Flat world astronomy problems
Aug. 26th, 2012 10:54 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
steorran_woruldeI've had a couple posts now set in a flat world I'm nicknaming "flat-like-a-penny", because I don't have a real name for it. I first came up with the idea for this world some time in my teens, but it's never been a major focus of my worldbuilding; it's a longstanding on-the-side project with not a lot filled in. Obviously, with a nickname like that, it is not like Domil in being astronomically equivalent to Earth..
The core idea is what the nickname refers to: the earth is flat - but it's not flat with one habitable side, it's flat like a penny with two habitable sides. One side is inhabited by humans, and the other side is inhabited by elves. Each would be living on the other's antipodes. In between the two sides flows the ocean of light, which extends beyond the main world to the celestial sphere that encloses the entire universe. The inside of the celestial sphere is not bare, but rather contains the material in which the stars grow. Stars grow kind of like trees, poking through the "ground" that covers the celestial sphere; I think, though, that they multiply with a runner-like system, so that their roots are all connected to each other. However, stars are not plant-like in that they are thinking, speaking beings.
So far, so good. Stars are small, but extremely bright, and far away on the celestial sphere, so they are point-like at night. That's star-like.
But go much beyond that, and astronomy gets tricky - even accepting the fact that on a flat world, celestial mechanics will be observably different from celestial mechanics on a round world, because celestial mechanics are so intricately tied to the shape of earth, and other objects' distances from it and motions relative to it and each other.
Apparent motion of the stars? That's probably doable; some relative rotation of earth/celestial sphere, whether we want to call it the flat world rotating, or the celestial sphere rotating. What's the axis of rotation? Well, I think I'll suppose that it's neither parallel nor perpendicular to the plane of the world, thus from humanland there would be one visible pole, some circumpolar stars (which never rise in elvenland), some stars that rise and set (and do the same in elvenland), and a portion of the sky that never rises above the horizon (but is circumpolar in elvenland). This still basically works, though it's clearly going to differ experientially from earth, since going "north" or "south" isn't going to change which stars are visible, while going between humanland and elvenland will basically do the celestial equivalent of a sudden hemisphere shift.
The sun and moon, though, get tricky. Let's suppose they're spherical. The problem comes in with angular diameter. Assuming the sun and moon should have roughly the same apparent size as sun and moon from earth, each of them should have an angular diameter of approximately half a degree.
Okay, so, angular diameter is determined by size and distance. Same size, twice as far away = half the angular diameter. Sun and moon are going to have to be pretty far away. At minimum, we need to figure out the size of the flat world, so we know how far away from the centre of the world their paths are. But, another issue: If the world is inhabitable right to its edge, and the sun and moon rise and set near the edge of the world, for someone who lives near the side of the world where they rise, the sun and moon will appear much larger at their rising (since it's on the same edge of the world) and much smaller at their setting at the opposite edge of the world. So that would suggest that it's desirable to add extra "padding" from the edge of the habitable world to the paths of the sun and moon, so that their apparent size doesn't change drastically if you aren't in the very centre of the world.
Okay, so, how big should things be?
For rough approximation purposes, I've been working with a main-habitable-world diameter that's a round number similar to the diameter of Earth. That'll give less surface area, since we're dealing with a disk rather than a sphere, but still in the same ballpark. Earth's diameter is - well, it depends where you measure it, but approximately 12,700 km. Let's make that 12,000. So, radius of the basically-habitable part of the world is 6000 km. Let's first of all ignore the edge-of-the-world problem. If someone was standing in the middle of the world, and the sun or moon was rising 6000 km away at the edge of the world, how big would the sun/moon have to be? Using this angular diameter calculator, I get that for an object 6000 km away to have an angular diameter of .5 degrees, that object has to be about 52 km in diameter. That's fairly big. And it still leaves the edge problem - someone living near the near edge of the world would see it as far huger than .5 degrees, and someone near the far edge of the world would see it as much smaller than 5 degrees. Someone at the opposite side of the world would be 12000 km away, and would see the sun/moon as having an angular diameter of only .25 degrees. Someone even only halfway between the middle of the world and the near edge would see the sun/moon as having an angular diameter of a whole degree.
So let me add some padding - maybe some mostly-empty ocean with perhaps some scattered strange and questionably-inhabitable islands; maybe some area where the ocean of light projects out beyond the main world for some ways before we come to the paths of the moon and sun. Some numbers I found that seemed semi-satisfactory while fiddling with things are (if I am interpreting my notes from the other day right, and got things calculated correctly):
Moon: 200 km diameter, path 24000 km from middle of the world
Moon's rising/setting:
From the middle of the world: 24,000 km away, moon's angular diameter .477 degrees.
From the near edge of the (habitable) world: 18,000 km away, moon's angular diameter .637 degrees.
From the far edge of the (habitable) world: 30,000 km away, moon's angular diameter .382 degrees.
Sun: 300 km diameter, path 36,000 km from middle of the world
Sun's rising/setting:
From the middle of the world: 36,000 km away, sun's angular diameter .477 degrees.
From the near edge of the (habitable) world: 30,000 km away, sun's angular diameter .573 degrees.
From the far edge of the (habitable) world: 42,000 km away, sun's angular diameter .409 degrees.
This seems like as good a solution as I'm going to get. The angular diameters still vary pretty substantially - they'd be plainly observable, I think, especially for the moon - but at least they're still all in the half-degree ballpark.
I'm not happy with the moon and sun having diameters that large. That's almost small-world-sized, and if they are small round worlds, why is the earth flat? But it seems unavoidable. If I put them any closer (to allow them to be smaller), the angular diameters will vary too much.
And that's not even thinking about the details of the paths of the sun and moon, or how exactly their angular diameters would work with solar eclipses. (And are there lunar eclipses? And if so, what causes them? Since it can't be the earth's shadow.)
Another flat-world-astronomy-related problem: Location-based climate? How does that work? Is the north cold?
The core idea is what the nickname refers to: the earth is flat - but it's not flat with one habitable side, it's flat like a penny with two habitable sides. One side is inhabited by humans, and the other side is inhabited by elves. Each would be living on the other's antipodes. In between the two sides flows the ocean of light, which extends beyond the main world to the celestial sphere that encloses the entire universe. The inside of the celestial sphere is not bare, but rather contains the material in which the stars grow. Stars grow kind of like trees, poking through the "ground" that covers the celestial sphere; I think, though, that they multiply with a runner-like system, so that their roots are all connected to each other. However, stars are not plant-like in that they are thinking, speaking beings.
So far, so good. Stars are small, but extremely bright, and far away on the celestial sphere, so they are point-like at night. That's star-like.
But go much beyond that, and astronomy gets tricky - even accepting the fact that on a flat world, celestial mechanics will be observably different from celestial mechanics on a round world, because celestial mechanics are so intricately tied to the shape of earth, and other objects' distances from it and motions relative to it and each other.
Apparent motion of the stars? That's probably doable; some relative rotation of earth/celestial sphere, whether we want to call it the flat world rotating, or the celestial sphere rotating. What's the axis of rotation? Well, I think I'll suppose that it's neither parallel nor perpendicular to the plane of the world, thus from humanland there would be one visible pole, some circumpolar stars (which never rise in elvenland), some stars that rise and set (and do the same in elvenland), and a portion of the sky that never rises above the horizon (but is circumpolar in elvenland). This still basically works, though it's clearly going to differ experientially from earth, since going "north" or "south" isn't going to change which stars are visible, while going between humanland and elvenland will basically do the celestial equivalent of a sudden hemisphere shift.
The sun and moon, though, get tricky. Let's suppose they're spherical. The problem comes in with angular diameter. Assuming the sun and moon should have roughly the same apparent size as sun and moon from earth, each of them should have an angular diameter of approximately half a degree.
Okay, so, angular diameter is determined by size and distance. Same size, twice as far away = half the angular diameter. Sun and moon are going to have to be pretty far away. At minimum, we need to figure out the size of the flat world, so we know how far away from the centre of the world their paths are. But, another issue: If the world is inhabitable right to its edge, and the sun and moon rise and set near the edge of the world, for someone who lives near the side of the world where they rise, the sun and moon will appear much larger at their rising (since it's on the same edge of the world) and much smaller at their setting at the opposite edge of the world. So that would suggest that it's desirable to add extra "padding" from the edge of the habitable world to the paths of the sun and moon, so that their apparent size doesn't change drastically if you aren't in the very centre of the world.
Okay, so, how big should things be?
For rough approximation purposes, I've been working with a main-habitable-world diameter that's a round number similar to the diameter of Earth. That'll give less surface area, since we're dealing with a disk rather than a sphere, but still in the same ballpark. Earth's diameter is - well, it depends where you measure it, but approximately 12,700 km. Let's make that 12,000. So, radius of the basically-habitable part of the world is 6000 km. Let's first of all ignore the edge-of-the-world problem. If someone was standing in the middle of the world, and the sun or moon was rising 6000 km away at the edge of the world, how big would the sun/moon have to be? Using this angular diameter calculator, I get that for an object 6000 km away to have an angular diameter of .5 degrees, that object has to be about 52 km in diameter. That's fairly big. And it still leaves the edge problem - someone living near the near edge of the world would see it as far huger than .5 degrees, and someone near the far edge of the world would see it as much smaller than 5 degrees. Someone at the opposite side of the world would be 12000 km away, and would see the sun/moon as having an angular diameter of only .25 degrees. Someone even only halfway between the middle of the world and the near edge would see the sun/moon as having an angular diameter of a whole degree.
So let me add some padding - maybe some mostly-empty ocean with perhaps some scattered strange and questionably-inhabitable islands; maybe some area where the ocean of light projects out beyond the main world for some ways before we come to the paths of the moon and sun. Some numbers I found that seemed semi-satisfactory while fiddling with things are (if I am interpreting my notes from the other day right, and got things calculated correctly):
Moon: 200 km diameter, path 24000 km from middle of the world
Moon's rising/setting:
From the middle of the world: 24,000 km away, moon's angular diameter .477 degrees.
From the near edge of the (habitable) world: 18,000 km away, moon's angular diameter .637 degrees.
From the far edge of the (habitable) world: 30,000 km away, moon's angular diameter .382 degrees.
Sun: 300 km diameter, path 36,000 km from middle of the world
Sun's rising/setting:
From the middle of the world: 36,000 km away, sun's angular diameter .477 degrees.
From the near edge of the (habitable) world: 30,000 km away, sun's angular diameter .573 degrees.
From the far edge of the (habitable) world: 42,000 km away, sun's angular diameter .409 degrees.
This seems like as good a solution as I'm going to get. The angular diameters still vary pretty substantially - they'd be plainly observable, I think, especially for the moon - but at least they're still all in the half-degree ballpark.
I'm not happy with the moon and sun having diameters that large. That's almost small-world-sized, and if they are small round worlds, why is the earth flat? But it seems unavoidable. If I put them any closer (to allow them to be smaller), the angular diameters will vary too much.
And that's not even thinking about the details of the paths of the sun and moon, or how exactly their angular diameters would work with solar eclipses. (And are there lunar eclipses? And if so, what causes them? Since it can't be the earth's shadow.)
Another flat-world-astronomy-related problem: Location-based climate? How does that work? Is the north cold?