Date: Tue, 17 Jun 2003 22:38:23 -0400 (EDT) From: "Keith F. Lynch" <kfl@KeithLynch.net> To: WSFA members <WSFAlist@KeithLynch.net> Subject: [WSFA] Re: Constructing Realsitic Solar Systems Reply-To: WSFA members <WSFAlist@keithlynch.net> > Ladies and gentlemen: I request some help in constructing a > realistic solar system for a fantasy novel universe. Fantasy? Or Science Fiction? For fantasy, make up your own rules. Anything goes. > I understand that there are various formulas (1) for determining the > planetary habitable zone around stars of various luminousities All you need to know is how large the sun appears in the sky, and what temperature it is. Divide its temperature by the fourth root of what proportion of the planet's sky it takes up, and that's the temperature of the planet. The full sky is always going to be 4 pi steradians, or 41,253 square degrees. In earth's sky, the sun is half a degree across, or 0.2 square degrees, so it takes up just about 1/210,000th of the whole sky. (Yes, most people would guess it takes up more. It doesn't.) The sun's temperature, typical of a G-type star, is 5780 K. The fourth root of 210,000 is about 21.4, so our planet ought to average about 5780/21.4 K. That's 271 K, or about 28 degrees Fahrenheit. That's a little low, since it doesn't take into account the greenhouse effect (i.e. that the earth is darker in the visible light part of the spectrum, where it gets most of its heat from the sun, than in the infrared part of the spectrum, where it re-radiates most of its heat), but it's in the right ballpark. (To convert from Kelvin (K) to Fahrenheit (F), subtract 273, then multiply by 9/5, then add 32.) Once you've calculated that for one planet in a solar system, the others are easier. A planet half as far away will see the sun as four times the angular area, so it will be the square root of two times hotter. A planet twice as far away will see the sun as one fourth the angular area, so it will be the square root of two times colder. Venus, being 0.72 as far from the sun as earth is, ought to be the square root of 1/0.72 times hotter. That's 319 K, or 115 F. This is the origin of the classic Heinlein/Weinbaum/Leinster tropical swamp Venus. They knew how to do the math. Unfortunately, it turned out that Venus has a runaway greenhouse effect, and is actually enormously hotter than that. For Mars, at 1.52 Earth's distance, I get -64 F, which is about right. The temperature of stars varies a lot, from hot bluish type O stars at about 40,000 K, to cool reddish type M stars, at about 3000 K. When seen from a planet that's a reasonable temperature, a type O star would have to be too tiny to show a disk. It would be like an electric arc in the sky. A brief glace would burn a permanent trail on your retina. A type M star, on the other hand, would be large indeed, much like in those fantasy paintings. Unfortunately for variety, type O stars probably don't last long enough for evolution to take place. And the reddish light from type M stars may not be able to drive photosynthesis, without which plant and animal life are impossible (as far as we know). Most of the stars you see in the sky, whether with the Hubble telescope, your unaided eye, or anything in between, are much hotter, brighter, and larger than the sun. However, dim reddish stars are far more common. There's a strong selection bias, since bright stars are of course more visible. A star 7.8 light years from us was just discovered. This is closer than the brightest star in the night sky, and less than twice as far as the closest known star. There's an even stronger selection bias in the few extrasolar planets that have been discovered. They all tend to be larger than Jupiter, but in a tigher orbit than Mercury. Mainly because that's nearly the only kind of planet we can detect with today's techniques. We can't conclude anything about what's typical from that. But at least we know that planets are common. It wasn't that long ago that many astronomers thought that planetary systems were extremely rare. Which would have made for a boring universe. > and (2) for translating the distances of planets from their primary > star(s) into lengths of years. As Ron already mentioned, Kepler's third law says that within any solar system, the square of the period is proportional to the cube of the distance. For instance, a planet at four times the distance will have a year eight times as long. Within our solar system, if you measure planet years in earth years, and planet distances in AU (where one AU is defined as earth's distance from the sun), the square of the period is *equal* to the cube of the distance. Planets' orbits can't be closely spaced, since they'd strongly perturb each other's orbits. And probably end up colliding within a few centuries. However, there's no known reason one earthlike planet can't be the moon of another one. Of course they'd have to be about the same size. Unfortunately, you probably can't have a *triple* planet. While three earthlike planets *could* orbit a the common center of an equilateral triangle, this arrangement isn't stable in the long term. Nor is it clear how it could get started that way. The late Robert Forward depicted such a double planet with the planets almost touching, making it possible to fly between worlds in an airplane. He did point out that this wasn't stable in the long run, and the planets would collide and merge in a few million years, which would certainly kill all life on both worlds. If you were to replace our moon with a second earth in the same place, it would raise enormous tides. People could only live in the mountains. Except that the planets probably would have become tidally locked to each other eons ago, causing days to be very long, with very cold nights and very hot days. The "moon" would remain stationary in the sky, like a synchronous satellite. A better plan might be be to replace the moon with a second earth four times further away, so that it would be the same size in their sky as our moon is for us. It would still raise higher tides than the moon, but only by a factor of two or so. Then neither world would be tidally locked, and people on one world could see all the continents, in turn, on the other world, and could tell, even in prehistory, that it was rotating, and make maps of it. I wonder if they could communicate before the invention of radio. Giant heliographs, perhaps? Too bad it's not plausible that people on both planets would be at anything remotely close to the same level of development. Just by chance, one would be millions of years ahead of the other. Their Neil Armstrong might find the equivalent of dinosaurs on the other world, but probably not cavemen, much less any kind of civilization. -- Keith F. Lynch - kfl@keithlynch.net - http://keithlynch.net/ I always welcome replies to my e-mail, postings, and web pages, but unsolicited bulk e-mail (spam) is not acceptable. Please do not send me HTML, "rich text," or attachments, as all such email is discarded unread.