Three hundred years ago in 1692, an article by Edmond Halley proposed that the Earth was hollow. Its theory was based on the value of lunar relative density given by Isaac Newton.
The first edition of Newton’s Principia (1687) found that “... the mass of the Moon will be to the mass of the Earth as 1 to 26, approximately”, citing the relative densities of Moon to Earth as 9 to 5.
This value of lunar relative mass was in excess by a factor of three, as the true mass ratio is 1:81. Arguably the most significant error in the Principia’s Book III, it left an ultra-dense Moon circling our Earth.
Edmond Halley simply invoked these figures: “Sir Isaac Newton has demonstrated the Moon to be more solid than our Earth, as 9 to 5; why may we not then suppose four ninths of our globe to be cavity?” It is remarkable that so erroneous a figure, having such unlikely implications, could be thus presented without need for further justification.
Halley’s theory appeared as the first significant deduction to be drawn from the Principia.
Newton’s estimate of lunar relative density was derived from the relative tideraising powers of the Sun and Moon.
The Principia had ascertained fairly well the relative density of the Sun, as a quarter that of the Earth (Book III, Prop. 37, Cor. 3), and so by comparing the components of tidal attraction of the two luminaries the lunar relative density was thereby inferred.
This was a quite valid method, as shown by the way that French theoretical astronomers used it in the mid-eighteenth century to obtain their estimates of lunar relative mass.
However, the Principia’s treatment thereof went greatly astray.
It started from the difference between spring and neap tides which occurred twice each month, taking data from Plymouth and in the Bristol channel that gave that ratio as 41 to 23, or 9 to 5.
Newton apprehended (in Proposition 37) that the tide-raising forces of the Sun and Moon varied inversely as the cube of their distances from Earth: only thus would the Moon have a stronger attraction for the tides than the Sun.
It was evident to Newton that the solar gravity pull (varying inversely as the square of the distance) was several hundred times stronger than that of the Moon, whatever assumptions about relative densities were made.
The Principia’s tidal argument hinged upon this inverse-cube relationship, with little by way of demonstration.
Its method of inferring lunar relative density from such considerations would have baffled his contemporaries.
Astronomy textbooks by Newtonians such as Whiston and Gregory in the early eighteenth century omitted this argument, for they had no means of following it.
The Principia formulated the equation (S+L)/(S-L) = 9/5, where S and L were tide-raising vectors varying inversely as the cube of distance.
Newton apprehended that the ratio involved differentials or gravity field gradients across the Earth and not the forces as such; and that these would sum to maximum values at both the full and new moon positions, but subtract as vectors when the forces were at right angles to each other, that is, at the quadrature positions.
This is all quite impressive, and solving the above equation would have given him L:S = 3.5:1, far less disastrous than his final result.
For comparison, the astronomically correct ratio of the tide-raising powers of the Moon and Sun is 2.17:1, though we may note that the mean value of this ratio around the shores of Britain is slightly over three to one, as the extent to which the solar (12 hour) and lunar (12.4 hour) diurnal rhythms resonate in the sea varies with local geography.
It was glowing, glowing, glowing
Glowing in the dark
It was sparkling, sparkling, sparkling
Sparking in the night
I took the law & threw it away
Cause there's nothing wrong
It's just for play
There's no law, no law anymore
I want to steal from the rich and
Give to the poor
Winter turns to summer
Sadness turns to fun
Keep the faith, baby
You broke the rules and won
Sha-la-la-la
Instead of solving this equation, Newton inserted various adjustments, of somewhat doubtful astronomical significance, bringing the L:S ratio to 6.3:1. In the Principia’s second edition of 1713, the computation was emended to give an Earth/Moon mass ratio of 39.371 to 1, which became in the third edition 39.788 to 1, thereby reducing its lunar mass estimate to merely 100% in excess of the correct value.
From this estimate the second edition obtained a baricentre position (i.e. common centre of gravity of the Earth-Moon system), misplacing it as permanently outside the Earth.
Scholars normally refer only to the second and third editions in the context of lunar theory, and I have found no mention of the first edition’s 1:26 Moon/Earth mass ratio estimate in the literature.
But developments after the first edition were not used by Halley in his advocacy of a hollow Earth, and we will not refer to them in what follows.
Halley viewed Newton’s tidal theory as one of the finest achievements of the Principia’s first edition, as the two reviews he wrote for it make clear.
If you're really interested in journeying down the path of anti-establishment insanity & need solid ground to stand on, take a couple thermometers out tonight and measure the moon light were it impacts the earth vs. where the moon light is shaded.
Once you go black, ya don't go back.
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