Expert: Philip Stahl - 5/10/2005

Question
Okay, first thanks for the second part -- while this may not clarify the mud exactly, at least the obscuring mud is now much better organized and understandable... -- or to put it another way, it may not exactly have answered the question, but it made that lack of answer make a great deal of sense.  (Somewhere I read that the Celts? or someone refered to the dipper as "The Wain,"  that is the wagon...  Looks a lot more like that than a bear to me too!)

Back to the first question -- I think we're getting lost in semantics here, so I will try to be more precise.  I know there is a precise time the moon is given as full and new (in GMT so we don't get hung up time zones and daylight savings, etc.) -- this is what is listed on calendars and almanacs.  However looking at the moon, it appears "whole" or "round" for more than one night.  What I am trying to confirm is that it is roughly 3 days (nights) from when the last bit of the earth's shadow disappears from the part in view at the end of the waxing phase to when the first bit of shadow again appears during the waning phase.  (I'm thinking of the average viewer without binoculars or etc. standing out at evening or night looking at the moon.)  Likewise there is an interval from when the last bit of visible waning moon cresent disappears to when the first visible waxing moon cresent appears.  Somewhere I ran into a reference than various ancient mythologies have a common thread of a god/goddess or hero descending to the underworld for three days and then re-emerging and that this is thought to be related to the the period of moon dark.  (We're taking some really old mythologies here -- Tigris/Euphrates cradle of civilization stuff, but I think it is supposed to be common to a lot of different unrelated cultures, but this is something I heard in passing years ago so don't hold me to it, okay?  The only two I'm can truly identify are (obviously) the comparitively recent Christian harrowing of Hell, and Ianna or Ishtar rescueing Damuzi from Erishkigal, though Persephone may fit in here somehow also...)   Back to the question -- do you have a specific time interval you can give me as well as a rough approximation?

Thanks!
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Followup To
Question -
Does the moon really appear full for 3 days and dark for three days between the last cresent and the new moon cresent?  

Does Venus really trace a star shape against the sky over a number of years?  (This comes from "The Da Vinci Code" were the author states that this is why the pentagram was associated with the Mother/Fertility Goddess who was under various names (Ishtar, Astarte, Aphrodite, and eventually Venus) associated with the planet.  I want to know if this is based on fact...)


Thank you!

-- Barb McCormack
Answer -
Hello.

Technically speaking, the Moon can only be "full" at a precise astronomical moment - defined by being in exact opposition to the Sun. That is, the full Moon must be *rising* at the same instant the Sun (on the same date) is *setting*. Since this can only apply to one time and one time only- then it cannot apply beyond that.

Very often, however, popular texts more or less "fudge" and describe an entire *interval* in the lunar cycle (say 3 days, as you noted) as being associated with the phase. While this may be ok in a rough sense, and for a popular presentation, it is not - as I noted- strictly true.

And no astronomer I know would ever make such association.

Re: Venus, to the best of my knowledge no 'star' shape has been traced by it over any number of years. However, it may - if its projected path is displayed say on an appropriate computer program - appear to behave (or appear) in any number of ways to a given observer.

My point is that any and all such projections in the end amount to no more than *subjective*  descriptions - somewhat analogous to the constellations in the night sky. (E.g. no actual or absolute pattern conforming to any 'Big Dipper' exists, only as it appears to a certain sub-group of people. Indeed, the ancient Chinese saw no 'dipper' at all - but rather a cart to carry their bureaucrats!)

You can think of any or all of these as a kind of cosmic 'Rorschach' - the sort of inky blot that psychologists used to show to their patients to see if they "perceived" any evident patterns. The blots were such that no two people were likely to see the exact same pattern, since each person came to the observation with a different background, perceptual selection bias and so forth.

And so also it is with the star patterns in the night sky, or the projected planet paths - seen over time. In the end, humans just have a penchant - in their brains - to see "faces" in clouds, or figures, implements in the stars- and project their own meaning and patterns onto them.

This has nothing to do with any objective findings or facts that reside in the objects themselves. Which is to say that it's no more likely Venus ever actually traced out a 'star' (or pentagram) in its planetary history than that an actual 'Big Dipper' exists in the night sky- such that every human would concur that pattern obtains.

Answer
Hello again,

Though the Moon may well “look” full for more than one night, the fact is that it isn't technically full. The technical assessment is based on the calculation of phase from:

P =  ˝(1 – cos n)

where n =  360 (A/S)

where A denotes the age (in days) of the Moon at a given observation date. And S denotes the Moon's synodic period(29.53059 days)

In effect, one can obtain a very excellent measure of when full Moon occurs based on the elongation angle, n of the Moon (with respect to Earth and Sun). Thus, an angle of exactly n = 180 degrees denotes the specific condition of opposition, and time of full Moon. (Which will coincide to the time of the *setting* Sun on that date)

Using the preceding equation, one finds that an age of 14.7652 days (two weeks and about 18 hours) yields 179.999 deg, so a time interval (from New) that conforms almost exactly to the full Moon.

But let's say the age of the Moon (past New) is 13 days.

This will surely "appear" nearly full, but on calculating one finds:

n = 158.48 degrees

Which is some 21.52 deg short of the precise full angle. Now, bear in mind here that - with respect to the Sun- the Moon moves *eastward* about 12 degrees per day. Thus, as the Earth rotates on its axis, the Moon appears to rise in the east, move across the sky, and set in the west. However, because of the daily eastward motion (on the celestial sphere) it appears to cross the meridian earlier by about 50 mins. each day. Meanwhile, this angular distance (12 deg per day) is not enough to cause the visual appearance of the phase to change appreciably.

So, here we have the core of the difference of where we are coming from, respectively. A purely visual assessment of phase (as you describe it) vs. a much more exact, angular assessment.  (Note that this angular measure has nothing at all to do with the choice of any kind of time, whether GMT, local standard or whatever).

Now, given only a visual basis of phase assessment, it is perfectly acceptable that one can estimate roughly 3 days (nights) from when the last bit of the earth's shadow disappears from the part in view at the end of the waxing phase to when the first bit of shadow again appears during the waning phase.

Once one veers into "specific time intervals" of course, the problems arise. Because then one finds different authors, etc. defining the relevant phases according to different angles n, and phases P.

Rather than get into all that, let's just use the rough (visual) basis for approximation, and leave it at ~ 3 days (nights).

Hope this helps.