[TML] Alderson disk

[shadow at shadowgard.com]

On 10 Dec 2007 at 21:53, Jerry W Barrington wrote:

> On 12/10/07 3:49 PM, Stuart Frew wrote:
> 
> >> So . . . a fantasy world that really IS a "flat earth."  The Sun would
> >> always be about at dawn, right?  So would you call it Dawnworld?
> >> There'd be a permenantly Light and Dark side to everything, wouldn't
> >> there?  Wait one.  Shadow squares, like with Ringworld?
> >> 
> > I believe that the sun could (technically, if you ignore the physical
> > effects of motion on the sun) bob up and down through a hole in the
> > middle.
> > 
> > So the sun would always be on one side but it could rise and set.
> > 
> > How do the weather patterns form, is the disk spinning at all?
> 
> Rise & set, yes, but only by a few degrees above the horizon (for any
> reasonable "bob").  The outer side of mountains will be permanently
> shadowed.

That's barely a bob at all. I went for the somewhat extreme 1 AU 
above to 1 AU below. Which gives a max angle of 45 degrees at the 1 
AU latitude of the disk.
 
> And the form I've seen of this disk before required an inner wall, to keep
> the atmosphere from falling into the sun.  This would form another shadow
> zone, possibly wider than Earth.

Not really necessary as someone here pointed out. The gravity at the 
edge takes care of it nicely.

> Oh, if your "bob" is on the order of months, that'll give you seasons (keep
> the bob small enough not to get months of dark!).  :)

Since the bob is caused by the sun freefalling umnder the surface 
gravity of the disk, months is pretty much out of the question.

Days works fairly well though.

> On 12/10/07 3:49 PM, Leonard Erickson wrote:
> 
> >On 9 Dec 2007 at 20:46, Richard Aiken wrote:
> >> I'm thinking the disk would have to be spinning.  The original
> >> primordial mass would have been spinning.  Stopping that would have
> >> been a needless waste of energy.  Besides, the centripetal force of
> >> the spin would be part of what's keeping the disk from collapsing into
> >> the star.
> > 
> > Not even *close*. To do that, it'd have to be spinning faster enough
> > to counter the effective "sideways" field. Which would throw
> > everything on the surfaces towards the rim.
> 
> And don't forget, the disk spins as a unit.  At some speed, the outer rim
> approaches the speed that it would fling things off (sets upper limit for
> rotation speed, probably less than 1/yr for 10 AU disk).  The inner rim
> would be nowhere near orbital velocity.  Of course, the inner and outer edge
> gravity would modify this.

I worked it out, and at a 5 AU radius the "centrifugal force" for a 1 
year rotation is only a fraction of a g. A fairly small fraction as I 
recall.
 
> > I also need to work out how atmospheric absorption affects the light
> > at different times of day and how that affects atmospheric temp at
> > various "latitudes" (distances from the center)
> 
> When you calculate, remember that the outer reaches suffer from both 1/R^2
> *and* the sun always being at lower elevation.  If your 45 degree elevation
> is as seen from the inner edge, the outer edge will only see 5.7 degree
> elevation.  If it was from the 1 AU circle, that yields 63.4 & 11.3.

I was figuring for the 1 AU latitude.
 
> Hmm.  I just realized, if the gravity falls off slowly like you mentioned,
> the scale height will be much more.  Lot's taller column of air.  More
> diffusion of the light?

Gravity doesn't fall off more slowly. It doesn't fall off *at all* 
until you are well beyond any reasonable atmosphere.

Above an infinite "plane", the gravity has no decrement. For a huge 
but finite disk like this, you have to either be close to an edge of 
the disk or a couple AU or so above it if you are in the "middle 
latitudes.
 
Given that earth's gravity doesn't decrease appreciable from the 
surface to loew orbit, scale height isn't going to change.

> >> Personally, I'd say escape would be easiest from the rim.  Any pointers to
> >> the math on the gravity?
> > 
> > The gravity at the rim is *worse*, because you have *millions* of KM
> > of rock pulling at you...
> 
> True, but most of it is millions of KM away too.  :)  Plus the rotation
> speed.

It still adds up. And the rotation speed isn't that high.
 
> >> And why 10 AU with a 1 AU hole?  Seems excessive, even for a broad
> >> interpretation of the habitable zone.
> > 
> > Well, I wanted to have the available areas range as far into "you've
> > got to be kidding" climate ranges as wasn't going to be impossible to
> > survive, and then go a bit beyond.
> > 
> > If I use part of it for a D&D campaign, well, it gives "interesting
> > places for the Frost Giants and Fire Giants and other such critters
> > to come from.
> > 
> > Besides, who says humans are the only species living there?
> 
> Well, unless you're going with quite exotic life, between freezing and
> boiling water is a pretty good limit.

Maybe. 
 
> For that matter, the Mercury-like regime is going to evaporate atmosphere.
> You have to recapture it somehow, or eventually all your air & water go
> away.  Same for the outer parts locking it all up in ice.

Thing is, due to the *lack* of decrement in the gravity, the 
molecules aren't going to escape, even at that temp.
 
> > Just consider the sort of stuff that might get traded across millions
> > of miles of climate zones.
> 
> Probably not all that much.  Given that some proportion gets sold in each
> increment of distance, it becomes exponentially improbable for any thing to
> be available for sale an arbitrary distance from it's origin.  Plus at the
> speed you were talking about limiting it too, imagine the wear and tear on
> an object traveling that far.  And the price would have to go up at least
> linearly with distance to be worth hauling it.  Pretty soon, nobody could
> afford it.

Still, I'd expect there to be some really exotic (and rare) stuff 
floating around.

> By the way, you might want to look at what others have done with the idea.
> Here's a few:

> <http://www.westendgames.com/forum/archive/index.php?t-291.html>  <-- this
> includes Larry Niven's description from 33 years ago.

I've got Niven's article in 30 year old books. :-)



--
Leonard Erickson (aka shadow)
shadow at shadowgard dot com