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This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with inverse cube force is shown to be more symmetric. Montgomery's ‘pair of pants’ metric is derived. The orbits are geodesics in a metric of negative curvature on the plane with three points removed. The Virial Theorem is suggested as an exercise.

This chapter includes a detailed study of the three body problem where one of the bodies is infinitesimal and the other two are in circular motion. This applies to the Sun-Jupiter-Asteroid, Earth-Moon-Satellite systems. Lagrange's surprising discovery of stable equilibrium points and orbits around them is explained. Jacobi's integral and Hill's regions are derived. A spin-off is a theory of stability in the presence of velocity dependent (Coriolis) forces: sometimes a maximum of the potential can be a stable equilibrium.

This chapter introduces the life and work of Liu Cixin, a Chinese science-fiction writer who has played a major role in reviving the genre in twenty-first-century China. The chapter discusses Liu’s work in the context of the genre’s history in China. Liu and other writers belonging to the same generation have created a new wave, in which the genre has gained unprecedented popularity in China. The main part of the chapter analyzes several major works by Liu and attempts to theorize the aesthetics and politics of the new wave as represented in Liu’s stories and novels. The new wave makes visible the hidden dimensions of Chinese science fiction, together with the darker side of reality that it speaks to.

In “‘Great Wall Planet’: Estrangements of Chinese Science Fiction,” Veronica Hollinger offers a few observations about Chinese SF, specifically in terms of its potential to defamiliarize what scholars have begun to refer to as “global science fiction.” She suggests five ways in which Chinese SF can estrange a taken-for-granted Anglo-American mainstream: 1) as an “alien” cultural product; 2) as a product of China’s “rise” as a global superpower; 3) as the product of an “alternate” cultural history; 4) as representative of something called “global science fiction”; and 5) as a kind of “second-language” version of the discourse of Anglo-American globalization. She uses fictional works by Liu Cixin and Han Song to emphasize her points.

Half a century after Poincaré first glimpsed chaos in the three-body problem, the great Russian mathematician Andrey Kolmogorov presented a sketch of a theorem that could prove that orbits are stable. In the hands of Vladimir Arnold and Jürgen Moser, this became the Kolmo–Arnol–Mos (KAM) theory of Hamiltonian chaos. This chapter shows how KAM theory fed into topology in the hands of Stephen Smale and helped launch the new field of chaos theory. Edward Lorenz discovered chaos in numerical models of atmospheric weather and discovered the eponymous strange attractor. Mathematical aspects of chaos were further developed by Mitchell Feigenbaum studying bifurcations in the logistic map that describes population dynamics.

This chapter discusses the N-body problem. In 1886, Karl Weierstrass submitted the following question to the scientific community on the occasion of a mathematical competition to mark the 60th birthday of King Oscar II of Sweden. Weierstrass asked that, ‘given a system of arbitrarily many mass points that attract each other according to Newton’s laws, try to find, under the assumption that no two points ever collide, a representation of the coordinates of each point as a series in a variable which is some known function of time and for all of whose values the series converges uniformly’. Henri Poincaré showed that the equations of motion for more than two gravitational bodies are not in general integrable and won the competition. However, the jury awarded the prize to Poincaré not for solving the problem, but for coming up with the first ideas of what later became known as chaos theory.