JONATHAN SWIFT

AND THE

REMARKABLE MOONS OF MARS

In order to ensure the celestial context of his Flying Saucer, Swift was given information which would make any thoughtful person reflect seriously on the significance of his revelation.
 

The occupants of that seraphic craft told him about two peculiar moons orbiting the planet Mars. As Swift put it:
 

They have likewise discovered two lesser stars, or satellites, which revolve about Mars, whereof the innermost is distant from the center of the primary planet 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 an half; so that the squares of their periodical times are very near in the same proportion with the cubes of their distance from the center of Mars, which evidently shows them to be governed by the same law of gravitation, that influences the other heavenly bodies. 

From the Voyage to Laputa, 

Part Three of Four Parts 

Travels into Several Remote Nations of the World 

 

This is one of the most famous, curious, and precise predictions in the annals of science.
 

The amazing nature of the prediction is contained in the fact that the two satellites of Mars were not known to the world for another one hundred and fifty years. They were not discovered until Asaph Hall saw them through the 26-inch refracting telescope at the Naval Observatory in Washington, DC in 1877.
 

Because of their very small size no earth-bound telescopes existed large enough to see them until 1848, when the 26-inch was built. It had sufficient light gathering power, and magnification to make such discovery.
 

Swift's prediction of the two Martian moons is so startling the scholarly and scientific worlds sought ways to deny its significance. The unique nature of the satellites is found in the words of William Sheehan in "The Planet Mars," the Univesity of Arizona Press, Tucson, 1996.
 

Swift's prediction is surprising in that he not only had the number of moons right, but he also placed them close to the planet - the distances of the actual Martian moons are 1.4 and 3.5 diameters (2.8 and 7.0 radii) of Mars, compared with 3 and 5 as given by Swift. One would almost be tempted to think that Swift obtained an actual glimpse of the moons through a telescope, were it not for the fact that there was no telescope at the time anywhere close to being powerful enough to show them. 

. . . After the proper discovery of the satellites by Asaph Hall in August 1877, it was immediately apparent that they were highly unusual objects. Phobos lies at a distance of 9,400 kilometers from the center of Mars, or only 6,000 kilometers from the Martian surface. (Mars as seen from Phobos would be an astounding sight; its disk would subtend an angle of 43o, and it would fill nearly half the sky from horizon to zenith!) The present period of revolution of Phobos around Mars is only seven hours and thirty-nine minutes. Thus it completes three full revolutions in the time that Mars takes to rotate once on its axis - a state of affairs so surprising that Hall at first thought there must be two or three inner moons! Owing to its rapid motion, Phobos rises in the west and sets in the east, and it remains above the horizon for only four and a half hours at a time. 
 

Because its orbital inclination is only about 1o, Phobos, for all practical purposes, lies in the equatorial plane of the planet. It is eclipsed by the planet's shadow 1,330 times every Martian year, managing to escape only for brief periods around the times of the summer and winter solstice. Observers on the Martian surface above 70o north and south latitude would never catch sight of it at all, since it would never clear the horizon.

 

During the intervening one-hundred and fifty years Swift's account of the two satellites was regarded purely as fiction. The Travels were satire; few believed Swift's stories were more than that. When Hall discovered the satellites many astronomers quickly realized Swift's remarkable prediction. Some believed Swift had been divinely inspired. Others, like Camille Flammarion, the eminent French astronomer, referred to it as "second sight," and asserted that the prophets of many religions had been far less accurate. But for most the prediction was shrugged off as a lucky guess.
 

In order to understand the attitude of the scientific and scholarly community it is necessary to review the background of the Martian satellites.
 

Their astronomical names, assigned by Asaph Hall, are Phobos for the inner satellite and Deimos for the outer. Curiously, Hall obtained these names from Greek myths for the two steeds pulling the chariot of Aries, the Greek name and god for the planet Mars. Literally they mean "Fear" and "Terror." Our word "phobia" comes from the Greek root which provides Phobos, and our word "demon" comes from a Greek root which also provides Deimos. Why did the Greeks believe the planet Mars had two steeds? Did they have knowledge handed down from ancient times but lost to historic record? We do not know. In seeking names for the satellites Hall advertised his discovery and asked for suggestions. A female correspondent, who knew the Greek myths, pointed out this fact, and Hall thereupon gave the two satellites their current names.
 

The idea that Swift made a lucky guess is based on the arrangement of the planetary satellites in the solar system. Galileo had discovered four satellites around Jupiter in 1610. Cassini had discovered five satellites around Saturn in the period from 1671 to 1684. Except for the Earth moon no other satellites were known in Swift's day. Therefore, as one proceeds outward from the sun, Mercury and Venus had no satellites; 

earth had one; Jupiter, next in line beyond Mars, was known to have four; Saturn was known to have five. If one takes this sequence and interpolates a number for Mars one should choose two or three. Astronomers believed Swift selected two and thus made his lucky guess.
 

But Swift was not the first to assign two satellites to Mars. Kepler, the famous astronomer, suggested it in a letter to Galileo in the year 1610, shortly after Galileo made announcement of his discovery of the satellites of Jupiter.
 

"I am so far from disbelieving the four circumjovial planets, that I long for a telescope to anticipate you, if possible, in discovering two round Mars, as the proportion seems to require, six or eight round Saturn, and perhaps one each round Mercury and Venus."

 

(For sources see Marjorie Nicolson's paper on "The Telescope and Imagination," in "Science and Imagination," Great Seal Books, Cornell University, Ithaca, 1956.)
 

Obviously, Swift was not original in assigning two satellites to the planet Mars. He easily could have borrowed the idea from Kepler or from other sources.
 

Superficially the assignment of guess-work to Swift seems reasonable. But closer examination of his description reveals a number of factors which give serious pause.
 

1) He is scientifically precise. Why would a clergyman and writer, a layman in scientific circles, use such exact phrasing in a work of fiction? Even if we grant that his account is a satire on science, he could have satirised in a far less precise manner.
 

2) He gives explicit values for the orbital periods. Why would he expose himself to ridicule by providing exact numbers?
 

3) He also gives explicit values for orbital radii. Why would he double his jeopardy in making such assignments?
 

4) He expresses the Keplerian law of planetary motions to indicate their precise behavior. No informed scientific reader could easily miss that precision. It seems as though he is inviting close examination of his numbers. Why would he do so if it is a mere fiction out of his head? Why would he invite scientific scrutiny?

5) The orbital periods given by Swift are considerably below the periods for satellites known in his day. He obviously was familiar with the Keplerian laws, and therefore it does not seem reasonable that he would be ignorant of the satellite periods measured by Galileo and Cassini. Why would he give numbers strikingly below the range of known values?
 

6) Hall's measurements of the satellite periods showed that Swift was uncomfortably close to the actual values. This fact, coupled with the previous fact, created a disturbing realization that Swift was doing more than inventing numbers.

 

The remarkable nature of the satellite prediction has continued to bother the modern scientific and scholarly community, but always their response has been one of disbelief. Carl Sagan, the famous modern astronomer, remarked that Swift's prediction was "uncanny." Nicolson and Mohler in "The Scientific Background of Swift's Voyage to Laputa," also were struck by this uncanny prediction.
 

"They (the Laputans) have made important discoveries with their telescopes, none more remarkable than that of the two satellites of Mars - which actually remained hidden from all eyes but those of the Laputans until 1877!"

 

Emile Pons, a French authority on Swift and editor of a Paris edition of "Gulliver's Travels," paid particular attention to this remarkable prediction, pointing out not only the agreement in the number of satellites but also the close agreement with the orbital periods measured by Hall in 1877. Nicolson and Mohler included a note in their paper remarking on Pons' belief that Swift had "second sight." However, they seemed unperturbed by the remarkable coincidence, maintaining that it was merely a "happy guess."
 

"It was inevitable that many writers, scientists and laymen, should have raised the question of the satellites of Mars. Our own planet was known to have one satellite; Galileo had discovered four about Jupiter; in Swift's time Cassini had published his conclusion in regard to the five satellites of Saturn. Swift, using no telescope but his imagination, chose two for Mars, the smallest number by which he could easily indicate their obedience to Kepler's laws, a necessity clearly shown him by Cassini; this number fits neatly between the one satellite of the earth and the four of Jupiter. To indicate the Keplerian ratio, he has made one of the simplest assumptions concerning distances and period, that of 3:5 for the distances, and 10 for the period of the inner satellite. It was not a difficult computation, even for a Swift, who was no mathematician, to work out the necessary period of the outer satellite, (3 cubed : 5 cubed = 10 squared : X squared). His trick proved approximately correct - though it might easily have been incorrect."

 

In making this assessment Nicolson and Mohler reduced the remarkable nature of the prediction to simple computation of numbers designed to satisfy the Keplerian ratio. They ignored the significance of Swift's precise scientific wording, Swift's unusual orbital periods much below the range of known values, and his striking proximity to the values measured by Hall. They saw that his numbers were simple 3, 5 and 10, and hence appeared to be mere "happy guesses" to ease Swift's computation.

The following figure illustrates the unusual nature of Swift's prediction.


 


 

The satellites of Earth, Mars, Jupiter and Saturn are shown with the orbital periods known in Swift's day, except for Mars. For the last I show the periods given by Swift together with the periods later measured by Hall. None of the planetary satellites known to astronomers at that time had orbits faster than the rotation period of the respective planets. Jupiter rotates in 9.8 hours; Saturn in 10.2 hours. The fastest orbital periods known were 42.5 hours for Jupiter's Io, and 45.3 hours for Saturn's Tethys. But Swift made both satellite periods much shorter than

the satellites of the other planets. In addition, both periods were shorter than the rotation period of Mars, a relationship which would not be acceptable to men like Newton who was still alive when Swift published the Travels. This unusual feature, later confirmed by Hall's discovery, is the reason Swift's prediction was so surprising and so disturbing.
 

The second figure shows these relationship with the scale expanded to exhibit Swift's periods more clearly.

 

 

The fact of these fast orbital periods continued to plague the scientific community. Other scientists were dissatisfied with the cursory treatment given by Nicolson and Mohler. S. H. Gould, in the "Journal of the History of Ideas," Vol 6 for 1945, pages 91-101, discussed "Gulliver and the Moons of Mars." He emphasized that Swift's orbital periods were much shorter than we would expect if merely from Swift's imagination. But to show that Swift was merely guessing he looked elsewhere for denial.
 

Gould investigated the planetary mass and the value necessary for Swift to provide such orbits. He showed that Swift was in great error on the mass and density for Mars, and therefore did, indeed, merely make a lucky guess. He thus wrote Swift off. Unfortunately, Gould also made a fundamental error.
 

In order to understand Gould's approach we must examine the history of the development of satellite equations, and Sir Isaac Newton's contribution to our understanding of the laws of

planetary motion. Kepler, using the wealth of accumulated observations he had inherited from Tycho Brahe, devised the relationship between the square of the orbital periods and the cube of the distance from the center of the planetary body. This explained how planets move around the sun, and satellites around the planets, but it did not provide information on the densities or the masses of the respective bodies. Mathematically it is written as follows:

 

p 2 = k r 3
 

where "p" is the orbital period, "k" is the Keplerian ratio, and "r" is the distance of the satellite from the center of the planet in planetary radii (normalized radii).
 

For reader convenience, the following table shows the planet and satellite values for the Moon, and two satellites each of Mars, Jupiter and Saturn.

 

 

Planet

Satellite Distance 
From 
Planet 
(km)

Ratio of 
Satellite Distance 
to Planet Radius 
(r)

Period 
in 
Hours 
(p)

(r)3

(p)2

Kepler's 
Ratio**

Gould's 
"K" 
Ratio

Earth

6,378 km radius

Moon

384,400.00

60.27

655.00

218,929.14

429,025.00

1.96

15.68

 

Mars

3,398 km radius 

Phobos

9,380.00

2.76

7.65

21.02

58.52

2.78

22.27

Deimos

23,500.00

6.92

30.30

331.37

918.09

2.77

22.16

 

Swift Mars

 

Phobos

 

3.00

10.00

27.00

100.00

3.70

29.63

Deimos

 

5.00

21.50

125.00

462.25

3.70

29.58

 

Jupiter

71,398 km radius 

Io

422,600.00

5.92

42.50

207.47

1,806.25

8.71

69.65

Europa

670,900.00

9.40

85.20

830.58

7,259.04

8.74

69.92

 

Saturn

60,330 km radius

Tethys

294,670.00

4.88

45.30

116.21

2,052.09

17.66

141.26

Dione

377,420.00

6.26

65.70

245.31

4,316.49

17.60

140.77

**For reader convenience this ratio is given without reconciliation of absolute quantities.


 

From Galileo's and Cassini's measurements Kepler's ratio was known to be constant for each satellite around the mother planet, but different from planet to planet. This may be seen in the Table.
 

Newton reasoned that K contained a value for the planetary mass, or was a measure of how much the planet pulled on the respective satellites to keep them in orbit around the parent body. Newton also reasoned that when the Solar System was being formed a primeval solar mass went into circular rotation, spewing out fragments of matter into a spiral pattern which later condensed into the several planets, thus providing a mechanism which keeps them moving in the ecliptic plane yet today. Newton reasoned further that the heavier elements would fly away from the sun less than the lighter elements, and therefore, that planets closer to the sun would be more dense. As one moved away from the sun the planets would become successively less dense. From this line of reasoning Newton then developed his concept of a universal gravitational constant, and a more rigorous equation for the satellite motions, involving the mathematical constant "Pi," the density of the planet, "m," and the gravitational constant, "G." This refined equation is written as follows:
 

p 2 = (4 Pi 2 / G m ) r 3
 

Returning to the first equation, Gould, recognizing the precise scientific nature of Swift's satellite numbers, proposed that Swift should give ratios which would fit with Newton's scheme of successively smaller densities as we proceed outward from the sun. If he used Swift's terminology he could calculate the values of "k" for Jupiter and Saturn, and thus test Swift's density (mass) values for Mars. In his words:
 

We may illustrate from the tables of Jupiter at the beginning of the second book of the "Principia." Adopting Swift's phaseology we have: "the innermost satellite is distant from the center of Jupiter two and five-sixths of his diameters and the second four and a half; the former revolves in the space of forty-two and a half hours, and the latter in eighty-five and a quarter." For the first moon we therefore divide the cube of two and five-sixth by the square of forty-two and a half. The result is almost exactly equal to one-eightieth. For the second moon we divide the cube of four and a half by the square of eighty-five and a quarter; this again, as expected, gives one-eightieth . . . Thus Kepler's ratio for Jupiter, which we may call the Jupiter-ratio, is equal to one-eightieth.

Gould was being fair with Swift by using the numbers known to Swift from Newton's "Principia," which differ somewhat from the values we know today. The above Table shows values calculated from current knowledge.
 

But Gould's reasoning contained an elemental flaw. He was tricked by Swift's verbal method of description. He took that method and applied it to the satellites of Jupiter and Saturn. The trick was in use of the word "diameters" rather than "radii."
 

To calculate Kepler's ratio, using diameters rather than radii, Gould divided the orbital radii by two. (He used Swift's radii directly.) Thus he changed Newton's 5 2/3 for Io to 2 5/6, and Newton's 9 for Europa to 4 ½. This then gave him a ratio eight times the true value. (23 = 8.) Therefore, when he calculated the value for Mars he found the mass of Mars to be twenty-two times as great as that of Jupiter. (3.7/80 = 1/22.) This was so far beyond Newton's theorized values Gould concluded that the numbers had to be wild speculation.
 

Newton had proposed that Mars should be about three times more dense than Jupiter. Gould reasoned that if Swift were attempting to stay within the range specified from Newton's theory he would have provided suitable numbers. Because of his use of diameters rather than radii, Gould concluded that Swift was merely dabbling with the numbers and could not have known the true values for Mars.
 

Gould was off by a factor of eight. Swift's density for Mars does, indeed, fall between the values for Earth and Jupiter if one uses radii instead of diameters. Using my method of normalized orbital radii and hours the "k" value is 3.7. This is not the actual value of 2.7 but very close.
 

Swift is vindicated. The density for Mars provided by his numbers is 2.36 times the density for Jupiter, not 22 times.
 

To show how clever Swift was in his description, I plotted the satellite periods and orbital radii on logarithmic scales. The slope of the lines is 2/3 which, in logarithms, expresses the ratio of a square to a cube. While this is intended for more technical readers it shows how close Swift actually came to the proper density for Mars. The position of the lines on the chart are dependent upon the relative densities, with the Earth to the left, Jupiter to the right and Saturn still further to the right. The astronomically correct line for Mars is shown, together with the line determined by Swift's radii values. It can be seen that Swift was doing far more than dabbling with numbers.

 

 

 

The values assumed by Gould are shown in the line separated far above the others. Obviously, Swift misled Gould and countless others by his use of "diameters."
 

At this point the reader is in a position to weigh Swift's prediction. Could Swift have guessed satellite orbits and planetary density so close to the actual values, in violation of, and beyond, knowledge current at the time? In reviewing the history of analysis of Swift's prediction one cannot help but be amazed how the human mind avoids implications it would rather not contemplate. Sagan believed Swift was uncanny in his prediction but did not investigate his context; Nicolson and Mohler avoided a penetrating analysis; Gould entered a deeper analysis but made an elementary false assumption. A most curious chain of circumstances has contributed to a continuing blindness of Swift's prediction.
 

I am especially surprised that no astronomer has published a similar analysis, with the graphical plot I show. Had they done so, they would have quickly identified Swift's "trick."
 

I shall now examine how Swift may have calculated his numbers. His reason for changing them from radii to diameters is the same as it was for the Flying Saucer. He could not take the risk of exposing himself for his personal safety. The evidence shows that Swift had to know both Kepler's laws of planetary motion and Newton's law of gravitation to provide precise numbers for proper orbital relationships and proper planetary density.
 

In arriving at his numbers Swift was constrained by something mathematicians call degrees of freedom. Swift obviously was astute enough to obey this constraint. He had the following freedom of choices:
 

1. Two satellite periods and the K factor.
 

2. Two satellite orbital radii and the K factor.
 

3. One satellite period, the K factor, and the other satellite orbital radius.
 

4. Two satellite periods and one orbital radius.
 

5. Two orbital radii and one satellite period. (The condition assumed by Nicolson and Mohler.)
 

If he chose values for both the orbital period and radius of Phobos, his K value became fixed. If he chose another value for the period of Deimos then the orbital radius was determined by the K value previously calculated for Phobos.
 

Let's assume he selected the periods as the easiest parameter to manipulate. Then he could choose a K factor suitable to his plan. (Choice #1.) From those selections his orbital radii would be determined.
 

Examination of Swift's numbers shows that the period for Phobos is 30% higher than the astronomical value. 7.65 hours X (1 + 0.3) = 9.95 hours. This value is amazingly close to the period of 10 hours Swift used, within 0.5%. Further examination shows that the period for Deimos is 30% lower than the astronomical value. 30.3 hours X (1 - 0.3) = 21.2 hours. This value again is amazingly close to the period of 21.5 hours Swift used, within 1.5%. Swift had a choice remaining. If we assume he selected the K factor we find that his value of 3.7 differs from the astronomical value of 2.78 by 25%: 3.7 X (1 - 0.25) = 2.78.
 

The remarkable result is seen in the rounded nature of the orbital radii if we assume Swift made these easy changes in the periods and the K factor. The cubes of the orbital radii are equal to the product of the square of the periods and the reciprocal of the K factor: R cubed = (1/K) X P squared.
 

If Swift chose 3.7 for K, and 10 hours for Phobos then R cubed is 27. The cube root of 27 is simply 3.

If Swift used 21.5 hours for Deimos then R cubed is 21.5 squared X 1/3.7 = 462.25 X .27 = 124.8 or 125 within less than 0.2%. The cube root of 125 is simply 5.

 

The amazing aspect is not that Swift manipulated the numbers so easily, but that they rounded off so neatly. We cannot help but wonder how he must have played with the values to find such neat numbers.
 

However, another possibility must be considered. The altered numbers could have been given to him directly by the craft operators, rather than real numbers which he later manipulated. They may have been as much concerned for his personal safety as he. Swift may never have known the actual values, but accepted the numbers he was given, probably with the assurance he could publish them safely.
 

In order to understand the nature of his prediction we must put it into context. We cannot isolate his description of the Martian moons from his account of the Flying Island. When he begins his discussion of the satellites he says "They have likewise discovered..." "They" are the occupants of the Flying Island. "They" told Swift about the two Martian satellites. Swift did not invent the numbers; he was given the numbers by occupants of a seraphic craft which was alien to this world, a perfect saucer-shaped object, which could hover in the air, and go into progressive motion as "they" pleased.
 

From this examination we can see why Swift was using a satirical context for his story.
 

We must consider the social conditions. A good portion of world population today rejects reports of flying objects, or that they are intelligently controlled by beings who come to this earth from other places in the universe. Most individuals today hesitate to admit that they have seen strange craft in the sky. How then with Swift? Would not a description presented as serious truth have done him irreparable damage? Would any contemporary person accept such utter nonsense? They would have considered him deranged. Therefore, he could not report these experiences as actual fact. He could not discourse in any serious way.
 

But if this were an actual experience, what psychological pressure would he have been under? Would he not have been profoundly changed in his attitudes and in his feelings after such an experience? Would this not have produced a deep desire to make it known in some way? Would he not have been greatly frustrated by the limitations of the social context and of the fearful consequences of revelation? Given that he would have a overpowering urge to make such things known, and yet fearful of his life, what would he do? Satire, a mode of writing in which he was expert, would serve as an excellent vehicle of expression. He could write about many things, and yet have it appear as a fiction. There would be no danger if he handled it properly. But suppose he gave exact values for the orbits of the Martian moons. Would that not place him in social jeopardy? If they had been discovered in his lifetime it would immediately become known that he knew the exact values. It could not have produced anything but extremely difficulty for him, even to the point of being accused as an agent of the Devil. It was better to obscure the numbers.
 

On the other hand one might argue that "they" were able to perceive social and scientific developments. Then the numbers would reflect some other concern for inadvertent discovery. Perhaps "they" wanted the numbers to remain obscure until a more appropriate time of discovery. Perhaps the numbers were intended to be an integral part of the revelation of the Flying Island. Then the nature of the numbers takes on an altogether different cast.
 

We should not neglect this possibility. We should take serious regard for the intelligence and foresight of beings who come here from the heavens.