Sunday, 4 January 2009

Cyann and Ilo's rings

The last time I introduced 'Le Cycle de Cyann', focusing on the wildlife. On browsing through 'La clé des confins' my attention was drawn to some astronomical explanations. In the second album of the series Cyann travels over the planet Ilo (there should really be a dot in the letter O, but I cannot reproduce that here). That planet is of interest as it has a very long and narrow continent winding almost like a snake over the globe. This provides an opportunity for Cyann to travel through a vast array of landscapes along with their accompanying biotopes, much to the enjoyment of the reader.

But there is another thing that struck me, and that is that Ilo has rings. I cannot say whether it is at all probable that an Earth-like planet has rings, but their presence certainly has some interesting consequences. From seeing photographs of Saturn, everyone knows that the rings cast a shadow on the planet. But that shadow will not always fall in the same area, provided the planet is tilted to a degree.

In midwinter the North pole is tilted maximally towards the sun, and so will the rings; hence they cast a large shadow on the southern hemisphere. But at the spring and autumn equinoxes the plane of the rings present to the sun edge on, so the rings cast a shadow on the planet no wider than the rings themselves. Here is one picture of Cyann, waiting for her lover on the equator, on the day of the equinox:

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She is facing the sun, and the rings behind her are lit, forming a luminescent vertical stripe in the sky. Looking in the other direction the rings form a dark stripe. Looks like an excellent setting for a romantic encounter.

The consequences of all this tilting are fairly complex. Think of how the ring shadows complicate winter: the shadow of the rings falls on the hemisphere that is tilted away from the sun, where it is winter anyway. But the shadows make the winter days even darker, but in complex ways: it is theoretically possible for the sun to come up, disappear behind the rings, come back again in midday, disappear behind the rings again, and finally to come back only to set on the horizon. All such matters are brilliantly handled in the book. Here are two pictures from 'Le clé des confins' showing how it works. One is an equinox picture, and the other is a solstice picture. If you need more explanations on why the sadows change shape, please go to the planet page on the Furaha site.

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These caught my attention as they resemble the images on the astronomy page of Furaha quite closely, in particular the way the terminator is drawn. The 2x1 ratio of the maps is a giveaway that there is some serious thought here. So I wondered whether I could copy all these ring effects, and sat down to some good old-fashioned Matlab programming. Here is how that started:

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You will see rays of the sun -the blue lines- starting from the edges of the rings. They are of course all parallel, and strike the planet (many don't of course, and these are not shown). The relative sizes of the planet and rings were taken from the book, and I estimated axial tilt to be 21 degrees. Once the x,y,z-coordinates of the rays falling on the planet are known, which only takes high school mathematics, these can be converted to latitudes and longitudes, et voilà. Project these over a rough map of the planet, redrawn from the book, and there we are:

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Nice, isn't it? It is quite close to the drawing in the book, but small changes in ring diameter and axial tilt have large consequences. I also found that ths shape of the terminator in the solstice picture in the book is not exactly right. I can only assume it is some copying error, because the rest is much too good to be guesswork. Do not underestimate the amount of thought that has gone into this. I know from experience that working out the form of the terminator can take quite a bit of effort. Bourgeon and Lacroix not only did that too, but also worked out correct ring shadows, as well as thinking up cultures, animals, etc. It's almost enough to make you desperate...

But I won't be! Instead, I think I will produce some animations of the shadows as they change in the course of a year. Later.


rodlox said...

quite interesting about the rings and how it was carefully worked-out.

glad to see you're up and about in the new year.

ps: just to help: "heroine" (you forgot a letter in the Cyann post)

Sigmund Nastrazzurro said...

Thanks! I'll be back with more work on the rings. Also thanks for telling em about the type (there's probably more); it's been corrected.