Newton, circa 1670sDepartment of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Newton's 1702 Lunar Theory  

The Moon-Test of 1684

How far would the Moon fall 'if stopped?' This arresting concept was the basis for the so-called 'Moon-test'. As the very first computation to appear in Book III (of the First Edition), it had a key significance, as linking together terrestrial and celestial mechancs. Newton calculated that, in one minute, the Moon 'if stopped' would fall the same distance as would an object on Earth in one second: a convenient 60:1 ratio, a result of the lunar distance being sixty Earth-radii. The 'Moon-test' was one of the most original things he ever did, as the notion of using the 27.3-day sidereal lunar month to demonstrate gravitational force had not hitherto ocurred to anyone.

The first record of it occurs in the autumn of 1684, when the manuscript De Motu delivered to Halley  described the general idea:

The computation was then written up, using a value of 60 Earth-radii as the lunar distance, a one-body computation of uniform circular motion around an immovable centre, which became Proposition IV of Book III. A recent commentary by Dana Densmore describes this calculation as "perhaps the most thrilling demonstration in the Principia," and advised In the next century, in 1713, the computation became a two-body problem, carried out to nine rather than five significant figures, though actually less accurate (See Lunar Mass Error.). If stopped, readers were informed, the Moon would fall 14.7706353 feet in one minute. (The first two digits are correct.)

These two versions appear in both Propositions 4 and 37, using two different sets of numerical values, with little explanation given for the discrepancy, being the only computation to appear twice in the Principia.There was no use of acceleration, or even of velocity, in this computation, despite innumerable popular accounts which have described it as measuring the acceleration due to gravity (Kollerstrom, 1991). That is how it would be done nowadays, but the text does not allude to such.

This calculation alluded four times to the Dutch natural philosopher Christiaan Huygens -- partly for his estimation of freefall's magnitude (the distance fallen in one second on the Earth's surface) as he derived it from experiments with pendulum clocks. Despite this Huygens later produced an account concerning his dismissal of Newton's gravity theory!

Huygens, circa 1680A Durable Myth

As everyone knows, claims were made that this computation had been attempted in the 1660s, and not until the researches of Tom Whiteside were historians able to escape from the ruinous clutches of this illusion. Earlier writers had puzzled over a supposed delay of nearly twenty-years, between the discovery of the law of gravity in or around the year 1666 and its first reported use in the years 1684-5. Let's quote from Whiteside's bold declaration, as it has (I suggest) exerted a greater influence upon Newton-studies in modern times, than any other single factor.

The implications of this claim were far-reaching, as discussed eg in Bernard Cohen's book on the subject: As Cohen observed, these accounts were made up between 1715 and 1718, 'when he [Newton] was deep in controversy about questions of method and of priority in discovery.' Rene Descartes had taught that the Moon was carried round the Earth in an ether-vortex, and his 'Cartesian' physics was what Newton had learnt at Cambridge. It worked by pushes rather than pulls, whereby the Moon overhead transmitted a downward pressure upon the Earth, via the ether-vortex. The Principia's Book Two demolished vortices lock, stock and barrel (though it took the French the best part of a century to appreciate the fact).

Newton's last indication of belief in the terrestrial vortex came in letters of 1681, in correspondence with the theologian Thomas Burnett, while the latter was composing his Sacred Theory of the Earth. Newton was concerned to explain 'ye causes of ye hills.' Over the ages, he explained, pressure exerted by 'ye pressure of ye vortex or of ye Moon' had tended to round out the hills and valleys of Earth (Correspondence). Newton's belief in vortices was only finally knocked out of him by the comet of 1682, known to posterity as 'Halley's comet' - but, that's another story.

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998