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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: DSLR Venus Lunar
From: George Huxtable
Date: 2010 Sep 18, 09:03 +0100
From: George Huxtable
Date: 2010 Sep 18, 09:03 +0100
Antoine has raised the question, though as I see it a somewhat trivial question, as to how much the unresolved image of a planet should be displaced, depending on its phase,.Trivial, that is, in terms of the numerical amount of the discrepancy, though in-principle it may well be of some interest. And, as Antoine suggests, a bit of fun can be got out of such hair-splitting. This question mainly applies to observations of Venus, the only navigational planet to go through the complete range of Moon-like phases. The others are all seen full-on, or rather nearly so. So I've been tempted into integrating up the shape of a planet's "crescent" (hollow or gibbous), assuming constant brightness, to see how far the centre of gravity (barycentre) of that light-patch is displaced from the planet's true centre. This makes the assumption, which may or may not be justified, that the eye would position the centre of such a blurred image at or near that barycentre. If we follow Meeus in using k as the illuminated fraction of the planet's disc, and use r for the angular radius of the planet. Then the lit patch can be defined as the area intercepted between a semicircle of radius r and one half or other of an ellipse, of major axis 2 r (shared with the base of the semicircle) and minor axis 2 r (1 ~ 2 k ). When k = 0.5, a half-lit planet, this ellipse degenerates to a straight line bisecting the planet, as expected. Antoine has named P to be the mid-point, on the bisector of the crescent, between the two edges of the lit area. That implies, to me, that P is displaced from the planet's centre by r ( 1 - k ), and Antoine appears to agree.. And he has, somewhat arbitrarily, defined another point M at half that radius, at r ( 1 - k ) * 0.5 He has had difficulty in choosing which of those values to use to represent the offset as visually observed, but inclined towards P. I have argued that P is implausible, because of the curved shape of such a crescent, and a somewhat smaller displacement should be chosen, taking account of the barycentre of the light patch, but have until now stopped short of predicting how much smaller it should be. Antoine, in his latest post, has invited me to agree to an "ideal point", midway between M and P, so at r ( 1 - k ) * 0.75 . However I think we can make a choice on a more logical basis. With a bit of integration, I now find that the answer is rather a simple one. I make the displacement of that light-barycentre from the planet's centre to be r ( 1 - k ) * 8 / 3pi , which works out to be r ( 1 - k ) * 0.85 . However, my maths is notoriously fallible, so it would be nice if someone else were to check it. If I've got it right, then Antoine's choice of P is the better guess of the two, but he could do better still by inserting that factor of 0.85. But the difference is only going to be a very few arc-seconds, and in practice it hardly matters, either way. =================== What was discussed above was "point 2" in Antoine's previous post. We now appear to agree about his point 1, that Meeus didn't treat this matter anywhere in his Astronomical Algorithms. The only quote that Antoine could find was this- " The position angle of the mid-point of the illuminated limb of a planet can be calculated in the same way as for the Moon - see Chapter 51 ". In my 2nd edition, that cross-reference is to chapter now-numbered 48, and it's clear from that chapter that the position angle discussed there is quite a different angle altogether, and has no relevance to the displacement from the true centre of the illuminated patch. So we can now eliminate Meeus from this enquiry. George contact George Huxtable at george{at}hux.me.uk , 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: Friday, September 17, 2010 4:28 PM Subject: [NavList] Re: DSLR Venus Lunar In further reply to [NavList 13884] Re: DSLR Venus Lunar 16 Sep 2010 18:29 from From: george---me.uk Sep 17, 2010 Dear George, In an attempt to "get right" rather than "get nearly-right" (I'm using your own terms here)the offset value computation (both its orientation and its magnitude) between : - the planet geometric center, and - the visual center of gravity of the light of its illuminated center I will answer your queries in the following 2 areas which you have covered lately: PART 1 - request for any quotation by Jean Meeus about "Point P", and PART 2 - a more careful review of the computations carried out by the NAUTICAL ALMANAC. It shows that the NAUTICAL ALAMANAC seems to use (or at least did use some 30 years ago) an offset point quite close from "Point P" (and certainly closer from "Point P" than from "Point M") as a figure for computing the Venus phase effect (angular value between its geometric and illuminated centers). ******* PART ONE QUOTE FROM YOUR POST [NavList #13881]: 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. UNQUOTE and QUOTE FROM YOUR POST [NavList #13884] " I can find no mention, in chapter 41 of my edition of Meeus, to the point on the axis of symmetry that bisects the two edges of the lit region, corresponsing to Antoines "point P". I think it must have been dropped. Perhaps Antoine will quote Meeus' very words on that matter. " UNQUOTE I WILL OFFER THE FOLLOWING REPLY : In any of the following books by Meeus (ASTRONOMICAL FORMULAE FOR CALCULATORS, ASTRONOMICAL ALGORITHMS, PLANETARY PROGRAMS AND TABLES) which I have, the only "possible" explicit reference ( "possible" because it could be interpreted differently ) to "Point P" - as I earlier defined it - shows at the bottom of page 267 of my copy of ASTRONOMICAL ALGORITHMS : " The position angle of the mid-point of the illuminated limb of a planet can be calculated in the same way as for the Moon - see Chapter 51 ". I must confess that, until now, I have not been able to retrieve in any of my Books by Jean Meeus : - nither any other explicit reference to "Point P", - or any endorsement by Jean Meuus that such "Point P" should or even could be used as an offset point to compute the phase effect for navigation purposes. ******* HOWEVER, There is an obvious and direct relationship between such "Point P" and the "illuminated fraction k of the disk of a planet", which is abundantly covered by Jean Meeus in the quoted chapter. As I am too lazy to either do again these calculations performed almost 30 years ago, or even to dig them out as they are buried deep somewhere into my archives, and to the best of my recollection the relationship between "Point P" and "k" is a most simple one : If we call "p" the ratio of the distance between the Planet center and "Point P" divided by the Planet semi-diameter, then : p = 1 - k, just this simple ! For a 100% illumination, k=1, and p=0, which means P is exactly in the center of the apparent disk, and For a 50% illumination when the planet looks like a "half Moon", P is halfway between the center and its circular edge rim, k=0.5 and p=0.5 and For a 0% illumination, P is exactly on the planet circular edge with k=0 and p=1. It is very possible that, so many years after I first carried out and shortly therafter buried these computations, the memories left in my mind were that Jean Meeus did pay attention to "Point P", while he only kept paying a close attention to "k". It is also possible that somewhere in some other reference book (I own a few of them) "Point P" is described as an adequate way to compute the planets phase effect. I have not been able to find such reference, which is probably not essential since, at least some time ago, the NAUTICAL ALMANAC did use a point quite close from "Point P" to compute the phase effect. ******* PART TWO QUOTE FROM YOUR POST [NavList #13884] To me, taking that point to be the apparent centre-of-light seems implausible. If the distribution of light was a uniform lit rectangle, on that axis, between those limits, it would then be expected to show a centre-of light at point P. Is Antoine asking us to believe that it makes no difference at all, to the apparent centre, if the tapered ends of that light distribution are bent around in a pair of curved horns? I don't accept that. In my view, the centre of gravity of the lit crescent is a much more plausinle model. Not that it matters much, in practice, the difference being no more than a few arc-seconds. But we might as well get it right, as get it nearly-right. UNQUOTE I will here show that the HMSO and US NAUTICAL ALMANAC did use at some time / still keep using (?) a point very close from "Point P" to account for the Planets phase effects. Just back to the example I quoted in a recent post. FROM THE ASTRONOMICAL ALMANACH FOR THE YEAR 1982 EXPLANATION SECTION bottom of page 259 QUOTE The additionnal corrections for Venus and Mars allow parallax and phase, and are given by " p cos H - k cos theta", where H is the altitude, theta the angle at the planet between the vertical nad the Sun: p and k are, for Venus, for 1982: from Jan.1 until Feb. 10 p = 0'5 and k=0'4 UNQUOTE For the date of 15 Jan 1982,00h00m00.0s TT, we get the following apparent data about Venus as follows: Right Ascension = 20h34m42s1 , Declination = S-14°10'24", Distance from Earth = 0.28238, Horizontal Parallax = 0'52, semi-diameter = 0'51, angular distance between Planet Center and "Point P" = 0'50 A quick study of the NA "correction formula" hereabove shows that that term "p cos H" is the well known term for correcting for parallax. Accordingly the term " k cos theta" computes the phase effect Correction (from "observed" into "true" to be performed AWAY from the SUN). And the tabular The amplitude of this phase correction (0'4) for this period of time makes it quite close from "Point P" (0'5). CONCLUSION AND SUGGESTION : We have certainly attempted our best to get things "right" rather than "nearly-right" by splitting hair just as we did, no ? I can and will take the blame for that ! However it is fun ! HOW ABOUT SETTLING FOR AN "IDEAL POINT" HALFWAY BETWEEN "POINT M" AND "POINT P" ? Frank !!! Are u here ??? Best Regards to you all Kermit Antoine M. "Kermit" Couëtte ---------------------------------------------------------------- NavList message boards and member settings: www.fer3.com/NavList Members may optionally receive posts by email. To cancel email delivery, send a message to NoMail[at]fer3.com ----------------------------------------------------------------