by Carl Sagan
To escape from Jupiter, such a comet must have a kinetic energy of ½ mv.2, where m is the cometary mass and v. is the escape velocity from Jupiter, which is about 60 km/sec. Whatever the ejection event—volcanoes or collisions—some significant fraction, at least 10 percent, of this kinetic energy will go into heating the comet. The minimum kinetic energy per unit mass ejected is then ¼ v.2 = 1.3 × 1012 ergs per gram, and the quantity that goes into heating is more than 2.5 × 1012 erg/gram. The latent heat of fusion of rock is about 4 × 109 ergs per gram. This is the heat that must be applied to convert hot solid rock near the melting point into a fluid lava. About 1011 ergs/gm must be applied to raise rocks at low temperatures to their melting point. Thus, any event that ejected a comet or a planet from Jupiter would have brought it to a temperature of at least several thousands of degrees, and whether composed of rocks, ices or organic compounds, would have completely melted it. It is even possible that it would have been entirely reduced to a rain of self-gravitating small dust particles and atoms, which does not describe the planet Venus particularly well. (Incidentally, this would appear to be a good Velikovskian argument for the high temperature of the surface of Venus, but, as described below, this is not his argument.)
Another problem is that the escape velocity from the Sun’s gravity at the distance of Jupiter is about 20 km/sec. The ejection mechanism from Jupiter does not, of course, know this. Thus, if the comet leaves Jupiter at velocities less than about 60 km/sec, the comet will fall back to Jupiter; if greater than about [(20)2 + (60)2]1/2 = 63 km/sec, it will escape from the solar system. There is only a narrow and therefore unlikely range of velocities consistent with Velikovsky’s hypothesis.
A further problem is that the mass of Venus is very large—more than 5 × 1027 grams, or possibly larger originally, on Velikovsky’s hypothesis, before it passed close to the Sun. The total kinetic energy required to propel Venus to Jovian escape velocity is then easily calculated to be on the order of 1041 ergs, which is equivalent to all the energy radiated by the Sun to space in an entire year, and one hundred million times more powerful than the largest solar flare ever observed. We are asked to believe, without any further evidence or discussion, an ejection event vastly more powerful than anything on the Sun, which is a far more energetic object than Jupiter.
Any process that makes large objects makes more small objects. This is especially true in a situation dominated by collisions, as in Velikovsky’s hypothesis. Here the comminution physics is well known and a particle one-tenth as large as our biggest particle should be a hundred or a thousand times more abundant. Indeed, Velikovsky has stones falling from the skies in the wake of his hypothesized planetary encounters, and imagines Venus and Mars trailing swarms of boulders; the Mars swarm, he says, led to the destruction of the armies of Sennacherib. But if this is true, if we had near-collisions with objects of planetary mass only thousands of years ago, we should have been bombarded by objects of lunar mass hundreds of years ago; and bombardment by objects that can make craters a mile or so across should be happening every second Tuesday. Yet there is no sign, on either the Earth or the Moon, of frequent recent collisions with such lower mass objects. Instead, the few objects that, as a steady-state population, are moving in orbits that might collide with the Moon are just adequate, over geological time, to explain the number of craters observed on the lunar maria. The absence of a great many small objects with orbits crossing the orbit of the Earth is another fundamental objection to Velikovsky’s basic thesis.
PROBLEM II
REPEATED COLLISIONS AMONG
THE EARTH, VENUS AND MARS
“THAT A COMET may strike our planet is not very probable, but the idea is not absurd” (page 40.) This is precisely correct: it remains only to calculate the probabilities, which Velikovsky has unfortunately left undone.
Fortunately, the relevant physics is extremely simple and can be performed to order of magnitude even without any consideration of gravitation. Objects on highly eccentric orbits, traveling from the vicinity of Jupiter to the vicinity of the Earth, are traveling at such high speeds that their mutual gravitational attraction to the object with which they are about to have a grazing collision plays a negligible role in determining the trajectory. The calculation is performed in Appendix 1, where we see that a single “comet” with aphelion (far point from the Sun) near the orbit of Jupiter and perihelion (near point to the Sun) inside the orbit of Venus should take at least 30 million years before it impacts the Earth. We also find in Appendix 1 that if the object is a member of the currently observed family of objects on such trajectories, the lifetime against collision exceeds the age of the solar system.
But let us take the number 30 million years to give the maximum quantitative bias in favor of Velikovsky. Therefore, the odds against a collision with the Earth in any given year is 3 × 107 to 1; the odds against it in any given millennium are 30,000 to 1. But Velikovsky has (see, e.g., page 388) not one but five or six near-collisions among Venus, Mars and the Earth—all of which seem to be statistically independent events; that is, by his own account, there does not seem to be a regular set of grazing collisions determined by the relative orbital periods of the three planets. (If there were, we would have to ask the probability that so remarkable a play in the game of planetary billiards could arise within Velikovsky’s time constraints.) If the probabilities are independent, then the joint probability of five such encounters in the same millennium is on the short side of (3 × 107/108)−5 = (3 × 104)−5 = 4.1 × 10−23, or almost 100 billion trillion to 1 odds. For six encounters in the same millennium the odds rise to (3 × 107/103)−6 = (3 × 104)−6 = 7.3 × 10−28, or about a trillion quadrillion to 1 odds. Actually, these are lower limits—both for the reason given above and because close encounters with Jupiter are likely to eject the impacting object out of the solar system altogether, rather as Jupiter ejected the Pioneer 10 spacecraft. These odds are a proper calibration of the validity of Velikovsky’s hypothesis, even if there were no other difficulties with it. Hypotheses with such small odds in their favor are usually said to be untenable. With the other problems mentioned both above and below, the probability that the full thesis of Worlds in Collision is correct becomes negligible.
PROBLEM III
THE EARTH’S ROTATION
MUCH OF THE indignation directed toward Worlds in Collision seems to have arisen from Velikovsky’s interpretation of the story of Joshua and related legends as implying that the Earth’s rotation was once braked to a halt. The image that the most outraged protesters seem to have had in mind is that in the movie version of H. G. Wells’s story “The Man Who Could Work Miracles”: The Earth is miraculously stopped from rotating but, through an oversight, no provision is made for objects that are not nailed down, which then continue moving at their usual rate and therefore fly off the Earth at a speed of 1,000 miles per hour. But it is easy to see (Appendix 2) that a gradual deceleration of the Earth’s rotation at 10−2g or so could occur in a period of much less than a day. Then no one would fly off, and even stalactites and other delicate geomorphological forms could survive. Likewise, we see in Appendix 2 that the energy required to brake the Earth is not enough to melt it, although it would result in a noticeable increase in temperature: the oceans would have been raised to the boiling point of water, an event that seems to have been overlooked by Velikovsky’s ancient sources.
These are, however, not the most serious objections to Velikovsky’s exegesis of Joshua. Perhaps the most serious is at the other end: How does the Earth get started up again, rotating at approximately the same rate of spin? The Earth cannot do it by itself, because of the law of the conservation of angular momentum. Velikovsky does not even seem to be aware that this is a problem.
Nor is there any hint that braking the Earth to a “halt” by cometary collision is any less likely than any other resulting spin. In fact, the chance of precisely canceling the Earth’s rotational angular momentum in a cometary encounter is tiny; and the probabili
ty that subsequent encounters, were they to occur, would start the Earth spinning again even approximately once every twenty-four hours is tiny squared.
Velikovsky is vague about the mechanism that is supposed to have braked the Earth’s rotation. Perhaps it is tidal gravitational; perhaps it is magnetic. Both of these fields produce forces that decline very rapidly with distance. While gravity declines as the inverse square of the distance, tides decline as the inverse cube, and the tidal couple as the inverse sixth power. The magnetic dipole field declines as the inverse cube and any equivalent magnetic tides fall off even more steeply than gravitational tides. Therefore, the braking effect is almost entirely at the distance of closest approach. The characteristic time of this closest approach is clearly about 2R/v, where R is the radius of the Earth and v the relative velocity of the comet and the Earth. With v about 25 km/sec, the characteristic time works out to be under ten minutes. This is the full time available for the total effect of the comet on the rotation of the Earth. The corresponding acceleration is less than 0.1 g, so armies still do not fly off into space. But the characteristic time for acoustic propagation within the Earth—the minimum time for an exterior influence to make itself felt on the Earth as a whole—is eighty-five minutes. Thus, no cometary influence even in grazing collision could make the Sun stand still upon Gibeon.
Velikovsky’s account of the history of the Earth’s rotation is difficult to follow. On page 236 we have an account of the motion of the Sun in the sky which by accident conforms to the appearance and apparent motion of the Sun as seen from the surface of Mercury, but not from the surface of the Earth; and on page 385 we seem to have an aperture to a wholesale retreat by Velikovsky—for here he suggests that what happened was not any change in the angular velocity of rotation of the Earth, but rather a motion in the course of few hours of the angular momentum vector of the Earth from pointing approximately at right angles to the ecliptic plane as it does today to pointing in the direction of the Sun, like the planet Uranus. Quite apart from extremely grave problems in the physics of this suggestion, it is inconsistent with Velikovsky’s own argument, because earlier he has laid great weight on the fact that Eurasian and Near Eastern cultures reported prolonged day, while North American cultures reported prolonged night. In this variant there would be no explanation of the reports from Mexico. I think I see in this instance Velikovsky hedging on or forgetting his own strongest arguments from ancient writings. On page 386 we have a qualitative argument, not reproduced, claiming that the Earth could have been braked to a halt by a strong magnetic field. The field strength required is not mentioned but would clearly (cf. calculations in Appendix 4) have to be enormous. There is no sign in rock magnetization of terrestrial rocks ever having been subjected to such strong field strengths and, what is equally important, we have quite firm evidence from both Soviet and American spacecraft that the magnetic-field strength of Venus is negligibly small—far less than the Earth’s own surface field of 0.5 gauss, which would itself have been inadequate for Velikovsky’s purpose.
PROBLEM IV
TERRESTRIAL GEOLOGY AND
LUNAR CRATERS
REASONABLY enough, Velikovsky believes that a near-collision of another planet with the Earth might have had dramatic consequences here—by gravitational tidal, electrical or magnetic influences (Velikovsky is not very clear on this). He believes (pages 96 and 97) “that in the days of the Exodus, when the world was shaken and rocked … all volcanoes vomited lava and all continents quaked.” (My emphasis.)
There seems little doubt that earthquakes would have accompanied such a near-collision. Apollo lunar seismometers have found that moonquakes are most common during lunar perigee, when the Earth is closest to the Moon, and there are at least some hints of earthquakes at the same time. But the claim that there were extensive lava flows and volcanism involving “all volcanoes” is quite another story. Volcanic lavas are easily dated, and what Velikovsky should produce is a histogram of the number of lava flows on Earth as a function of time. Such a histogram will, I believe, show that not all volcanoes were active between 1500 and 600 B.C., and that there is nothing particularly remarkable about the volcanism of that epoch.
Velikovsky believes (page 115) that reversals of the geomagnetic field are produced by cometary close approaches. Yet the record from rock magnetization is clear—such reversals occur about every million years, and not in the last few thousand, and they recur more or less like clockwork. Is there a clock in Jupiter that aims comets at the Earth every million years? The conventional view is that the Earth experiences a polarity reversal of the self-sustaining dynamo that produces the Earth’s magnetic field; it seems a much more likely explanation.
Velikovsky’s contention that mountain building occurred a few thousand years ago is belied by all the geological evidence, which puts those times at tens of millions of years ago and earlier. The idea that mammoths were deep-frozen by a rapid movement of the Earth’s geographical pole a few thousands of years ago can be tested—for example, by carbon-14 or aminoacid racemization dating. I should be very surprised if a very recent age results from such tests.
Velikovsky believes that the Moon, not immune to the catastrophes which befell the Earth, had similar tectonic events occur on its surface a few thousand years ago, and that many of its craters were formed then (see Part 2, Chapter 9). There are some problems with this idea as well: samples returned from the Moon in the Apollo missions show no rocks melted more recently than a few hundred million years ago.
Furthermore, if lunar craters were to have formed abundantly 2,700 or 3,500 years ago, there must have been a similar production at the same time of terrestrial craters larger than a kilometer across. Erosion on the Earth’s surface is inadequate to remove any crater of this size in 2,700 years. There are not large numbers of terrestrial craters of this size and age; indeed, there is not a single one. On these questions Velikovsky seems to have ignored the critical evidence. When the evidence is examined, it strongly counterindicates his hypothesis.
Velikovsky believes that the close passage of Venus or Mars to the Earth would have produced tides at least miles high (pages 70 and 71); in fact, if these planets were ever tens of thousands of kilometers away, as he seems to think, the tides, both of water and of the solid body of our planet, would be hundreds of miles high. This is easily calculated from the height of the present water and body lunar tide, since the tide height is proportional to the mass of the tide-producing object and inversely proportional to the cube of the distance. To the best of my knowledge, there is no geological evidence for a global inundation of all parts of the world at any time between the sixth and fifteenth centuries B.C. If such floods had occurred, even if they were brief, they should have left some clear trace in the geological record. And what of the archaeological and paleontological evidence? Where are the extensive faunal extinctions of the correct date as a result of such floods? And where is the evidence of extensive melting in these centuries, near where the tidal distortion is greatest?
PROBLEM V
CHEMISTRY AND BIOLOGY
OF THE
TERRESTRIAL PLANETS
VELIKOVSKY’S thesis has some peculiar biological and chemical consequences, which are compounded by some straightforward confusions on simple matters. He seems not to know (page 16) that oxygen is produced by green-plant photosynthesis on Earth. He makes no note of the fact that Jupiter is composed primarily of hydrogen and helium, while the atmosphere of Venus, which he supposes to have arisen inside of Jupiter, is composed almost entirely of carbon dioxide. These matters are central to his ideas and pose them very grave difficulties. Velikovsky holds that the manna that fell from the skies in the Sinai peninsula was of cometary origin and therefore that there are carbohydrates on both Jupiter and Venus. On the other hand, he quotes copious sources for fire and naphtha falling from the skies, which he interprets as celestial petroleum ignited in the Earth’s oxidizing atmosphere (pages 53 through 58). Because Velikovsky believes
in the reality and identity of both sets of events, his book displays a sustained confusion of carbohydrates and hydrocarbons; and at some points he seems to imagine that the Israelites were eating motor oil rather than divine nutriment during their forty years’ wandering in the desert.
Reading the text is made still more difficult by the apparent conclusion (page 366) of Martian polar caps made of manna, which are described ambiguously as “probably in the nature of carbon.” Carbohydrates have a strong 3.5 micron infrared absorption feature, due to the stretching vibration of the carbon-hydrogen bond. No trace of this feature was observed in infrared spectra of the Martian polar caps taken by the Mariner 6 and 7 spacecraft in 1969. On the other hand, Mariner 6, 7 and 9 and Viking 1 and 2 have acquired abundant and persuasive evidence for frozen water and frozen carbon dioxide as the constituents of the polar caps.
Velikovsky’s insistence on a celestial origin of petroleum is difficult to understand. Some of his references, for example in Herodotus, provide perfectly natural descriptions of the combustion of petroleum upon seepage to the surface in Mesopotamia and Iran. As Velikovsky himself points out (pages 55–56), the fire-rain and naphtha stories derive from precisely those regions of the Earth that have natural petroleum deposits. There is, therefore, a straightforward terrestrial explanation of the stories in question. The amount of downward seepage of petroleum in 2,700 years would not be very great. The difficulty in extracting petroleum from the Earth, which is the cause of certain practical problems today, would be greatly ameliorated if Velikovsky’s hypothesis were true. It is also very difficult to understand on his hypothesis how it is, if oil fell from the skies in 1500 B.C., that petroleum deposits are intimately mixed with chemical and biological fossils of tens to hundreds of millions of years ago. But this circumstance is readily explicable if, as most geologists have concluded, petroleum arises from decaying vegetation, of the Carboniferous and other early geological epochs, and not from comets.