by Carl Sagan
I therefore cannot find the legendary base of Velikovsky’s hypothesis at all compelling. If, nevertheless, his notion of recent planetary collisions and global catastrophism were strongly supported by physical evidence, we might be tempted to give it some credence. If the physical evidence is not, however, very strong, the mythological evidence will surely not stand by itself.
LET ME GIVE a short summary of my understanding of the basic features of Velikovsky’s principal hypothesis. I will relate it to the events described in the Book of Exodus, although the stories of many other cultures are said to be consistent with the events described in Exodus:
The planet Jupiter disgorged a large comet, which made a grazing collision with Earth around 1500 B.C. The various plagues and Pharaonic tribulations of the Book of Exodus all derive directly or indirectly from this cometary encounter. Material which made the river Nile turn to blood drops from the comet. The vermin described in Exodus are produced by the comet-flies and perhaps scarabs drop out of the comet, while indigenous terrestrial frogs are induced by the heat of the comet to multiply. Earthquakes produced by the comet level Egyptian but not Hebrew dwellings. (The only thing that does not seem to drop from the comet is cholesterol to harden Pharaoh’s heart.)
All this evidently falls from the coma of the comet, because at the moment that Moses lifts his rod and stretches out his hand, the “Red Sea” parts-due either to the gravitational tidal field of the comet or to some unspecified electrical or magnetic interaction between the comet and the “Red Sea.” Then, when the Hebrews have successfully crossed, the comet has evidently passed sufficiently farther on for the parted waters to flow back and drown the host of Pharaoh. The Children of Israel during their subsequent forty years of wandering in the Wilderness of Sin are nourished by manna from heaven, which turns out to be hydrocarbons (or carbohydrates) from the tail of the comet.
Another reading of Worlds in Collision makes it appear that the plagues and the Red Sea events represent two different passages of the comet, separated by a month or two. Then after the death of Moses and the passing of the mantle of leadership to Joshua, the same comet comes screeching back for another grazing collision with the Earth. At the moment that Joshua says “Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon,” the Earth-perhaps because of tidal interaction again, or perhaps because of an unspecified magnetic induction in the crust of the Earth-obligingly ceases its rotation, to permit Joshua victory in battle. The comet then makes a near-collision with Mars, so violent as to eject it out of its orbit so it makes two near-collisions with the Earth which destroy the army of Sennacherib, the Assyrian king, as he was making life miserable for some subsequent generation of Israelites. The net result was to eject Mars into its present orbit and the comet into a circular orbit around the Sun, where it became the planet Venus-which previously, Velikovsky believes, did not exist. The Earth meantime had somehow begun rotating again at almost exactly the same rate as before these encounters. No subsequent aberrant planetary behavior has occurred since about the seventh century B.C., although it might have been common in the Second Millennium.
That this is a remarkable story no one-proponents and opponents alike-will disagree. Whether it is a likely story is, fortunately, amenable to scientific inquiry. Velikovsky’s hypothesis makes certain predictions and deductions: that comets are ejected from planets; that comets are likely to make near or grazing collisions with planets; that vermin live in comets and in the atmospheres of Jupiter and Venus; that carbohydrates can be found in the same places; that enough carbohydrates fell in the Sinai peninsula for nourishment during forty years of wandering in the desert; that eccentric cometary or planetary orbits can be circularized in a period of hundreds of years; that volcanic and tectonic events on Earth and impact events on the Moon were contemporaneous with these catastrophes; and so on. I will discuss each of these ideas, as well as some others-for example, that the surface of Venus is hot, which is clearly less central to his hypothesis, but which has been widely advertised as powerful post hoc support of it. I will also examine an occasional additional “prediction” of Velikovsky-for example, that the Martian polar caps are carbon or carbohydrates. My conclusion is that when Velikovsky is original he is very likely wrong, and that when he is right the idea has been pre-empted by earlier workers. There are also a large number of cases where he is neither right nor original. The question of originality is important because of circumstances-for example, the high surface temperature of Venus-which are said to have been predicted by Velikovsky at a time when everyone else was imagining something very different. As we shall see, this is not quite the case.
In the following discussion, I will try to use simple quantitative reasoning as much as possible. Quantitative arguments are obviously a finer mesh with which to sift hypotheses than qualitative arguments. For example, if I say that a large tidal wave engulfed the Earth, there is a wide range of catastrophes-from the flooding of littoral regions to global inundation-which might be pointed to as support for my contention. But if I specify a tide 100 miles high, I must be talking about the latter, and moreover, there might be some critical evidence to counterindicate or support a tide of such dimensions. However, so as to make the quantitative arguments tractable to the reader who is not very familiar with elementary physics, I have tried, particularly in the Appendices (following the References), to state all the essential steps in the quantitative development, using the simplest arguments that preserve the essential physics. Perhaps I need not mention that such quantitative testing of hypotheses is entirely routine in the physical and biological sciences today. By rejecting the hypotheses that do not meet these standards of analysis, we are able to move swiftly to hypotheses in better concordance with the facts.
There is one further point about scientific method that must be made. Not all scientific statements have equal weight. Newtonian dynamics and the laws of conservation of energy and angular momentum are on extremely firm footing. Literally millions of separate experiments have been performed on their validity-not just on Earth, but, using the observational techniques of modern astrophysics, elsewhere in the solar system, in other star systems, and even in other galaxies. On the other hand, questions on the nature of planetary surfaces, atmospheres and interiors are on much weaker footing, as the substantial debates on these matters by planetary scientists in recent years clearly indicate. A good example of this distinction is the appearance 1975 of Comet Kohoutek. This comet had first been observed at a great distance from the Sun. On the basis of the early observations, two predictions were made. The first concerned the orbit of Comet Kohoutek-where it would be found at future times, when it would be observable from the Earth before sunrise, when after sunset-predictions based on Newtonian dynamics. These predictions were correct to within a gnat’s eyelash. The second prediction concerned the brightness of the comet. This was based on the guessed rate of vaporization of cometary ices to make a large cometary tail which brightly reflects sunlight. This prediction was painfully in error, and the comet-far from rivaling Venus in brightness-could not be seen at all by most naked-eye observers. But vaporization rates depend on the detailed chemistry and geometrical form of the comet, which we know poorly at best. The same distinction between well-founded scientific arguments, and arguments based on a physics or chemistry that we do not fully understand, must be borne in mind in any analysis of Worlds in Collision. Arguments based on Newtonian dynamics or the conservation laws of physics must be given very great weight. Arguments based on planetary surface properties, for example, must have correspondingly lesser weights. We will find that Velikovsky’s arguments run into extremely grave difficulties on both these scores, but the one set of difficulties is far more damaging than the other.
PROBLEM I. THE EJECTION OF VENUS BY JUPITER
VELIKOVSKY’S hypothesis begins with an event that has never been observed by astronomers and that is inconsistent with much that we know about planetary and cometary physics, namely, t
he ejection of an object of planetary dimensions from Jupiter, perhaps by its collision with some other giant planet. Such a propagation of catastrophes, Velikovsky promised, would be “the theme of the sequel to Worlds in Collision” (page 373). Thirty years later, no sequel of this description has appeared. From the fact that the aphelia (the greatest distances from the Sun) of the orbits of short-period comets have a statistical tendency to lie near Jupiter, Laplace and other early astronomers hypothesized that Jupiter was the source of such comets. This is an unnecessary hypothesis because we now know that long-period comets may be transferred to short-period trajectories by the perturbations of Jupiter; this view has not been advocated for a century or two except by the Soviet astronomer V. S. Vsekhsviatsky, who seems to believe that the moons of Jupiter eject comets out of giant volcanoes.
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 AMONGTHE 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 tempe
rature: 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 probability 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.