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 eight-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.
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