This is discussion archived from a time before the current discussion method was installed.
Jove Hack: There be spoilers here!
Niven may be famous for working out his ideas in his head. Some of the science still ends up wonky. At a scifi convention after Ringworld was published MIT students were going around chanting, "Ringworld is unstable." Niven homaged this in a later work, first by addressing the problem in a later book. Second by having Louis Wu ask incredulously "You actually worked out the math?" to a revelation in-book.
It's an offshoot of an introductory college physics problem. An object inside of a hollow sphere is in zero-gee. The gravitational forces from the surrounding sphere all cancel out. Being at the center of a ring is a form of this problem, but enough different that the position is unstable. As long as the sun is at the exact center of the ring, everything's fine. Any pertubation will lead to disaster.
