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KRONOS Vol X, No. 2
ULTRAMASSIVE OBJECTS AND THE BODNER/BRANDT HYPOTHESISTo the Editor of KRONOS:
I believe that the paper by Bodner and Brandt on ultramassive objects in the Solar System and their effects on Earth is seriously flawed in its astronomy, physics, and geology. None of the conclusions enumerated in the article are borne out by the actual mathematics. It is regrettable that the paper, which Bodner tells me was vigorously refereed, should be held up as an example of the best celestial mechanics which KRONOS can offer. [See KRONOS VI: 2, pp. 3-17. - LMG]
The first and most sensational claim, that a massive object (one million times lunar mass) passing "near" Earth (at, say, one hundred lunar orbits distance, or about twenty-five million miles) would "cause massive tidal waves and earthquakes, and serious damage to the Earth's crust . . . [and] . . . would have extremely profound effects", is false. Such effects would be due to tidal stresses within Earth's surface, and such stresses depend on the difference in attraction between points on the close side of Earth and on the far side of Earth, relative to the gravitating body. This is why the Moon, whose gravitational force on Earth is barely a half of one percent as great as is that of the Sun, has an equal if not greater tidal effect - because it is so much closer that the "near-side"/"far-side" difference is so much greater. The Appendix to this letter demonstrates that the tidal effect of the hypothetical Bodner-Brandt object on Earth is on the same order of magnitude as the tidal effect of the Moon on Earth - hardly of the value to cause the catastrophic effects cited by Bodner and Brandt. The rapid time scale of the postulated encounter mitigates further against any measurable effect, due to elastic lag time of Earth's crust.
Orbital changes can, of course, be anticipated, but hardly of a significant order of magnitude. Using a value of 5 ft/sec2 for lunar surface acceleration, the value of acceleration for an object 25,000,000 miles away, with a mass of 10^6 times the lunar mass, is
106 x [5/(25,000)2] ~ 0.01 ft/secs2
This gives an accelerated distance, in an encounter lasting, say, 12 minutes (720 seconds), of
s= ½ at2 = ½(0.01)(720)2 ~ ½ mile.
During the same interval, Earth's own orbital motion will have carried it about 13,000 miles - so the gravitational effect of the Bodner-Brandt encounter is on the order of one part in twenty-five thousand, enough to be measured, but hardly reason to throw out current calendars.
In the Bodner-Brandt Appendix I ("Probability Considerations") there are further problems. If there are 4.5 billion massive objects distributed through the Milky Way, which has a volume of about 2 x 1013 cubic light years, one can indeed make an estimate of the probability of any of the objects being within the volume of the Solar System (which is 6 x 10-10 cubic light years). If these ultramassive objects are travelling at the speed of light (an upper bound), they traverse one Solar System volume every fifteen minutes or so, or 35,000 per year. All of them then traverse 35,000 times 4.5 billion such units every year, or about 160 trillion units. There are about 3 x 1022 unit volumes in the galaxy; divide that by the number traversed in one year, 1.6 x 1014, and you have about 2 x 108 years between traverses for any particular Solar System - that is, two hundred million years. If the objects are only moving at one tenth the speed of light, it becomes two billion years, etc. A probability theory approach to this question would no doubt provide more reliable numbers but hardly alter the results by more than an order of magnitude or two. This does not justify the authors' statement that "on an intuitive basis we believe there exists some appreciable probability of a rapidly moving object coming within . . . our solar system . . . in some fixed time frame, i.e., several millennia". The opposite is true.
In conclusion, Figure 3, the "Bulging/Flipping Effect", is a fantasy.
James E. Oberg
What would be the tidal effect on Earth of a hypothetical "Bodner-Brandt Object" with mass of one million lunar masses at one hundred Earth-Moon distances?
Unit gravitational force of Moon on Earth = GM/R2, where M = mass of Moon R = Earth-Moon distance r = radius of Earth
TM=Moon's tidal force = [GM/(R-r)2] - [GM/(R+r)2] (1 )
By algebraic manipulation:
TM = (4GMr/R3) [1/(1-r2 /R2)2] (2 )
For r << R, TM ~ 4GMr/R3, (3 )
because for Earth- Moon, the term in brackets in (2 ) ~ 1.0006.
Compute TBB' the tidal force of the Bodner-Brandt object, where M' = 106M and R' = 102R
TBB = 4GM' r/(R')3 = 4GM(106) /(102R)3 = 4GM/R3 = TM (4)
Hence, the internal tidal stresses of such an object are of the same order of magnitude as those induced already by the Moon. No catastrophic results are to be expected.
Michael E. Brandt Responds:
James Oberg's letter in response to the article by Michael Bodner and myself can be summed up in two words - childishly naive. Oberg believes he can hoodwink both the staff and readers of KRONOS by using high school algebra to try to induce us to believe that Newtonian gravitation hardly exists. After reading his letter, someone with no knowledge of basic physics would get the impression that the planets revolve about the Sun as a consequence of tidal attractions only. In our article, Bodner and I stated:
Also, as stated in footnote 10a of that paper:
If Oberg had taken the time to read our paper fully he might have responded less impulsively. In an earlier handwritten letter to Bodner and myself, Oberg claimed that "the Bodner-Brandt effect is trivially absurd". According to his reasoning, this effect is tidal in nature only. However, the effect that WE described is purely gravitational - an effect that can alter the orbital paths of planets, causing catastrophic results (see my article, this issue). To make matters worse, Oberg neglects to consider that the real effect is a phenomenon of many objects not just of Earth and a massive object.
[*!* Image] Figure 1. Labels: Tidal forces exerted here. Gravitational force exerted here (center point).
Figure 1 illustrates both the tidal forces and gravitational attraction exerted by an object labelled B on object A. On the line of centers between the two bodies, object B exerts tidal forces on the line segments (radii) on either side of object A's center point. Tidal forces are exerted on points to the left and right of the center point that are equidistant from that point. The only point along that line of centers not having a companion point on the opposite side of the center point is the center point itself - and thus there is no tidal force at the center point of object A, only the gravitational force given by the inverse-square law GmAmB/r2 . This is the force and the effect we were talking about and the one that Oberg neglects.
As far as the probability of such an event occurring, we have another example of the misuse of statistics by Oberg in order to justify his own twisted arguments. The fact is that such events (objects both large and small traversing the solar system) have occurred many times in recorded history. This is even clearer in light of the data from the Voyager missions, as well as the speculations of Clube, Napier, and others. If we extrapolate from past experience, we can conclude that these events WILL occur in the future. Just when the next such event will happen is anyone's guess, since the phenomenon is a random process whose probability distribution function is not clearly understood. This is precisely the point Bodner and I were trying to make; and therefore I claim our estimates are as good as (if not better than) Oberg's.
It is interesting to point out that in Oberg's prior handwritten correspondence he wrote "copyright James E. Oberg". This is just one more example of how astronomers and other detractors of Velikovsky have attempted to "copyright" their self-serving versions of science.
The real tragedy of this is how faithful pursuers of science have been dragged into a war of words and rhetoric by those among us who are deathly fearful of the truth. I now have a better understanding of the cancer around us, of which Oberg is but a single malignant cell.
To the Editor of KRONOS:
Lynn E. Rose has given us several different versions of what "Velikovsky seems to have had in mind" with his "Brahman charts of the sky" allegedly indicating that the north pole was at Baffin Island. I readily concede that I have not proven that such a source "cannot possibly exist" - that would be very hard to do for every unsupported claim - only that Velikovsky's statement does not make sense as worded. [See KRONOS IX:2, pp. 96-99. - LMG ]
But when Rose argues that since "both Calcutta and Bombay are roughly ninety degrees from Baffin Island. . . . This in itself is supportive of Velikovsky's suggestion", I cannot quite follow his reasoning. Velikovsky did not mention Bombay. What does Bombay have to do with it? Nor did he say anything about the latitude of Calcutta - only its present longitude, which is irrelevant.
If the latitude of Calcutta was worth noting on a celestial chart 2700 or 3500 years ago, there must have been an urban center there at the time - something which Rose has not established. We have a few cylinder* seal impressions from the Indus valley civilization, which ended in the second millennium, and then no inscriptions from India until the middle of the third century B.C.(1) "The complete absence of any words connected with writing in the Rg Veda, despite its size and the many contexts in which such words might be expected to occur, is", according to A. L. Basham, "almost certain proof that the Aryans were illiterate" when it was composed.(2)
Nevertheless, it is possible that they were not only literate, but also great astronomers and cartographers, and that they transmitted accurate geodesic knowledge down to modern times. It is even possible that included in that knowledge was the statement that the site of Calcutta was once on the equator. But there is no reason to believe so, either. And there is a very solid reason for doubting it - namely the great pyramid, which points squarely toward the present north pole, not Baffin Island.
Rose says that "More than one of Velikovsky's 'unknown' sources has subsequently been found". But in view of the sometimes great discrepancies between his "known" sources and Velikovsky's descriptions of them, one should be cautious in evaluating claims for which no reference is given. Remember the "Hindu astronomical tablets . . . composed in the first half of the first millennium before the present era [which] show a uniform deviation from the expected position of the stars at the time the observations were made"? They turned out to be planetary tables calculated by John Bentley in the nineteenth century of the present era.
In support of his contention that the poles had been displaced within historical times, Velikovsky cited yet another ancient document. A number of cuneiform tablets inscribed with mythological poems known collectively as the Baal-Anat cycle were unearthed at the ancient city of Ugarit, on the southern coast of Syria. Citing Virolleaud's 1938 translation, Velikovsky wrote: "The people of Ugarit . . . addressed Anat, their planet Venus: 'You reverse the position of the dawn in the sky'."(3) And on another page of Worlds in Collision, Anat is represented as having " 'exchanged the two dawns and the position of the stars' ".(4) No page-reference was given.
Having made a persuasive argument for identifying the goddess Anat as the planet Venus, he seems to have found evidence that this body was responsible for disturbing the rotation of the Earth. But not all of Velikovsky's references can be accepted at face value. One would search the text in vain for this "quotation". There is no such passage. However, one finds the following, on pages 26-7 (In Virolleaud's translation, it is Anat who addresses Baal, the "rider of the clouds".):
Velikovsky has confused French verser ("to pour") with English reverse, and taken rosee ("dew") as signifying dawn, evidently thinking of the rose-tinted sky of dawn. In English it would run:
With these transmutations we are transported into a landscape created by the personal imagination of a man who once described himself as "the prisoner of an idea",(6) where "nothing . . . that doth fade, but doth suffer a sea-change into something rich and strange".(7)
It is still conceivable that Velikovsky's "Brahman charts of the sky", as reconstructed by Rose, with the latitudes of two or more cities noted thereon, may exist. If so, they should not be terribly difficult to locate. In view of Rose's vigorous efforts to rescue it from dismissal, perhaps he will look upon this task as one which is particularly committed to him. But until it is found, the evidentiary value for recent polar shifts of this unsupported claim is nil.
It is Mage who has taken the more agressive part engaging in disputations over ancient calendars, but when I pointed out, among other things, the existence of XVIIIth Dynasty texts mentioning the epagomenae, it was Rose who responded. I have been admonished that it is not enough to cite the appropriate passages in the scholarly literature. I did so only as a hint to the wise: these and other texts will be taken up in a detailed study, not in a letters column. But when Rose says that the evidence has not yet been examined, he speaks for himself.
What we are talking about [are] transcriptions and translations of papyri and inscriptions which mention the epagomenal days. When they date from the XVIIIth Dynasty or earlier, Rose refers to them vaguely as "claims" and "reports".
I agree wholeheartedly that "all such investigations must . . . be conducted in terms of what the evidence is - " and not on the basis of pronouncements made by anybody - whether it be "the uniformitarians", Velikovsky, Mage, or Rose.
Advising others what they should believe carries with it a responsibility to make reasonable efforts to locate and study the available evidence. Mage wants to accept the reading of the Osorkon flood inscription at face value, while rejecting all the earlier references to the epagomenal days as systematic errors in translation. To do so, he must show that there is some significant difference between earlier and later writings. But if one is not willing even to look at the publications, this will be difficult to do. Generalized suspicion is not an argument. As for Velikovsky's "overwhelming non-Egyptian evidence for world-wide calendrical changes", I have seen most of that material, and it is highly selective, some of it wildly inaccurate, and much of it bears little or no correspondence to the interpretations put upon it. Rose ends with a few shafts referring to the Osorkon flood inscription. They will soon find their answer elsewhere. But why should Breasted be held responsible for the epigraphy of a hieratic text he had never seen? There seems to be a tendency here to assume that if you can't find something in Breasted, it must not exist.
REFERENCES1. A. L. Basham, The Wonder that was India (N. Y., 1967), p. 396.
2. Ibid, p. 34.
3. Worlds in Collision, p. 177.
4. Ibid., p. 112.
5. Charles Virolleaud, La deesse 'Anat: Poeme de Ras Shamra (Paris, 1938). Cf. the following: "She poured the dew of heaven, (and) [the showers] [that] she poured (were as many as) the stars." G. R. Driver, Canaanite Myths and Legends (Edinburgh, 1971), p. 85; "Dew that the heavens pour, rain that the stars pour." Arvid S. Kapelrud, The Violent Goddess: Anat in the Ras Shamra Texts (Scandinavian Univ. Books, 1969), p. 51;"The dew that the heavens pour, [The ra] in that the stars pour." Cyrus H. Gordon, "Poetic Legends and Myths from Ugarit," Berytus, Vol. 25 (1977), p. 78.
6. To Eric Larrabee, who wrote the introduction to Stargazers and Gravediggers
7. Ariel, in Shakespeare's Tempest
Prof. Lynn E. Rose Replies:
Mr. Mewhinney has now decided that he will "readily concede" that he has indeed not proven that the "Brahman charts" mentioned by Velikovsky could not possibly have existed! If only he had said that back in 1982! His attempt to prove that there were no such charts, "nor could there have been", is precisely what I have objected to all along. My references to Calcutta and Bombay were but one part of an attempt to illustrate to Mewhinney the possibility of such a chart. I spoke in terms of what "might" have been the case if the chart had referred to two different sites, "such as" Calcutta and Bombay. That both of these sites would have been about ninety degrees from the former pole is indeed supportive of Velikovsky, but any two appropriately-placed sites would have sufficed for my purposes; I chose Calcutta and Bombay only because I thought that it would be easy for Mewhinney and others to find them on a globe. Questions about their antiquity are thus quite beside the principal point at issue here. (In any case, the kind of logic by which any important site "must" have been "an urban center" is unfamiliar to me. Does this logic apply to Dodona? To Stonehenge?)
Mr. Mewhinney argues on and on about this and that, but there is nothing in these latest remarks of his that would require any change whatsoever in my previous comments (see KRONOS IX:2, pages 97-99). The one thing that is both new and noteworthy here is that back in only the second sentence of his remarks he has already quietly conceded the very point that this exchange was all about in the first place!