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Swift, the Galileo Code and the Moons of Mars
From The Gulliver Code
- a Catalogue of ten Thousand fixed Stars, whereas the largest of ours do not contain above one third Part of that Number. They have likewise discovered two lesser stars, or satellites, which revolve around Mars, whereof the innermost is distant from the center of the primary exactly three of his diameters, and the outermost five: the former revolves in the space of ten hours, and the latter in twenty-one and a half, so that the squares of their periodical times are very near in the same proportion with the cubes of their distances from the center of Mars; which evidently shews them to be governed by the same Law of Gravitation that influences the other heavenly bodies.
Some cult literature has sprung up to address how Swift could have known about the Martian moons, since they weren't discovered until 1877. Some have suggested that Swift himself was a Martian!
In reality, the idea that Mars might have two satellites goes back to Johannes Kepler's 1610 memoir, in which he misconstrued Galileo's anagram to his friends announcing his discovery of Saturn's rings. The anagram was:
s m a i s m r m i l m e p o e t a l e u m i b u n e n u g t t a u i r a s
the correct solution of which was:
Altissimum planetam tergeminum observavi. "I have observed the highest (most distant) planet [Saturn] to have a triple form."
Kepler, a born riddle solver, made strenuous efforts to decipher Galileo's string of characters, but he misconstrued the scrambled message to mean:
Salue umbistineum geminatum Martia proles. "Hail, twin companionship, children of Mars", or "I greet you, double knob, children of Mars".
When Kepler originally learned of Jupiter's four moons, and compared this with the Earth's one Moon, he had already predicted from mathematical progression that Mars must have two moons (by the geometrical progression 1,2,4...). Now Kepler surmised that Galileo had discovered two Martian moons exactly as he had predicted!
It is highly likely that Swift's close friend Dr. John Arbuthnot knew about Kepler's speculations, and did some calculations of his own, which he passed on to Swift. Arbuthnot was involved deeply with the Royal Society and allied with Newton and Halley in their project to publish the Historia coelestius of John Flamsteed, the Royal Astronomer, against his objection that the work was not finished.
Since no Martian moons had been found by the early eighteeth century, Arbuthnot probably assumed that they must be very small, very close to the planet, or both. Clearly, he was familiar with Kepler's third law, so he knew the orbital periods T and radii R needed to give the same value of R^3/T^2. To give the results in round numbers he needed to solve the diophantine equation (at least approximately)
R1^3 T2^2 = R2^3 T1^2
Since 21.5 is 43/2, his solution reduces to the fact that (5^3)(20^2) = 50000 is nearly equal to (3^3)(43^2) = 49923.
Gulliver's fictional moons turned out to be surprisingly like their real counterparts. When Asaph Hall discovered the two Martian moons, Phobos and Deimos, at the US Naval Observatory in 1877, using a telescope hundreds of times more powerful than Galileo's, their orbits proved to be quite similar to those described in Swift's novel. The inner one Hall called Phobos (Fear) and the outer Deimos (Terror), after the horses that drew the chariot of Mars in mythology. The distances of these from the center of Mars are 2.743 and 6.891 times the radius of Mars, respectively, and the periods of revolution about Mars are 7 hr, 39 min, and 30 hr, 17 minutes.
These orbital periods are roughly similar to those guessed by Swift/Arbuthnot, but the radii were too big by about a factor of two. As a result, the mass of Mars that one would infer from Swift's data is about (3.86)10^24 kg, which is roughly 64% of the EARTH's mass, whereas the actual mass of Mars is only (6.43)10^23 kg, which is almost exactly 1/6 the mass "predicted" by Gulliver's Laputans.
Copyright © Alastair Sweeny. All Rights Reserved
