Interesting start. Tempting to add a few more details, maybe on annular eclipses, occultations and transits as well. I'm sure Phaeton can help - Rank 7 Philosopher with Astronomy and Mathematics *g*.
--Keith 23:06, 22 Oct 2006 (NZDT)
Happy for you to add some stuff. I'm working on getting the mathematics of eclipses right. I know the answers are on some webpage or in a book, but the geometry is fun (!). Once I'm happy that I can track the moon's path with node progression and perigee regression, we just need to agree on some constants for the rates of change, and the times of the eclipses should fall out! The trick is to make them fit some cycle, but not be too predictable. Also, the Full/Penumbral/Umbral, partial magnitudes, and exact locations visible are stuff I haven't figured out the maths for yet. I'm trying to stick to high-school trig rather than any fancy tricks, so that it can be easily approximated by the conic section tables available in the 1400's. If we can get half-saros correlations between lunar & solar eclipses, excellent!, but I think that we may not be so lucky.
The idea is that GMs need not understand the astronomy, and that a sun/moon/eclipse table can be dynamically generated for any lat/long/time period, for those who care, and those who don't can ignore this stuff completely.
--Andreww 11:36, 23 Oct 2006 (NZDT)
Fair enough. I'll check my textbooks and see what I can come up with. I'm also a little concerned since the Alusian moon has a slightly shorter synodic period (28 days as opposed to 29.5 days, that the Saros cycle is going to be slighly different. Plus the orbital inclination of Alusia's moon may also be different than our own. Be nice to find an algorithm that could calculate Saros cycles for different orbital parameters. Is the lunar orbit elliptial or more circular? But yeah .. the Babylonians did it .. so should the Alusian philosophers.
--Keith 18:23, 23 Oct 2006 (NZDT)
Keith, nice re-write & images. The Saros cycle is based on the synodic, draconic & anomalistic months almost matching after 223/241/238 months respectively. We can set the draconic & anomalisitc month lengths as we choose to give any Saros cycle we want. I'm working with exactly 10 years at the moment, because its easier to spot errors in the maths. I'm also assuming the e of the Lunar & Solar orbits is as per Earth. Of course the Chaldaeans could use actual observations, rather than trig. I'm assuming Phaeton (as an astronomer) would use observations, but the navigators amongst us would use a combination, and the philosophers may not want to get their hands dirty with actual data' at all. If you, or anyone else wants the maths, email me, and I'll send you some small .js/html files I'm tuning.
--Andreww 22:45, 27 Oct 2006 (NZDT)
This is all quite interesting stuff, but are we sure we want to turn Alusia into a world that precicly folows mathematics and science? I remember well an adventure where the moon changed orbit. (But I suppose the model could always just get updated)
--Neil 11:20, 30 Apr 2008 (NZST)
Actually... forget that comment completely. After actually READING it (gotta do that more often), it will work fine blending the magical and non-magical if required.
--Neil 11:23, 30 Apr 2008 (NZST)
This page is currently an orphan but I cannot find a suitable location for it. Could one of you chaps add it into the pages you have done so it gets a home :-) --Mandos 08:56, 30 Apr 2008 (NZST)
Fixed --Keith 18:46, 30 Apr 2008 (NZST)