NavList:

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
----------------------------------------------------------------