Setting
The story is set at the fictional neutron star Levoy's Star (abbreviated "Voy"). The gas giant Goldblatt's World (abbreviated "Gold") orbits this star just outside its Roche limit. Thus, Gold's gravity is insufficient to hold its atmosphere, which is pulled loose into an independent orbit around Voy. This orbiting air forms a ring known as the Gas Torus. The Gas Torus is huge—one million kilometers thick—but most of it is too thin to be habitable. The central part of the Gas Torus, where the air is thicker, is known as the Smoke Ring. The Smoke Ring supports a wide variety of life.
There is no "ground" in the Smoke Ring; it is a world consisting entirely of sky. Thus, most animals can fly, even the fish. Furthermore, since the Smoke Ring is in orbit, it is in free fall. There is no "up" or "down". Most animals have trilateral symmetry, allowing them to see in all directions.
Most plants in the Smoke Ring are quite fragile, as they do not have to support their own weight. A notable exception to this rule are the eponymous Integral Trees. These are trees that are up to 100 kilometers long. Tidal locking causes them to be oriented radially, with one end pointing in toward Voy and one end pointing out. The ends of the tree feel a tidal force of up to 1/5 g. Each end consists of a leafy "tuft", which is where photosynthesis occurs. Compared to trees on Earth, the tufts are both canopy and roots.
Each tuft of a tree is up to 50 kilometers from the tree's center of mass. Thus, a tuft is either orbiting too slowly (the "in" tuft) or too quickly (the "out" tuft), compared to the atmosphere, which is in orbit at all points. The ends of the tree are subject to a constant hurricane-force wind. This wind bends the ends into the shape of an integral symbol: ∫. The trees are "fed" by the constant inflow of materials to their tufts caused by water and food being blown into the tufts, or alternately onto the trunk, where the gravity-like tidal forces pull the material out towards the tufts.
The Smoke Ring was colonized 500 years prior to the beginning of the story by a crew of 20 astronauts on board an interstellar "ramship". Their descendants have adapted to the free-fall environment by growing taller and developing prehensile toes. Small numbers of devices from the original crew are coveted items in the Smoke Ring society.
Read more about this topic: The Integral Trees
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