Sunday, 14 May 2017

Upgrade your planet: add rings!

This is the first on two or three posts on adding rings to Furaha, or any other fictional planet. The reason to add any is simple: rings add drama! Ron Miller, an excellent artist specialising in astronomical illustration, provided fascinating examples of how dramatic rings can look by transplanting Saturn's rings to Earth. He has shown and discussed the results a few years ago on this io9 page (the comments are also interesting).
 
Click to enlarge; copyright Ron Miller (used with permission)
Here is one of his examples, showing a view from Guatemala. Impressive, isn't it? Somehow I only started wondering whether rings would look just as good on Furaha a short while ago. I certainly studied rings before, in the context of the planet Ilo, as can be seen from this post and this one.
Click to enlarge; copyright Gert van Dijk
The animation above shows the planet Ilo and was taken from the main Furaha site (under the 'astronomy/seasons' tab. It shows how the shape of the areas lit by the sun changes over a year; the curved horizontal band is the ring shadow.

Adding rings to a view as expertly as Mr Miller did is not a simple matter of drawing some curves in the sky. Once you start thinking about the problem, you will realise that their aspect depends on how large they are, but also on where you are on the planet, on the direction your 'camera' is pointing in, and finally on the 'lens' you are using, by which I mean the visual angle. And as if that is not enough, the lighting of the rings differs for every hour and day of the year. Some places on the surface will be in the shadow of the rings, and at other times the planet will cast a huge shadow on the otherwise sunlit rings.    

So I started exploring these matters. I am not certain I will actually add rings to Furaha, but it is fun to explore. In this post I will start with basic ring astronomy (mind you, the only astronomy I can deal with is of a very basic variety). Planetary rings consist of many pieces of ice or rock, from boulders to dust particles, all circling a planet in its equatorial plane, and only there. There can be no rings directly overhead on the poles. In Earth's solar system, rings usually do not form one continuous band from the inner to the outer radius, but are divided into several distinct ringlets with gaps in between. These are apparently the effect of moons that sweep clean parts of the rings through their own gravitational effects. While there must be strict Newtonian rules underlying where these ringlets and gaps are placed, the large variety of ring shapes in our own solar system suggests that there is wiggle room here, allowing some creativity on the wordbuilder's side. Just compare the rings of the gas planets, for which this Wikipedia article is a good start.

click to enlarge; copyright:  http://astronomy.nju.edu.cn
The image above can be found at this website; it compares the various ring systems and stresses another important feature: rings are always situated inside a planet's Roche limit, or 'tide limit'. The word 'tide' here has nothing to do with seas, but concerns 'tidal forces' acting on a piece of ice or rock coming close to a large mass (a planet or sun). The gravitational forces act differently on the parts of an object closest and farthest away from the planet. These tidal forces will break up an object if it is within a certain distance of the planet, and that distance is the Roche limit. The breaking of the object, say an asteroid, goes on until the remnants are small enough to stay whole. If you start this process with a large enough object, the resulting pieces may collide with one another, breaking off more pieces, adding to the fun. The Wikipedia page on Roche's limit shows very clearly what happens to a heavenly body when it crosses the limit, and also contains a formula to calculate how far out from a planet the limit lies (this is the formula for 'fluid' objects).

distance= 2.44 * radiusP * (densityPlanet /densityAsteroid)^1/3

The distance is in km, and is governed by the planet's radius (radiusP, in km) and on a fraction, involving the density of the planet divided by that of an asteroid coming near the planet. If you wish to express the Roche limit in units of the planetary radius, you can just leave RadiusP out. If the asteroid has the same density as the planet, the fraction is one, and then the formula simply reads: 'The Roche limit is at 2.44 planetary radii'. But asteroids are probably less dense than a terrestrial planet, making the fraction greater than 1, so the Roche limit will be further out. I found estimates for various types of asteroids ranging from 2 to 5 gram per cubic centimeter, and the density of Furaha is 5.9 gram per cubic cm (the Furaha planetary system was kindly worked out by Martyn Fogg). So we can take the Roche limit for Furaha up to 3.5 radii.

Click to enlarge; copyright Gert van Dijk
Here is a ring of which the outer margin is exactly 3.5 planetary radii away from the centre of the planet. The planet is shown at the point in its orbit where the northern pole points directly towards the sun (the summer solstice). The glowing orange arrow show the direction of sunlight, and the thin lines show the plane of the orbit (and the direction perpedicular to it). The rings are 50% transparanet. You can see the shadow of the planet on the rings, and you can just also see the shadow of the rings on the planet.

That ring seems overly large, so I will set for a safer maximum value for the outer radius of the ring at 2.5 radii out from the centre of Furaha. But what should the value for the inner radius be? That is less clear; the outer parts of the atmosphere would form an effective limit, but I do not think I want the rings to come that close: bits and pieces might rain down continuously, and if these are large enough they will mess up the biosphere. So let's start with a fairly narrow ring with an inner radius of 1.8 to 2.0 radii.

click to enlarge; copyright Gert van Dijk
So here we are; that looks better. I also adjusted the transparency of the rings: this one is 67% transparent. How much light should the the rings let through? If the density of rocks in the rings is high and the rings are thick, not much light will come through. The reason this matters is because the rings casts shadows on the daylight side of the planet. They do so on the Northern or Southern hemisphere depending on the time of year.

click to enlarge; copyright Gert van Dijk
Here is a simple scheme explaining that. Furaha's axis is tilted by 18.3 degrees, and so are the rings. When it is summer in the Northern hemisphere (at the left), the North pole is tilted towards the sun, and the shadow of the rings falls on the Southern hemisphere. When it is winter in the Northern hemisphere (at the right) the ring shadow darkens the Northern hemisphere. I do not want these shadows to be big and black, because that will have large and unpredictable effects on the climate, the weather and the life forms (well, I certainly cannot predict them, and that is the actual limiting factor). So I prefer narrow transparent rings: I still get drama without too many unknown problems. I will assume that a small asteroid, breaking up and filling a large area, would result in largely transparent rings. In fact, it is the other way around: the rings are about two thirds transparent, because the asteroid forming the rings contained exactly the right amount of matter to make it so.

The final matter is the composition of the rings; they can theoretically be made of ice or of rocks. I doubt ice would last long this close to the sun, so the rings are made of rock. Earth's moon consists of  very dark rock, and yet its appears bright enough in the night sky to have inspired generations of poets; that seems a suitable unit of measurement for drama. Let's therefore assume that the putative Furaha ring system is made of dark rock.

So far we have the main features of the ring system in place, based on science, as it should be, but with a fair amount of handwavium. I am not certain about whether I should give up on Furaha's two tiny moons. Ideally, I should calculate appropriate gaps in the rings, but admit that at present I do not have the knowledge to do so. Any readers who can do so are friendly invited to comment on the matter!

Click to enlarge; copyright Gert van Dijk
This image shows Furaha with some fancy rings, for even more drama. The inner one is nearly completely transparent.  Another step in deciding whether or not I should add rings to Furaha may be to calculate the effects of this particular ring system on the lighting of the planetary surface. But, having done so once for Ilo, I already have a fairly good idea of what the effects for Furaha will be.

click to enlarge; copyright Gert van Dijk
This is another image of the same fancy rings, now from a lower point of view that lets you see the Southern hemisphere with the ring shadows. These shadows do not look too bad. Now that we have reasonable options to design rings, it is time to take the next step: what do the rings look like from any point on the surface of the planet, for any point in time of the year? That will require another post...                          

Friday, 5 May 2017

Kwals 2: from universal back to local

Since the last post I have busily worked on some two-page spreads, one of which shows an advanced kwal. Each spread probably takes about 25 hours of work: there is an animal to design, one 6000 x 4200 painting to do, text to write, a silhouette to design and paint, a map to be made, and often an additional illustration to do. If I ever produce a book again, I will write it as normal people do, not paint it...

Anyway, designing the kwals proved less than easy. In the previous post I designed kwals with central valves to let in water on the upstroke, but when I sat down to design species built on that concept, I was became less and less satisfied with it. It seemed biologically possible, possibly plausible, but not painterly pleasant. So here is what happened next.

Click to enlarge; copyright Gert van Dijk

This is a quick sketch of a 'gatkwal'. It is still very much like Earth's jellyfish, with its single bell at the top of the body, with tentacles dangling below it, in part from the edge of the bell, and in part from the central body below the bell. The major departure here is the hole in the bell, meant to let water stream through on the upstroke. Obviously, the water has to stream right through, meaning the body must not block the hole. So there are spokes connecting the bell to the body underneath. Of course, this comes about embryologically as a hollow cylinder with secondary fenestrations in its sides. Same thing, really. Here there are six spokes, meaning that the gatkwal has six-sided symmetry, representing a doubling compared to the prototypical three-sided radial kwal design (we'll get to that).
   When the bell contracts, it sends down a rotating torus of water, as happens with Earth's jellyfish (see the previous post).

Click to enlarge; copyright Gert van Dijk
While I was thinking about the three radial 'pie slices' that make up a kwal, I started pulling on the edges of the bell, which then together no longer formed a nice circular edge, but a three-lobed shape. Take that idea and separate the lobes more and more until they are fully separate. We now have a kwal with three bells instead of one. The first stages of these trikwals are not shown here, but the finished painting is about one such, the 'tribune' ('Tribunus vacans'). The musculature of the bells had to evolve: rather than only having circular muscles to squeeze the bell together, there is now a more complex arrangement to control movement in the 'longitudinal radial' as well as 'transverse radial' directions. And those in turn necessitated rods of less compressible material (the 'chordae') embedded in the jelly to give the muscles something to work against. With all these changes, kwals became less like jellyfish with every step. This is ironic, as they started as supposedly 'universal' shapes. By now that are probably quite specifically Furahan. Just as well, I guess.
  Anyway, here is the 'klapkwal', in which the three bells have evolved some more: each bell has two halves that fold together as they are lifted up, but open as they are driven down. It is here shown during an upstroke. It looks a bit like a plant, but that is because the context is missing: you have to imagine it drifting through the ocean.

Click to enlarge; copyright Gert van Dijk
Here is another advanced kwal, which is as yet nameless. Its bells have evolved to beat slowly through the water. In this case they are supple on the upstroke but less so on the downstroke, which is shown here. Mind you, this is probably as far as the design can go: it is tempting to speculate how far kwal evolution can move towards quicker or more efficient propulsion. The problem is that the rest of the design may not allow this. The biggest obstacle is probably the way kwals feed, which is by dangling tentacles in the water and waiting until something edible blunders into them. The elaborate tentacles offer considerable resistance to movement. This is not a real problem at low speeds, but does form a major hindrance at high speeds. To move quickly, kwals would have to acquire a different feeding mechanism. The conversion would have to happen in small steps, as this is how evolution works: it is like rebuilding your house a bit at a time, while you keep living in it. But designing a whole new feeding mechanism is more like tearing down the house before you can rebuild another one. Unfortunately, that leaves you with nowhere to live.
  So these 'rowing bells' may be the most advanced feature kwals will ever possess. Still, give them another 100 million years or so, and let’s see what happens.