NavList:

Sep 16, 2010

Dear George,

In reference to your post published in [NavList 13881] :

Excellent comments from you, once again and Thank You very much for them.

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The main point actually is : where exactly does the "center of gravity of a planet brightness" lie relatively to its center of geometric figure ?

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Let us call "POINT P" the mid-point between the terminator and the outer (circular) shape, on the symmetry axis of the apparent Planet. This point is
well defined in Jean Meeus's ASTRONOMICAL ALGORITHMS book. (I own book SN 026287 Copyright 1991 with handwritten "Errata as of Dec 1993", and apparently Chapter 40 of my copy bears the same title as Chapter 41 of your later and presumably "more perfect" 1998 edition).

Let us also call "POINT M" the point HALFWAY between the geometric center of the planet and "POINT P".

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UP UNTIL THE MID 1980's, I was using "POINT M" to modelize the effect of the Planetary phases. I had then performed the very same calculus integration which you just mentioned. Its result showed that the "barycenter of uniform brightness" is sufficiently close from "POINT M" in all configurations, so that I could safely use "POINT M" instead of this exact "barycenter of uniform light" without any appreciable error for my purposes and accuracy criteria (all systematic computation errors to stay below 6" on the final computed results).

Pending extra investigation on additionnal dates which I have just started to-day, I think that - on the ground of my Jul 26, 2007 example - Frank's On Line Computer currently uses a "phase offset point" very close from "POINT M" as defined here-above.

I am also noticing that "POINT M" is very close from the Point you are advocating in your last post: this is self explanatory because I performed the same "surface integration" as the one you just mentionned.

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HOWEVER, a close study of some published Research on planetary photometry data (somewhere in my many archives folders) convinced me to discard "POINT M" and to use "POINT P" instead.

To the best of my recollection, and in addition to pin-pointing the light itensity / brightness of every pixel as seen from a human eye - how they could do it then remains a mystery to me ... - such Research showed that the IRRADIATION EFFECT had the result of bringing the actual "light barycenter" away from the planet geometric center and that as a global result the actual "light barycenter" was very close from "POINT P", especially when seen from a small aperture optical device (Human eyes and/or Sextants are certainly good examples for such devices), a result which certainly challenges or at least questions the assertion that one [should] " assume uniform brightness of the illuminated fraction ".

Accordingly, in the past 25 YEARS I HAVE BEEN USING "POINT P" AS AN OFFSET POINT TO REPRESENT THE ACTUAL CENTER OF BRIGHTNESS OF A PLANET.

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IMPORTANT NOTE : The choice of "POINT P" by preference to "POINT M" also seems to be FULLY SUPPORTED by the Nautical Almanac.

As an example, in the HMSO & US NAUTICAL ALMANAC for the YEAR 1982 on page 259 (EXPLANATION PART), the maximum Height correction for the phase of Venus is listed as 0'5 for the period Jan. 1 until Feb.10

For 1982 Jan 15, the apparent geocentric semi-diameter of Venus is 0'51, which certainly shows that the height correction recommended aims to correct for a visible "Light Gravity Center" which is "POINT P" and cannot be "POINT M".

AS CONCLUSIONS :

1 - Hypotetical Recent discoveries - unknown to me - might have brought the Planets "Light Gravity Center" away from "POINT P" (which I am using, and which was used then - and still is ? - by the Nautical Almanac some 30 years ago) and towards the vicinity of "POINT M" (which Frank's In Line Computer seems to be using).

Whoever has information about such Hypotetical Recent Discoveries (or precepts to use "POINT M" instead of "POINT P") I am currently unaware of, will be most welcome to share this information with our NavList Group.

If so, I will correct my own computations to make them more in line with current computing practice, I will have become more knowledgeable and I am thanking in advance whoever will shed additionnal light on this topic.

2 - Thank you again for your contribution here George. I am also looking forward to hear and read the viewpoint and feedback of Frank on this topic.

Best Regards to all

Antoine M. "Kermit" Couëtte

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