MadSci Network: Physics |
David: Yours is an excellent question. The actual value of the constant, however, is not really the issue. Its numerical value is merely an artifact of the system of units in use and since you have cited the constant in MKS units I am compelled to say that this is a number with which Sir Isaac was entirely unfamiliar. The MKS system of units was not in use in England at the time of Newton's formulation. The Law of gravitation makes use of Newton's second law of motion which defines the force on an object. Since the gravitation law uses previously defined quantities, it requires a constant to make the numbers work out right. By the way, the precise measurement of the gravitational constant itself was the work of Cavendish in 1798. Putting that aside, however, it is helpful to look at the form of the law, its inverse square nature. This is the insight of Newton that deserves some comment. According to Jacob Bronowski in "The Ascent of Man," Newton first formulated the idea of universal gravitation during the plague year of 1666. In Bronowski's words: "The moon was a powerful symbol for him. If she follows her orbit because the earth attracts her, he reasoned, then the moon is like a ball (or an apple) that has been thrown very hard: she is falling towards the earth, but is going so fast that she constantly misses it-- she keeps on going round because the earth is round." In the ensuing two decades Newton published nothing about gravitation and seemingly failed to extend his researches into the problem of the planet's motions round the sun. In 1684 Sir Christopher Wren, Robert Hooke (of spring constant fame) and Edmund Halley entered into a debate on the subject. Halley travelled to Cambridge to ask Newton's opinion: "After they had been sometime together, the doctor (Halley) asked him what he thought the curve would be that would be described by the planets, supposing the force of attraction towards the sun to be reciprocal to the square of their distance from it. Sir Isaac replied immediately that it would be an ellipsis. The doctor, struck with joy and amazement, asked him how he knew it. 'Why,' saith he,'I have calculated it.' Whereupon Dr. Halley asked him for his calculation without any further delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it, and then to send it to him." The Principia was published three years later, including the calculations in question. Bronowski speculates that the key problem was to understand the question in Section 12 of the Principia on "How does a sphere attract a particle?" He had done his original calculation treating the earth and moon as particles. He finally discovered that this assumption is only valid for azimuthally homogeneous (radial inhomogenieties are certainly permissible) spheres and only if the inverse square law of attraction holds. The proof of this concept required the invention and manipulation of the calculus. No wonder it took him so long. So things came together nicely. The data was already there in Kepler's and Brahe's figures. The inverse square law resulted in the attraction of heavenly bodies as if they were point particles and in the correct periods and shapes of the orbits. Newton's law appeared to be truly universal for 230 years. Not bad. For other descriptions of the process of formulation and refinement of the law of gravitation I recommend Bronowski's book "The Common Sense of Science," and Richard Feynman's "The Character of Physical Law." Ray Nelson
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