# Newton's Knowledge of the Radius of the Earth

## Abstract

IN a paper entitled "The Story of Newton's Inverse Square Law and his Use of a False Radius of the Earth" (J. Brit. Astro. Assoc., 50, 2; 1939), John Miller states that the story of Newton's alleged ignorance of the true radius of the earth is open to considerable doubt. The data at the disposal of Newton were the time the moon required to revolve around the earth and the moon's distance from the earth in terms of the earth's radius. The latter was known from the days of Greek astronomy to be about 60, and this was independent of the true radius of the earth. A few simple formulæ are derived by Mr. Miller, and from these a relationship is established between the true radius of the earth and certain constants, the basic assumption being the inverse square law. Miller's final formula enables the true radius of the earth to be found, but, of course, if a false value of the radius is used in this formula, the equality breaks down; in other words, the inverse square law seems invalid. It is alleged that Newton took the radius of the earth to be 3,440 miles, and as it was impossible to fit this value in with the inverse square law, his work was delayed nearly twenty years.

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