While examining an anonymized manuscript proposing a solution to the brachistochrone problem, the Swiss mathematician Johann Bernoulli identified its author as Isaac Newton. He is said to have remarked: "Ex ungue leonem" ("the lion is known by his claw").
The Old Lion's greatest triumph, as he roared in 1685, was probably the publication of his masterpiece, Philosophiae naturalis principia mathematica ("Mathematical Principles of Natural Philosophy"). In particular, he applied his method to the famous two-body problem, which preoccupied the scholars of the day: how do two mutually interacting bodies A and B, treated as point masses, evolve over time when the overall system {A, B} is considered in isolation from the rest of the world? Thus, although our satellite certainly remains in orbit around the Earth, it undergoes a great many "parasitic" motions that are difficult to describe. That is precisely what the two-body problem is all about!
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Newton and the two-body problem
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In Newton's astronomical treatment of B moving around A in the coordinate system (A, x, y, z), six constants of motion arise:
