank who has it right.

George

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

----- Original Message ----- 
From: "Antoine Couette" 
To: 
Sent: Wednesday, September 15, 2010 12:29 PM
Subject: [NavList] Re: DSLR Venus Lunar


To the attention of Greg Rudzinski and Frank E. Reed
Dear Greg and Frank,

In [NavList 13860] Re: DSLR Venus Lunar From: gregrudzinski---com Date: 13 
Sep 2010 17:39, Greg you requested to Frank :

" Frank does your program compensate for the difference of visible Venus 
and the center of Venus ? I am assuming that it does. "

*******

Pending Frank's reply on this specific subject, I have dug out in my 
archives a quite interesting Moon-Venus Lunar. This example is interesting 
both because it was a daylight Lunar with Venus rather close from the Sun 
being difficult to visually acquire in the (preset) sextant, and also 
because the difference between Venus apparent center and apparent center of 
light (phase effect) exceeded 0.3', not to mention that on this late 
afternoon (Sun close to the horizon) the Moon declination had a rather high 
unusual South value (S 28°16'9).

*******

1 - Here are the data of this Venus Lunar :

Date : 26 Jul 2007,
UT and GPS position at instant of Lunar Distance observation: 19h43m53s3 
and N4732.8W00517.6
Height of Eye: 5.20 m (17 ft), Temperature 21°C (69.8°F), Pressure 1018.2 
mb (30.07 In Hg)
Observed Sextant distance between Venus center of light and the Moon near 
limb:  110°54'4 (corrected for Sextant Error)

*******

2 - With a DeltaT Value of 65.7 seconds of time, and with the following 
corrections from Center of Planet to Center of illuminated planet (phase 
effect):

RA correction = -0'300 and Declination correction = +0'155

my computed Lunar Distance error was 0.0' (lucky day!)

NOTE: the "phase effect" correction values given hereabove are computed 
through assuming that the "planet center of light" is the "mid-point of its 
illuminated disk as seen from the Earth" . This computation method seems a 
customary and well accepted one (See Jean Meeus's "ASTRONOMICAL ALGORITMS", 
Chapter 40 "Illuminated Fraction of the Disk and Magnitude of a Planet")

*******

3 - In order to understand how Frank's Computer currently deals with this 
phase effect, I just tossed the numbers given in 1 hereabove into Frank's 
computer and I got the unexpected following results:

---   Error in Lunar : 0'2 , Approximate Error in Longitude : 0° 05'1  ---

Why is this result an unexpected one for me? Simply because almost 100% of 
the time - at least for Stars - I compute Lunar results just the same as 
the ones derived by Frank's Computer. In other words, I almost always get 
the following comments from Frank's On-Line Computer, at least for Stars :

 --- Error in Lunar 0°00'0 ---


*******

4 - Luckily enough, on the same day and from the same position, Antares - 
although not visible at all then - was above the horizon. So I just 
computed a (fictitious) Moon-Antares Lunar distance (i.e. Sextant Distance 
with no instrumental error). For the exact same conditions as in 1 
hereabove, I got a distance of 14°33'7

When processing all these Moon-Antares Lunar numbers through Frank's 
computer, I am getting the Following result :

---   Error in Lunar : 0'0 , Approximate Error in Longitude : 0° 00'0  ---

As expected, this result is in general agreement with the ones I get by 
comparison to Frank's results.

*******

5 - I then decided to investigate this case a bit further through asking 
myself :

What would have been the Observed Moon-Venus Lunar distance, had it been 
possible to observe Venus geometrical center instead of its light center?

I can easily compute such case by simply removing the phase effect 
corrections indicated in 2 hereabove. As a result, I get a "modified" 
Moon-Venus Lunar Sextant distance equal to 110°54'0

When I reprocess this "modified" distance in Frank's Computer, I get the 
following result :

---  Error in Lunar : -0'2 , Approximate Error in Longitude : 0° 07'1

*******

6 - Before going any further, I decided to check that the significant 
differences between our results can NOT be attributed to significant error 
in my apparent coordinates computation.

I therefore crosscheck my computed data against INPOP08 
(http://www.imcce.fr/fr/ephemerides/formulaire/form_ephepos.php)

For Delta-T=0, at TT=19h43m53s3, I am computing the following values:

Moon  RA=17h34m28s90 , Dec=-28°16'51"57 , HP=55'802 , and
Venus RA=10h14m06s34 , Dec=+ 6°54'54"15 , Dist=0.356303 UA

While the INPOP08 results for the same conditions are as follows:

Moon  RA=17h34m28s95 , Dec=-28°16'51"23 , HP=55'798 , and
Venus RA=10h14m06s05 , Dec=+ 6°54'55"85 , Dist=0.356325 UA

So I can rule out any error in the coordinates I am using. They all comply 
to my own 0.1' accuracy criteria.

*******

7 - AS A RECAP

7.1 - I simply wanted to check how your on-line computer, Frank, deals with 
the Planets phase effect.

7.2 - In 1, 2 and 3 hereabove I compared computations of a same Moon-Venus 
Lunar in which the Venus phase effect is quite significant.

7.3 - From earlier posts, since you Frank compute apparent coordinates with 
an accuracy (much) better than 6", it was necessary for me to rule out any 
significant error in the accuracy of the Apparent Coordinates I am using. 
This check has been addressed in 6 here-above and to a lesser extent in 4 
here-above where we get exactly the same results for a (fictitious) 
Moon-Antares Lunar. Check is fully OK.

*******

8 - CONCLUSION

And finally, by 3 and 5 hereabove I have come to and I am submitting the 
conclusion that the phase effect you are computing in your on-line computer 
seems to fall halfway between "no phase effect at all" and "phase effect 
equal to mid-point of the illuminated planet limb" as earlier referenced.

Last note to Frank (not quite off topic) : thank you for having (lately ?) 
introduced the ability to use your On-Line Computer with FULL DECIMAL 
VALUES for time and distances.

*******

Please, be so kind, Frank, as to comment on the analysis I have made 
here-above and as to confirm to our community how and to which extent your 
on-line computer deals with the planet phase effects.

Best Regards to you all

Kermit

Antoine M. "Kermit" Couëtte

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