You didn't? Hrm. I've been banging on about this stuff what seems like years (because it is, in fact, years...); perhaps this is symptomatic of communication on this subject.
> I favor a longer period for [the Southpath] than does Greg at this time.
Good for you, and bad for Greg, then! I suggest a "wheels within wheels" sort of approach: a gross variation, with a relatively short period, and fairly regular, evident motion; and a smaller, longer-period less easily predictable component "superimposed" on it. The sorts of contortions used by builders of mediaeval orreries, (wheels quite literally built on other wheels) or come to that, the number of terms in modern approximations to the equations of motion of the moon, both come to mind.
This sort of approach has several advantages: it's "realistic"; it means we get several cycles for the price of one, and we can try and get Mythological Mileage out of each of them; and it allows a culture to think it's sussed out the system, only to find in 100, or 1000, or 10,000 years' time that you have to censure/fire/execute your chief priest (again).
Better yet, rather than merely having the Dodging Gate and Eastern Mouth supply the variability, inject some periodicity/irregularity into the course each of the Southpath bodies follow between them. They needn't follow either great circles or "vertical" arcs, surely, they could exhibit "side-to-side" motion, changes in speed, retrograde motion...
> Although this is NOT because of the tilt of the Dome north and
> south, day length varies in exact proportion to the tilt.
It does? I thought you had zero tilt at the equinoxes, and the shortest day at the largest tilt? (If this has changed, insert loud cheers.)
> At this point, I favor a sinusoidal model (is that the right term?),
> rather than a fixed change one, to allow day length to change faster
> at the equinoxes* than at the solstices*.
Yay! And yes, it is the right term. ;-) If you wish any help or input on calculating same, Steve, drop me a line with the relevant parameters, and I'll see what I can do... (I can appreciate that if so much as a cos*ne were to appear on the Digest, some people might get nasty high school maths flashbacks, so I'll be merciful for the time being.)
> Unless things change, on the Summer Solstice* day length is 14 hours 24
> minutes (Theyalan reckoning), with a night length of 9 hours 36 minutes.
This is a pretty arbitrary choice, though, IIRC what you said previously on the subject, _and_ is based on the fixed change-of-day-length, isn't it? This also seems a rather modest difference, from the PoV of "high-latitude" places, like Scotland and Dara Happa.
> At midwinter*, night length is longer than day length at midsummer,
> because of the greater tilt of the Dome.
This doesn't really follow, though. What determines day-length is basically just the speed Yelm travels at, when he's above the horizon, as the "distance" he has to travel is always the same. Unless he's lower (in altitude, as well as just angle) in the sky in Winter, which is a thought.
Mythologically, I think a "speed change", either continuous, or one-off at the horizon would work, though. In the summer, Yelm would move most slowly in the Upper Sky, maximising his time there, and coming closest to the Imperial splendour of his Godtime masterly inactivity. Then he'd start to increase in speed as he "fell" to the horizon, continuing to increase his rate of progress as he travelled the underworld, only beginning to slow again after he'd left the Halls of the Dead.
In the winter, flip this picture around, with Yelm's onerous duties in Hell detaining him more and more, slowing him down there.
Personally, I still favour The Good Old Days, wherein Yelm and Lightfore majestically bestrode the zenith at Midsummer, recreating for one brief day the Perfect(ish!) Sky. Sorta. All this loses is a few pesky Summer Stars, which I never cared much for anyway. ;-) (They don't appear in the GRAY model, IIRC, and Elder Secrets contradicts itself and everything else so much as to be more trouble than it's worth, then it throws up problems like this, IMHO.)
A further problem with the "northern tilt" model is that it doesn't entirely fit with GRAY. It has _one_ of the pillars of the world, the southern one, being broken, causing a tilt in that direction. Don't we need to dispose of another pillar to get a swing going to the north, as well? (Too late at night to start looking up GRAY, pardon my paraphrasing.)
Besides, we can always get the Summer Stars back as Jumpers, or planets, or a constellation of "planetoids" on a separate crystal sphere, rather than having to break the actual Sky Dome itself into two semiindependently moving bits. Mind you, it's briefly amusing to imagine the Mostali gnashing their (mercury-filled) teeth: "How the Gr*wing Hell are we gonna fix _that_?!"
> my original calculations were off, and we have to redo them. This was
> only pointed out to me a week ago, I'm afraid.
Didn't I point out some problems/objections with this about six months ago? Maybe discussion just petered out (nothing personal, Messrs Metcalfe, Michaels, et al!), as it's wont to do...
> Currently, the model I am working from assumes that the two equinoxes*
> (Freezeday, Disorder Week, Sea Season and Clayday, Fertility Week, Earth
> Season) have day and night of equal length. The problems with day and
> night length above may force this to change, however.
I'm a tad confused. Why not change the day length thing to suit the equinoxes, rather than vice versa? Despite my squeamishness about the "big and small quarters", and moreso about the dreaded bidirectional tilt, having in particular the autumnal equinox at a Cool Date was the redeeming feature of this model. Losing that, and still having the other aspects would highly sub-optimal, in my view. Admittedly, there may be other Cool Dates in Earth Season, particularly from the viewpoint of the assorted Pelorian earth cults.
Isn't this model still buggy when it comes to getting four seasons plus a Sacred Time, though? If DHn Sacred Time were to occur at midwinter, this wouldn't be such a problem, though (mutter, mutter).
> * Please note that use of the words "equinox" and "solstice" is not
> following strict RW terminology, but is used for convenience.
Your use of midsummer, midwinter, and equinox makes etymological sense, the only problem is with solstice. ("When the sun is still.") Two terms which we may be able to swipe from astronomy are aphelion and perihelion. (These don't correspond to the solstices on earth, but they could do on Glorantha -- though which is which could be argued either way.) Having the "equinoxes" other than at the Quarter Days is a mite confusing, admittedly, but not fatally "wrong".
Stuff on the "Gloranthan Zodiac" farmed off into separate message.
> [the Twin Stars] had no visible
> cyclic nature until the coming of the Red Goddess. At the moment they
> were illuminated**, they began to exhibit a cyclic nature
That seems a bit literalistic to me. Becoming Illuminated isn't simply a matter of being shoved into a Standard Lunar Cycle; it's about coming to understand and transcend one's _own_ cyclic (and otherwise) nature.
> An area of exploration for you -- even a flat world will have parallex
> effects if the stars are close enough.
The flatness of the world is in fact not really relevant to the question of whether one gets observable parallax from different locations on Glorantha; that's why I was careful to distinguish between "latitude" and "parallax" type effects.
Why would one ever get "latitude" effects on a world with no latitude? Well, if the "bendy light" theory is correct, then presumably it reproduces _all_ the visual phenomena of living on a curved surface, not just an apparent horizon. That would imply the Sky Dome appearing differently in different places. (By definition, "correctly" in Yuthuppa, and "wrong" everywhere else.)
(On earth, of course, there's the further issue of stellar parallax, measured over _time_, rather than terrestrial distance, but I'm not going to touch that one...)
> The current working model has the
> Sky Dome approximately 20,000 km in radius (though admittedly one is far,
> far into the God Plane at this point, it is used to determine certain
> potential physical correspondences -- I gotta start somewhere).
I dunno about 20,000 km being necessarily "far, far into the Godplane", though I see what you're getting at: it's a lot bigger than the Mundane World. Even so, you'd get humungous parallax effects with numbers like this. (Yes, use of scientific terms such as "humungous" means that I haven't worked it out yet.) Does this "apparent distance" hold for both the Yelm, and all the planets? I presume the Red Moon appears as if it's closer yet...
> An example of why this might be important is that it affects the
> constellation in which a given planet (such as Lightfore) is seen to be
> in at a certain time.
It doesn't, not if the planet and the Sky Dome are equally distant, which is what I take you to be saying. If the RM is closer, then which objects it occludes would vary, though.
> The degree of axial tilt appears to not change over time
It'd make sense to me if it were to change. After all, it used to be zero, and now it's not! [1] If it were still changing, say on the order of a tenth of a degree to a degree per Age, that wouldn't seem too shocking. Well, other than to the Buseri than failed to figure it into their Hero Wars predictions...
> and I don't know what orbital transit is, nor do I see how
> eccentricity of orbit could affect things here.
Obviously as Glorantha isn't a planet, the "orbital" notions have no direct equivalents. But that doesn't mean we can't merrily fake the same, or vaguely similar effects... Basically what I suggest it would come down to is an excuse/precedent to add additional components to the motion of the Sky Dome, or to the Southpath planets, or perhaps even (heresy alert!) the Sunpath planets (other than Y&LF).
> Elder Secrets says that Pole Star has a yearly wobble, which implies to
> me that he does not just move due north and south, and I am investigating
> just how far to the east or west we can move him
The phrase used in ES suggests to me the reverse, if anything. Though again, I wouldn't take ES's word for much.
> I favor ten years for Dara Happan reasons, but it could be longer.
This seems quite an important one, as it affects the whole Dome. Perhaps a "major wobble" with a period of _approximately_ 10 years, a secondary component which used to be 47 years, and is now about 54 or so (raising the interesting question of what's the period of the variation of the variation!). Or vice versa. Or some other attributions of such periods to different aspects of planetary/stellar movements.
> >More serious "lacks" in the Sky are non-integral periods for different
> >heavenly objects (and worse, ones that don't have pretty trivial lcm's,
> >for the most part),
> Yes, this is a serious lack, and one which we unfotunately are stuck
> with.
Well, only if Greg continues to stick it to us! ;-) If it were "discovered" that (say) the period of UlEria wasn't _precisely_ 8hrs, but actually 8.000001 hrs, then would anything be lost or mucked around with? If things of this ilk were ordained, then we'd get saronic/ great year type effects essentially for free. (Yay!) You may object that this "contradicts" ES, but if everything in 3rd ed. publications were correct to 5 decimal places, I for one would be more than content -- or more content than I am, at least!
> But this makes sense when you consider that the Gloranthans _know_
> the sky was perfect once, created by the Gods to be perfect, which is not
> necessarily the case on earth -- did any ancient peoples wish that the
> planets were more regular, or wonder how they got screwed up?
Not sure about this, but it wouldn't surprise me if they did, as it would fit the "Golden Age" myth pattern perfectly. I must browse Fraser... Certainly there are "first night" stories, and about how the moon first rose. But even if this isn't true in myth, it's true in history! Lots of people of earth thought that the sky _was_ more regular, only realising it wasn't when their calendar got screwed up. Witness the Egyptians and the Romans, for two. Those wacky English, quaint chaps that they are, actually staged a riot about some of the eventual fallout from this, in what my faulty memory says may have been as late as the 17th century. "Give us back our 11 days!" "Take it up with the laws of planetary motion, berk!"
> Well, with the Southpath we do get varying rising and setting points, at
> least for three of the planets (well, for 2 1/2 of them anyways).
Yes, but only for 2 1/2 of them, and the model for this you proposed was rather mysteriously unmysterious. (If the Sunpath planets varied just a _tad_, this would help, too.)
> As far as I can tell, we only get retrograde motion in Lost Rocks
Is there any reason why some of the planets could/should not exhibit retrograde motion? Is this a matter of Greggly Fact, or just inherent in the Working Model? Again, I don't see what problems this would cause, and it would give more variability, at no (Gloranthan) "cost" that's evident to me. Note that if Glorantha were similar to earth in this respect, _all_ the Southpath and Sunpath planets (apart from LF, presumably) would show retrograde motion, to some degree or other. I'll settle for a couple of them. ;-)
> Additionally, given that the Blue Moon _is_ a moon, I would expect that
> the apparently variable 2-7 day period of the Blue Moon actual follows a
> somewhat complicated cycle
This may very well be, but conversely, it may be the body the DHns are least likely to be able to predict with any success. Could be used in a sort of post hoc, ergo propter hoc sort of celestiomancy, though. (See "comets".) ;-)
> Note that the current model has the Blue Moon (invisible, of course)
> always rising in the east at the exact moment that a certain star of the
> constellation Lorian is due east -- Annilla rising upon the Blue Dragon.
I don't pretend that I can calculate all the consequences of this in my head, but this would appear to give at most annual variation in Her Streakiness. Again, that seems very limited, compared to her anecdotally alleged unpredictability. There's a hazard in making her cycle either too tied to other visible phenomena -- someone would notice by observation -- or too prone to repeating over time, whereupon someone would twig, from records previously kept.
> Another possible source of importance to Gloranthan star seers is the
> length of time before Dawn and after Dusk in which light is visible.
Again this would presumably come to how fast Yelm's chariot is galloping, in this case through the underworld. And also on whether he moves at an "angle" through Hell, extrapolating from his path from the sky.
This would pretty much by definition only be annually variable, though.
> It is worth pointing out that I believe some of the more conservative
> Buseri perform all of their calculations as if the lengths of day and
> night were equal every day (an idea which I believe also originated with
> Nick); they might ignore certain other variations in the sky as well, to
Yes, I agree with this entirely. For the most part, I picture them clinging desperately to old facts (or old models which may never actually have been quite correct), only changing when they absolutely have to. (E.g., Moonson orders a purge against those that just predicted a bumper crop of wheat, to be harvested in mid-Winter, in a province with Pentans currently all over it...)
_Probably_ most of the priests who think that Yelm is stationary have been at least pensioned off by now. But ya never know...
> Given that Pole Star may have a slight wobble, it is possible to have
> Lightfore and the Sun always follow a "perfect" Sunpath (through where
> Pole Star is supposed to be), while the Sunpath planets travel a path
> through Pole Star, wherever he is.
That's true, but I was thinking of somewhat greater variation than that. (Greater variation, not necessarily greater amplitude.) Such as over a number of years having the Sunpath planets deviate somewhat _from the Sunpath_ (perhaps oxymoronicly, but it makes sense to me). One could still have certain fixed points in their wanderings, mostly obviously the eastern horizon, the zenith (or Pole Star, indeed), and/or the Western horizon, if these points are critical.
I do favour a further "Pole Star Wobble" too, though. I was thinking of this as being a much longer term effect, though: say 50-500 years...
> Crystal Sphere if you follow a Greek model of the Heavens (which I do),
Crystal Spheres I like, it's the extra semi-solid ones that make me bilious. ;-)
Slainte,
Alex.
- --
[1] Or so the Received Wisdom goes. Some Informed Sources even within
Dara Happa don't believe it, though, according to a Greg Leak. I shall only
drop annoying hints, as this is supposed to be a Secret -- it was only
a _small_ barful of people he told. ;-)
End of The Glorantha Digest V5 #426
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