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|Posted By: SiliconDream <email@example.com>||Date: 10/23/99 3:12 a.m.|
In Response To: Re: Climate? (Loren Petrich)
I decided to find what the best angle is for Soell to make with the Halo's rotational plane, so here it is: in radians, ArcTan[D/R], where 2D is the north-south thickness of the ring, and R is the radius. I'd post all the calculations I did, but they don't copy well from Mathematica to here. Below this critical angle, the incident light is proportional to:
And above it, the incident light is proportional to:
\!\(\[DoubledPi]\ Sin[\[Theta]] -
2\ ArcCos[\(D\ Cot[\[Theta]]\)\/R]\ Sin[\[Theta]] -
\(2\ D\ Cos[\[Theta]]\ Cot[\[Theta]]\
\@\(\(-D\^2\) + R\^2\ Tan[\[Theta]]\^2\)\)\/R\^2\)
I don't expect you to be able to read that unless you can copy it back into Mathematica, but basically the incident light goes to zero as Theta (the angle Soell makes with the rotational plane) goes either to 0 or to 90 degrees, which is the appropriate behavior.
Anyway, it looked to me from the hologram like 4D = R, approximately. (Nathan didn't mention anything about the relative dimensions of the Halo when he talked about the errors of the hologram today or yesterday, so I'm hoping they're pretty accurate.) That means that the Halo gets maximum sunlight when Soell's about 14 degrees away from its plane of rotation. Soell should actually be a little higher than this, as my calculation exaggerated the darkening associated with the angle between the sunlight and the ring surface, and underrepresented the darkening associated with the shadowing of the spaceward side by the sunward side. This inaccuracies stem from my assuming Soell was infinitely far away, so that its rays were parallel. So I'd say 15 degrees is a good approximate angle of maximum sunlight.
What does this mean for Halo's climate (assuming all the complicated factors like precession and nutation average out)? Well, if the maximum angle that the Halo's rotational plane makes with Soell is less than 15 degrees, then the year will be of the 2-winters, 2-summers form I suggested in my original analysis. If the maximum angle is greater (say, 22 degrees like the Earth), then there's going to be a [severe winter-summer-mild winter-summer] cycle that runs twice a year. And if the maximum angle is 90 degrees or close to it, the year will have four equally cold winters and four summers.
|Climate?||Loren Petrich||10/21/99 2:37 a.m.|
|Re: Climate?||SiliconDream||10/21/99 11:55 a.m.|
|Re: Climate?||Matt Soell||10/21/99 5:00 p.m.|
|Re: Climate?||Deathwhore||10/21/99 5:06 p.m.|
|Matt Soell? *The* Matt Soell?||Mark Levin||10/21/99 7:28 p.m.|
|uh... who is matt soel?||Ben Schodek||10/21/99 9:14 p.m.|
|Who indeed...||Louis F.||10/21/99 9:28 p.m.|
|Re: Who indeed...||Jägermeister||10/22/99 12:05 a.m.|
|No, but you're close :) (NT)||Freewill||10/22/99 10:06 a.m.|
|Re: No, but you're close :) (NT)||Åstro the Space Duck||10/22/99 5:10 p.m.|
|Re: Matt Soell? *The* Matt Soell?||Nathan||10/22/99 9:28 a.m.|
|Re: Climate?||Loren Petrich||10/21/99 5:49 p.m.|
|Re: Climate?||SiliconDream||10/23/99 3:12 a.m.|
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