The Integral Trees by Larry Niven
Winner of Locus Readers Poll SF Novel for 1985.
The setting of this story is a unique habitat -- a ring of atmosphere ("the Smoke Ring") in a binary star system (including a neutron star). Since this is not a planet, there is very little gravity. Within this ring there are a number of kinds of life, the largest being the "integral trees". These are plants with tree-like trunks tens of miles long. At each end of the "trunk" is an area of foliage curving off towards one side (so that seen at a distance the whole looks like a mathematical integral symbol).
Hundreds of years ago a human exploration ship came here. The people left the ship and settled in the ring, mostly living on the Integral Trees. There are now a few small bands of people living off the remnants of their technology and what they can get from local materials and food. They have limited memory of the ship or Earth.
Meanwhile, all these years the people have been watched to one degree or another by Discipline, the ship that brought them here. The ship's systems consider the humans living in the ring to be mutineers who abandoned the ship and their mission. It considers itself the representative of The State and hopes to get the people to return. The ship doesn't have enough data storage to keep all the information that has been collected over the centuries, so it has been regularly editing and eliminating parts of its "memories".
The central characters live on one particular integral tree which is in trouble and splits apart in the middle. This forces them to leave the lives they are used to and seek a new home. In the process they come across an old landing craft and are contacted by Discipline.
During the story, we learn much about various things. The binary system. Conditions in the Smoke Ring. How things move with very little gravity. What happens to life if it drifts towards the edge of the Ring (where the atmosphere is thin). The effects of the neutron star when it passes relatively near. How the bodies of the people have adapted to the low gravity. And so on.
Larry Niven also wrote a sequel, The Smoke Ring.