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The 100-Billion-Body Problem

A full-scale computer simulation of the galaxy we call home must trace the motions of at least 10^11 stars and other objects over several billion years.

Brian Hayes

Isaac Newton earned his fame by solving a two-body problem: He showed how gravitational attraction binds the Earth and the Sun into elliptical orbits. His formulas worked equally well for the Earth and the Moon or the Earth and an apple, but Newton was stumped when he tried to apply his law of universal gravitation to a three-body problem, such as the combined Sun-Earth-Moon system.

By the middle of the 19th century, astronomers and mathematicians had devised tools capable of tackling an Click to Enlarge Imageeight-body problem—calculating the orbital motions of the Sun and the seven known planets. Unlike Newton’s solution of the two-body problem, these methods gave only approximate results. Nevertheless, they were accurate enough to reveal a tiny discrepancy between theory and observation, which led to the discovery of an additional planet, Neptune.

The challenge now is to solve a 100-billion-body problem. Computational astronomers are preparing to simulate the motions of all the stars in a galaxy the size and shape of the Milky Way, tracing the stars’ trajectories over a period of several billion years. The team working on this computational extravaganza—a Dutch-Japanese collaboration led by Simon Portegies Zwart of the Leiden Observatory—has already completed a pilot study of 51 billion stars.

In all of these “N-body” models, the individual particles obey very simple laws of motion, yet a large ensemble of particles can dance a surprisingly intricate and lively ballet. Gravitation organizes astronomical bodies into a hierarchy of structures: planetary systems, clusters of stars, galaxies, lacy webs of galaxy clusters that stretch across the entire visible universe. N-body studies may help illuminate the mechanisms that create these forms. In the case of the Milky Way, the 51-billion-star simulation shows a featureless disk evolving into a majestic pinwheel with a central bar and several bright spiral arms. Still larger simulations should reveal finer details, just in time for comparison with new satellite observations expected in the next few years.

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