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lines at constant speed. The comet of November 1680 was travelling toward the Sun, whereas that which appeared 2 weeks later was travelling away from it. Flamsteed suggested that perhaps they were one and the same object, which had reversed its motion in the vicinity of the Sun. (Actually, this comet passed extremely close to the Sun, within 1 solar radius, and so the reversal of direction was extremely rapid.) Flamsteed corresponded with Newton, who became interested in the orbits of comets. He denied initially that the two comets could possibly be the same object, but later changed his opinion. So perhaps comets were subject to the same forces of attraction as planets.40

In 1684, at the Royal Society, Wren, Halley, and Hooke discussed the problem of motion under an inverse square central force. Hooke claimed that he could derive the laws of planetary motion from the inverse square relation, but Wren and Halley were sceptical, particularly as Hooke refused to divulge his methods. Halley decided to consult Newton. Newton, to Halley's amazement, claimed already to have solved the problem using mathematical techniques he

38 Brackenridge (1995) discusses in detail the processes by which Newton arrived at this fundamental dynamical result.

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