Equixenths, Periyelms, etc.

From: Alex Ferguson <abf_at_interzone.ucc.ie>
Date: Mon, 30 Jun 1997 21:28:30 +0100 (BST)


Stephen Martin says, of his not-quite-quarter days:
> Let me clarify -- The distance between Spring and Autumnal Equinoxes is
> 135 days on the summer "side" and 159 days on the winter "side".

Ah, I see.

> Spring and Autumn would likely be the same length of time.

No, see below.

> >Not sure I follow. You've just proposed that Summer and Spring
> >are each almost two weeks shorter than Autumn and Winter;

> I proposed nothing about Spring -- I proposed something about Summer.

I assumed by Summer you meant from summer "solstice" to autumnal equinox, and that spring would be from vernal equinox to summer "solstice". After all, you'd just asserted what the quarter days were, and that is the usual definition. Certainly none other was in evidence. Given these, the seasons are of the following lengths:

Spring: 67
Summer: 68
Autumn: 79
Winter: 80

So with a half-day tweak, that is, putting the equinoxes at midnight and mid-{summer|winter} at noon, or vice versa, or something to that effect, then S/S and A/W each come out to be respectively equal. This may even make sense, though I'll have to go think about it some more.

(Note this doesn't work as the DH seasonal calendar, though if we selectively ignore Greg, maybe it'd fly as the pre-Nysalor DH year... Or failing which, as a Darkness thing from Yuthuppa.)

> > this doesn't tally at all with the 1.6 degree difference between
> > northward and southward tilt you propose later. A proportionate
> > difference would be a couple a days [...]

> And how can the appropriate difference be a couple of days?

A _proportionate_ difference would be 294 * 1.6/360. ~= 1.3 days. Which has no necessary correspondance to anything much either, mind you. After all, almost all of earth has such a "tilt", and still experiences equal Quarters.

> 10.6 / 9 = 1 1/6,
> so the difference in lengths between equinoxes should be the same

Now I see where you're coming from. The next question is, even given this ratio, how do you arrive at the absolute numbers? The only pertinent fact I can think of is that Polaris is always within the Upper Circle, which means the maximum swing would be about 15 degrees, if the diagram on GRoY p80 is "to scale".

> That's how I figured the dates, anyways, if my math is faulty
> please let a mathemetician or astronomer let me know.

I'm enough of a mathematician to tell you that 159/135 = 1.1777777..., not 1 1/6 ( = 1.1666666...), and enough of an astronomer to have a hard time seeing how much of a (feasible) correspondance between "real" celestial mechanics and Gloranthan ones there ought to be (not least as establishing any observable facts is extremely slippery). Let me at least try to determine what assumptions your calculation is based on. I'm surmising:

	o  That at the equinoxes, the sunpath is directly overhead
	   (as if one was at earth's equator);

	o  Each successive day varies in length from the preceeding
	   by an equal amount (not true of earth at all).
	   (2m7s (and a bit), trivia fans.)

How did I do?

[ES quote]
> Clearly, the Dome rocks north of center, then back, then south, then
> back.

In at least one place in _each_ of ES and GRoY, it gives at least as unequivocably that the midsummer sun passes directly overhead, so I don't know why you think this is so "clear". (Unless Greg has made another "clarification" of this, apparently contradicting his previous one. To be fair to FGS, I don't know what he's said about this at any stage, just the different assumptions made by his various Chief Priests.)

> No, the Dome rocks both north and south, though Nick's Starmaps program
> has it go to center at midsummer. This was an attempt, if I remember
> correctly, to justify having both summer and winter stars, impossible
> given the Elder Secrets model.

I'm not quite sure what you mean by the ES model, given all the acknowleged inconsistencies therein. But I see what you mean about the summer stars; are there any significant such, though? I'll be sure to pore over the ES and GRoY lists later. (I know they're alluded to collectively, I mean particular instances.)

> [Steve needs] a second major dome, one which tilts but does not
> rotate. With this Dome in place, the dome again tilts both north and
> south of the center.

I'm all confused again... When you say "a second major dome", are you speaking of Buserian-style "horizon/underworld" lines on the "frame" (or on the sky itself), or are you talking about some sort of "Crystal Dome" required to account for the celestial mechanics of it all? (As in, a crystal sphere with most of the bottom sawed off.) I can see the need for the first, though not the second -- surely we're just talking about a single Dome, with two components of motion? Multiple crystal domes might make a suitably wacky Western theory, though... (and would explain a south-only tilt too).

> As for the relationship between the position of the Sunpath and the
> length of day, as I said in my post there is none directly, since the
> distance the Sun travels is identical regardless of how far north or
> south the Sunpath is.

Indeed so. This also raises the question of whether the sun has the same apparent speed across the sky all day, or if speeds up near the zenith in winter, and slows down in summer. (That almost made sense for a moment, though it made my head hurt thinking about it.)

> But, for esthetic reasons, days should be longer in summer and
> shorter in winter, and having them correspond to the amount of
> tilt gives what I feel to be acceptable durations.

Perhaps I have too much of a high-latitude aesthetic, but I'd have found greater variability to be more intuitive. Though, while Dara Happa's a pretty "high latitude" place, I don't know if the length of the days and nights are a pan-Gloranthan phenomenon. I suppose they ought to be, if the sun rising and setting dead east and west everywhere is (not Greg made his mind up about that).

Slainte,
Alex.


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