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KRONOS Vol IV, No. 4
THE CABOTS, THE LOWELLS AND THE TEMPERATURE OF VENUS
GEORGE ROBERT TALBOTT
The following tripartite contribution focuses first upon the general problem of misrepresentation of Dr. Velikovsky's thesis by some members of the academic scientific community, and totally demolishes the already dying assertion that "no real scientist agrees with Dr. Velikovsky". The author, himself conservative, does indeed agree, as do others in orthodox scientific activities. This is amply shown in Scientists Confront Scientists Who Confront Velikovsky; and of course in the already published KRONOS articles.
Secondly, in Velikovsky and the Temperature of Venus, the essential results of a fully quantitative treatment are outlined, and these results, arrived at independently and entirely apart from the prior work of Dr. Ransom* (Pensee II, Fall 1972, p. 18), are compatible with his conclusions. Dr. Ransom's specification of 1184° Kelvin for Venus 3500 years ago with a present temperature of 700° Kelvin and Dr. Talbott's specification of 1500-2000° Kelvin 3500 years ago with a present temperature of 750°Kelvin, though distinct, lead to the same important result - namely that Venus was "candescent" 3500 years ago. Cooling rates of bodies, like radioactive decay, conform to definite laws; and given the mass, surface area, specific heat and mode of heat transfer, the path from one temperature to another and the time required are provable, definite and conclusive. The only assumption which is crucial in Dr. Talbott's calculation is that sunlight is a secondary source of' eat energy on Venus. The December space probes, it is hoped, will settle the question of' the validity of this assumption.
The final and most important section, entitled Temperature History of a Large Mass, is a detailed analysis, not only of the correct method of finding temperatures of radiating bodies, be they large or small, but also of the truly devastating errors in attempts to show a "cold Venus" at the present from an assumed 6000°Kelvin state 3500 years ago. This analysis is not an opinion, but a matter of usable, reliable applied thermodynamics and heat transfer.
[Footnote: *See "A Note on the Temperature of Venus" by C.J. Ransom elsewhere in this issue. - The Ed]
The skeptical reader is provided with the complete computer program and with the data used by Dr. Talbott, so that he can judge for himself, make the computer runs for himself, and arrive at the proper conclusions for himself. While far more elaborate programs have been written by Dr. Talbott for the same kinds of computations, the simplified version in this tripartite work is adequate to "ball park" all of the necessary figures.
[*!* Image: KIV_2a.JPG]
The temperature of Venus in Degrees Kelvin Versus Time in Years: A Plot of 3500 Calculated values.
NOTE: The shape of this curve and the relationship between temperature and time are fixed by the mass and surface area of Venus. This locks into one coherent scheme a time scale of 3500 years, the present known surface temperature, and a candescent state 3500 years ago. Shifting the sink temperature from 200 Kelvin to 400 Kelvin only shifts the 3500 year temperature by 8 degrees Kelvin. The rate of change of temperature today is only 0.066 Kelvin/year, defeating debunking attempts based upon failure to measure sizeable drops. There is no "fixing" or "doctoring" of data; this is a cooling curve for a mass which is identical in shape and size to Venus.
[*!* Image: INSERT KIV_2b.JPG]
A Plot of 2776 Calculated Values of Venus' Temperature Using the Data Shown Below.
The following data set contains a somewhat different specific heat value than Talbott's 3500 year graph, although the essential argument remains the same. Dr. Velikovsky, in a personal conversation with Talbott, suggested shifting the origin to -776. This indicates an initial temperature of 1400 Kelvin with a rate of change today of about 0.08 Kelvin/year.
SCIENTISTS CONFRONT SCIENTISTS WHO CONFRONT VELIKOVSKY
The new Cornell University Press publication, Scientists Confront Velikovsky, is truly a valuable documentary on professional debunking, prestige coteries and expert gamesmanship. I am pleased that this book was published; the egocentricity is amusing, and the book makes explicit what is usually done by gossip designed to demolish careers. In the future, when advances in physical science disclose the mechanism of gravity, it will be instructive to reexamine the confident arguments of the current celebrities.
The authors frame a superficially plausible but logically untenable hypothesis to explain "public interest" in Velikovsky's thesis, but avoid any serious discussion of professional interest. Donald Goldsmith inadvertently lets the cat out of the bag on page 22, in an astonishingly candid passage:
Mark this well. There is a very great difference between being a good scientist, knowing your mathematics, physics, chemistry and biology, and being a scientific Cabot or Lowell. And a good scientist may be insulted or mocked with impunity, but not a scientific celebrity. The difference is very interesting and cannot be explained as a result of tangible superiority of the elite. When the authors speak of "THE scientific community", it is important to remember that it is the fashionable scientific community which is meant. Most scientists live outside of that community and are tolerated as long as they conform. It is quite apparent that the real hostility toward Velikovsky has arisen not from most scientists, but from those who imagine themselves the center of the academic circus. To write as though "THE scientific community" has, in monolithic fury, rejected Velikovsky is to exaggerate shamelessly.
What many scientists find deceitful in this Cornell publication is the pretense that scientific referees and critics are fair and objective, that the only people they attack are either "heretics" without foundation, or phonies without qualifications. As a matter of fact, they attack everyone and each other as well. Asimov properly cites the cases of Mayer and Joule who were generally ignored in relation to the prestigious academic Helmholtz, and others admit that good ideas were hooted down and mocked - but with Velikovsky the matter is "different". He is an "exoheretic" with a crackpot theory.
I think that there is a more useful classification than that of "exoheretics" and "endoheretics". It is the distinction between crackpot theories enunciated by scientific celebrities, and theories from "outsiders" with or without scientific skill, which are denounced by scientific celebrities. Velikovsky's thesis is a theory compiled by a scholar with impressive scientific ability whereas theories of what did and did not happen in the whole universe over the past twenty million years are crackpot theories by celebrities of considerably less talent but greater prestige.
Celebrity scientists hold a number of theories for which there is inadequate factual evidence. These theories are in the nature of fashions or popular prejudices which the erudite are supposed to espouse. I mention this because of the silly implication that what "scientists as scientists" believe is always supported by careful measurement and computation. But leaders of the Cabot and Lowell community have plenty of crackpot ideas of their own, such as their sober assertions about the age of the universe, or about the age of life in the universe, or about the origin of the universe. It all depends upon who asserts the crackpot theory, and how well it serves its ends.
Prestigious scientific officialdom gives so much support to some crackpot theories that it is virtually impossible to discredit them. For example, IQ testing holds a sacred place although every rational consideration of biographical facts shows that Leonardo da Vinci, Galois and Einstein would not promise exceptional ability by criteria of rapid-fire puzzle solving, reading speed and clerical efficiency. Thousands of forgotten pretenders would pass them up on all of those measures, but IQ testing is a pillar of celebrity science. Objections raised to it are interpreted, argumentum ad hominem, as evidence of being a "crank".
The criticisms offered in Scientists Confront Velikovsky conform to a common pattern. Pretending detachment and objectivity, the critics begin by a dedicated rejection of Velikovsky's views and then try to find rational support for this prejudice in the laws and equations of physics. Any scientist worth his salt begins with what actually happens, and then tries to explain the phenomenon, hopefully in terms of known laws and relationships and if necessary by new considerations. Since what Velikovsky asserts may or may not have actually happened, it would seem that some discussion, even on the critical side, might have been devoted to seeing how physical science could account for the events, assuming, harmlessly and hypothetically, that they really did occur. Instead, much merriment was generated in trying to show that a distinguished doctor of medicine - the least of his attainments but still an impressive one - did not understand the difference between hydrocarbons and carbohydrates!!! With every effort to be charitable, I have to call that insolence par excellence. It is of course a high school debate strategy designed to infuriate and hence incapacitate an opponent.
Velikovsky did not approach his thesis mathematically. He is criticized on the one hand for giving wrong quantities, and on the other for not giving any at all, as when he called Venus "hot". None of his critics seem aware that the same techniques they use in debate can "prove" the impossibility of many observed phenomena. Impressive quantitative arguments can be given for the impossibility of infrared spectrometric analysis of organic compounds, of man's ability to land on the Moon, and of the classical flight of the bumblebee. There are, of course, fallacies in the arguments, but sometimes they are hard to find. One should harmonize fact and theory, not argue as at an Arabian bazaar that the fact cannot occur. The separation of a mixture of gases into a set of pure ingredients, like pouring a cup of sugared and creamed coffee into a tube and getting back pure cream, pure sugar and pure coffee would seem like nonsense to someone who didn't know anything of gas and liquid chromatography. I'm sure there are plausible-sounding arguments against the possibility of such things.
Thermodynamic treatment of Hawaiian volcanoes - present, terrestrial and observable - is extremely difficult and controversial. If one had not stood in the presence of an erupting Mauna Loa, and yet tried by the plastic toys of debate, to convince someone of the mammoth proportions of the event, there is no doubt in my mind that impressive "counter equations" could be written to "debunk" what really occurs. These "counter equations" would be wrong, not intrinsically but in the sense of being inapplicable, irrelevant and trivial.
Constructive uses of mathematical arguments are plentiful and impressive. Predictions of lunar and solar eclipses, deduction of the shift of the perihelion of Mercury from tensor applications in general relativity, deduction of Rydberg's constant in atomic spectroscopy, brachistochrone and catenary analysis in generalized mechanics are all breathtakingly beautiful to those who live by these tools. Equations, it would seem, are most profound when used constructively. They become shallow and obstructive when used to argue about what "cannot happen", or about what "cannot be done". As late as my high school days, bright boys with slide rules and engineering aspirations were praised by otherwise competent teachers for "proving" that all of the fuel in California could never take a rocket ship or any other vehicle to the Moon. Adolescent Velikovskys were mocked without mercy for asserting a contrary thesis. There were lots of equations, friction factors, diagrams and self-assured yo-hos, but in July 1969-
Perhaps Velikovsky expected too much sophistication of his critics when he wrote casually of the possibility of "manna" carbohydrates generated from available oxygen, carbon, hydrogen, and unearthly amounts of energy. As a Doctor of Medicine familiar with insulin shock treatment and the biochemistry of the nervous system, it is impossible that he should have missed the connection between aldehydes and sugars, or that his hypothesis is based upon errors in high school chemistry. As an authority in medical science and its associated disciplines, he had followed such "unlikely" events as the synthesis of demerol, a morphine substitute, from catalytic hydrogenation of an "improbable" starting material, isonicotinic acid methyl chloride!!
Celebrity scientists always see the "soundness" of anything which has already happened or been demonstrated even to the most destructively captious observer. But given the proposed synthesis route for demerol, it is a safe bet that, in the beginning, it would have been hooted with ivy league confidence. Yet for a cultured and civilized scholar, one to whom knowledge is less novel than to his critics, the route is possible. With the whole world of organic and biochemical transformations familiar to him, large scale generation of a carbohydrate sans photosynthesis did not appear impossible. Nor was there any contradiction in the supposition that, even if carbohydrates had formed, inedible hydrocarbons might also have formed from the same general source. Perhaps the hypothesis is in error; but this is not quite the same thing as confounding carbohydrates and hydrocarbons. To point out a possible error is one thing; mockery is quite another. One must decide whether he wants to read or misread. Communication requires cooperation of the recipient, and if the recipient wishes to misunderstand, he is surely free to do so. Nowhere in Velikovsky do I find a chemical theory comparable in audacity to the thesis regarding the creation of life by a bolt of lightning through an ammonia cloud, but again it all depends upon whose pot is cracked, not upon the merit of the argument.
If I were told that an electron had spontaneously changed into a proton, or that a lavendar kangaroo was teaching experimental chronology at Oxford University, I would feel safe in chuckling disbelief. After all, basic laws of physics and biology are allegedly violated, and I can't swallow that. But there is nothing in Velikovsky's account which is in violation of the laws of physics, only an assertion of what is currently thought to be improbable.
It is of course possible that the events proposed by Velikovsky did not occur. Even if one were to write out a complete mathematical description, entirely compatible with orbital mechanics, thermodynamics and all the rest, depicting a molten, incandescent mass leaving Jupiter and becoming the planet Venus, it would not prove that the events really happened. What is dishonest in the Cornell publication is the implication that considerations in physics, elementary or advanced, "prove" that a physically viable and detailed description of that kind is impossible, or that, having caught the great man in ambiguities, his life work is a proper object of derision.
Velikovsky is a "broad brush" scholar. Our century is one of "scholarly criticism". Debunkers outrank creators in academia, and it is not fashionable to insist that most of the great work in scientific history was accomplished by broad brush people who would be made into hash by our current scientific celebrities. It is only a prejudice, I suppose, that places constructive work before making hash. And as for Goldsmith's conjecture about the universal desire for "acceptance" by the Cabots and Lowells, that is as unlikely as Galileo casting a wistful glance at the medieval inquisition. Nothing positive would come of it.
VELIKOVSKY AND THE TEMPERATURE OF VENUS
In the following notes, it must be understood that an advanced and mathematically sophisticated argument is being given in descriptive form. The reader who wishes to see the full argument and its associated computer program is referred to the enclosure pages. Suffice it to say here that allegedly "devastating attacks" on Dr. Velikovsky's thesis of a recent origin of Venus are based upon incorrect thermal reasoning, and this is not a matter of opinion but of thermodynamics and heat transfer. The calculations given in Scientists Confront Velikovsky are not being criticized for being simple and clear - these are virtues. The criticism is based upon their demonstrable irrelevance. The radiation calculation (pages 100-101) only shows that an identical amount of heat energy can be transferred at 77°K over a 3500 year interval or at 6000°K over a 50 minute interval. That calculation has nothing whatever to do with cooling rates - it doesn't even contain a reference to thermal capacitance!! Responsible calculations show that a mass of Venusian magnitude will scarcely shift in temperature at all after 50 minutes in the photosphere.
But the relevant point is proven in a fully quantitative manner that a massive, molten body - quantitatively, a mass equivalent to Venus and having the Venus surface area, and molten at between 1500°K and 2000°K - will transfer heat internally by flowing magma, and will radiate its heat in such a way that in exactly 3500 years its temperature is expected to be exactly 750°K, which by measurement it is. Velikovsky's 3500 years, the present surface temperature of Venus, and the mass, surface area and specific heat of Venus are inextricably bound together. The only "assumptions" in the proof are as follows:
(1) Venusian internal heat transfer is dominated by what amounts to "forced" convection, as when hot fluid magma in turbulent motion is circulated throughout the body and to its surface as lava.
(2) Venusian external heat transfer is by radiation (in conformity to the well-known Stefan-Boltzmann law) into a thick cloud bank at between 200° K and 300°K.
(3) Sunlight is a secondary source of heat energy on Venus. The largest incident load is reflected by the high Venusian albedo, and the absorbed energy is partly dissipated in photochemical reactions. All of this is admissible and highly probable with an envelope of thick and highly reflective clouds.
If these assumptions are made - and please note that they are reasonable correlates of the hypothesis that Venus is heavily shrouded and was candescent only 3500 years ago - the rest is mathematics and physics. In 3500 years, the mass will have a mixed mean temperature of 750°K provided that its time zero temperature was between 1500°K and 2000°K. Moreover, the surface temperature and mixed mean temperature of a planet candescent only 3500 years ago would be very close to the same value. Arguments based on the transfer of heat by conduction through the Earth's crust, and the associated heat conduction and diffusion equations for the Earth, have no relevance whatever in the present argument. The Earth is very old and measurement supports this contention. Here, heat from a molten interior communicates by conduction through a thick, ancient crust. But even on the Earth, as anyone in Hawaii knows, there are times when forced convection predominates, as when Mauna Loa erupts!
It is really impossible to argue intelligently that the present measured temperature of Venus can be deduced exactly from a model which is "naive" or "inappropriate". The computer program, using the mass, surface area and mean specific heat of Venus, using starting temperatures of from 1500°K to 6000°K in 500°K increments, and using a 3500 year range (in conformity to Dr. Velikovsky) shows a mixed mean temperature of between 700° K and 800° K, and a value of exactly 750°K for the 1500°K to 2000°K starting temperatures. The computer program and supporting data are not mysterious or inaccessible, and have been sent to the Editor of Science. The cooling curve algorithm is exact and fully verifiable by tractable laboratory models. We have seen nothing comparable in precision for deducing an exact 750°K from the much advertised "greenhouse effect".
In conclusion, I think it is appropriate to insist that some scientifically sophisticated people who, by even the most quarrelsome measure, are professional scientists, agree with Dr. Velikovsky. And we would like to know what facts, measures, devices and mathematical tools undisclosed to us are in possession of the opposition. The density of mockery, derision and arrogant confidence is without basis, and should not be accepted as evidence of such possession. Scientists Confront Velikovsky is missing the leading words,"A Few Angry...."
TEMPERATURE HISTORY OF A LARGE MASS INITIALLY AT 1500 TO 6000 DEGREES KELVIN, COOLING BY RADIATION INTO A 200 DEGREE KELVIN SINK, COVERING 3500 YEARS
A computer program has been written, taking into account mass, specific heat, surface area and initial temperature which shows that a mass having the characteristic properties of Venus and at 1500°K to 2000°K 3500 years ago, and radiating into a 200°K sink in conformity to the Stefan-Boltzmann law will have a predicted mixed mean temperature of exactly the presently measured temperature of the Venus surface.
The program is first applied to easily managed laboratory models of alumina and plastic, to show that it is thermodynamically correct in predicting temperature profiles.
The present paper does not attempt to prove that Venus was at 1500°K to 2000°K 3500 years ago, only that its known temperature history is coincident with that hypothesis, and that the hypothesis is physically sound. It is clearly realized that mixed mean temperature is being compared to surface temperature. This comparison is feasible for newly formed massive bodies provided that there is heavy internal turbulence as, e.g. with circulating magma, lava flow and circulation of molten materials or other forced convective means. Heavy internal turbulence is compatible with one hypothesis of the source and age of Venus (Reference 3).*
The thesis that a mixed mean temperature of a relatively new planet can characterize its surface is based upon sound heat transfer principles. Magma travels through so-called "lava tubes", some of which can be observed empty and near the surface of the earth on the Island of Hawaii. The connection between Mauna Loa's magma reservoir and the volcanic system of Kilauea and Halemaumau is by such tubes. If a planet's entire mass were molten 3500 years ago, it would be tunnelled through by "lava tubes" conveying magma from regions of higher pressure to those of lower pressure. Moreover, unlike the deep channels beneath the Hawaiian system, live magma would flow closer to the planet's surface in the manner of the now "dead" and empty tubes near the Hawaiian surface, for example the Thurston Lava Tube. The process is complicated, to be sure, with all of its isothermal phase changes and the presence of a substantial crust, but the descriptive fact remains that a planet tunnelled throughout by channels approaching its surface, and in a plastic or even fluid state in large volumes of its composition, will have a thermal gradient foreign to at least the present Earth.
The central point as far as heat transfer and thermodynamics are concerned is that cooling rate is inversely proportional to mass/ surface area ratio and to specific heat; a massive body with a relatively small surface area and a high specific heat cools at a much lower rate than a lighter body with large surface area and low specific heat. Calculations of planetary cooling rates which ignore these parameters are not relevant.
Enclosure (1) shows the temperature history of an alumina sphere first heated by radiation and then cooled by radiation. Data given show initial temperature, sink temperature, source temperature, and the heating and cooling tables. All of the data used are listed. Enclosure (2) shows the temperature history of a plastic sphere; again, both temperature history and thermophysical constants are given.
The predicted results are close to what experienced personnel anticipate, and are in fact correct. Enclosure (3) shows the computer program, written in FORTRAN IV, and a list of definitions of terms and symbols in the program. Basically, the algorithm finds energy radiated from or to an object in a small time interval and adjusts temperatures accordingly.
Enclosure (4) shows the temperature history of a spherical body having the mass, specific heat and surface area of Venus, given initial temperatures of from 1500°K to 6000°K throughout, and a radiation sink temperature of 200°K (Reference 3). It will be noted that an assumed 3000 second exposure to a 6000°K source has no effect (measurable) on a mass of that size already at 2000°K. This is a carping detail; the point is established that, if the body somehow has an initial 1500°K to 2000°K temperature, and if its mixed mean temperature is modified throughout the computational process in conformity to the Stefan-Boltzmann heat energy radiated away, we come up with exactly the present measured surface temperature.
This result can be taken seriously or regarded as an amusing coincidence, depending upon the reader's disposition. Using a lower sink temperature does not greatly alter the result. On the other hand, if mass and specific heat and surface area other than those of Venus are used, we don't get our 750°K result at 3500 years. This would, at first glance, appear interesting.
Another result of the inquiry is that it really doesn't make much difference whether the initial Venus temperature is 6000° K or 2000°K. This is shown clearly in Enclosure (4).
Fourier's theorem has been applied by the author in diffusion analysis and in conductive heat transfer analysis (Reference 1). Many of the arguments allegedly showing a low surface temperature after a few years erroneously use this conductive model, which would be valid only for a very old planet like the Earth:
[*!* Image INSERT KIV2_14.TIF]
Here x represents distance from a zero reference into the solid, t represents time, D thermal diffusivity, T(x,t) temperature at distance x and time t, and To the initial temperature of the body. It will be noted that, in order to apply Fourier's theorem easily, T(x,t) is taken to be zero when x = 0 at any time t, thus the equation does not model any large radiating mass or its temperature history.
Another objection to the thesis of a 750°K temperature, due to explosive origin, attempts to arrive at a time-dependent temperature with no consideration of surface area, mass and specific heat (Reference 2). I give the argument here for completeness, and examine what it really does show:
DH1 = heat acquired in 3000 seconds at 6000°K source, watt-seconds
Using the Stefan-Boltzmann law, we derive (in detail) the following:
We assume, in finding DH1, that the receiving body is at zero degrees Kelvin, and in finding DH2 that the heat sink is at zero degrees Kelvin. This is a trivial advantage in heating and a mammoth advantage in cooling due to the difference between Dt1 and Dt2. The assumption is also made that A1 = A2, although A1 could certainly be significantly larger than A2. But under these assumptions we obtain the following:
[*!* Image: INSERT KIV216A.TIF]
The result, though interesting, does not "devastate" anyone's theory, as the author and publishers would have us believe (Reference 2). All that is shown is that an amount of heat radiated in 3000 seconds at 6000°K also can be radiated in 3500 years at a mere 77°K or, to make it quantitative:
[*!* Image: INSERT KIV216B.TIF]
If exact details of how heat arose in the body are at issue, then one must assume photosphere exposure exceeding 3000 seconds and compatible with orbital mechanics, or else acquisition of heat from an ejecting source. Sunlight and radioactive sources remain alternative hypotheses, though the pattern shown in Enclosure (4) is even more astonishing as a coincidence than as a consequence of Velikovsky's hypothesis where it appears natural.
The mixed mean temperature of the Earth or of any planetary body of comparable age is of course higher than its surface temperature. Thermal gradients for the Earth are estimated using equations similar to the one I give for conductive transfer. Any mass of planetary magnitude which was in a molten* state only 3500 years ago will not have a thermal gradient comparable to that of the Earth. Surface and internal structure, under this assumption, would be more similar in temperature, and mixed mean temperature could be used to compute radiative losses at the surface, as with a hot fluid subjected to turbulent mixing. This is not inconsistent with partial formation of a crust. The mode of transfer is compound, but forced convection and radiation would predominate and conduction would play a smaller role than in the case of the Earth. These elementary principles of thermodynamics apply to planets as well as to less dramatic objects. No spooky new principles enter the picture, just because the object is huge. With each eruption of Mauna Loa or Kilauea in Hawaii, combined conductive, radiative and forced convective heat transfer occur.
[Footnote: *See Chris S. Sherrerd, "Venus' Circular Orbit," Velikovsky Reconsidered (N. Y., 1976), p. 132. The Ed.]
If one assumes, in the manner of the authors of Reference (2), that Venus is billions of years old (and this too, is an assumption), then the use of a mixed mean temperature to characterize its surface is invalid. There would be too few "Mauna Loas". Conduction would predominate in the transfer of heat from the interior to the surface, and the measured 750°K surface temperature would have to be the result of radioactive sources or of sunlight, as the Reference (2) authors correctly insist.
To explain away the 700°K-800°K computed temperatures, using Velikovsky's 3500 years of cooling from a molten state, whether at 1500°K or 6000°K, and also using the astronomically established mass, surface area and specific heat of Venus, will require considerable effort. If such effort can be expended constructively, within the scope of thermodynamics, it will be most welcome.
Broad brush scholarship is characteristic of many men and women of scientific genius. Professional critics can make light of the patriarch but the overwhelming value of his contributions stands untouched.
1. Philosophy and Unified Science, Parts I and II, Dr. George Robert Talbott, Ganesh and Co., Ltd., Madras India (1977), Auromere Press (U. S. Distributor), 785 Alcott Ave., Pomona, California 91766.
2. Scientists Confront Velikovsky, Dr. Donald Goldsmith, Dr. Norman Storer, Dr. Peter Huber, Dr. Carl Sagan, Dr. J. D. Mulholland, Dr. David Morrison, Foreword by Isaac Asimov, Cornell University Press (1977).
3. Worlds in Collision, Dr. Immanuel Velikovsky, Doubleday & Co., Inc. ( 1950).
Enclosure (1): Alumina Sphere, Physical Data and Temperature HistoryAlumina Sphere Mass: 3.2144 x 105 grams
Specific Heat: 9.1872 x 10-1 watt second/gram °K
Surface Area : 1 .1675 x 104 cm2
Initial Temperature : 673°K (400°C)
Heating Source Temperature: 1073°K (800°C)
Time Increment, Heating : 60 seconds
HeatingTime: 3000 seconds
Sink Temperature, Cooling : 300°K (27°C)
Time Increment,Cooling : 60 seconds
Cooling Time : 3600 seconds
Emissivity = 1.0 (black body)
Enclosure (2): Plastic Sphere, Physical Data and Temperature HistoryPlastic Sphere Mass: 1.3658 x 105 grams
Specific Heat : 1.67 watt second/gram °K
Surface Area : 1.1675 x 104 cm2
Initial Temperature : 473°K (200°C)
Heating Source Temperature: 573°K (300°C)
Time Increment, Heating : 60 seconds
Heating Time : 3000 seconds
Sink Temperature, Cooling : 300°K (27°C)
Time Increment,Cooling : 60 seconds
Cooling Time : 3600 seconds
Emissivity = 1.0 (black body)
Enclosure (3): Radiation Cooling Program
PROGRAM DEFINITION LISTEM, mass of the body heating or cooling by radiation
CP, specific heat of the body
A, surface area of the body during cooling
B, surface area during heating (A = B in our calculations)
FE, emissivity factor, dimensionless (FE = 1 in our calculations)
FA, form factor, dimensionless (FA = 1 in our calculations)
TZRO, initial temperature of body (absolute) prior to heating or cooling; this term is modified as heating or cooling occurs, i.e., as heat is gained or lost by radiation.
T, temperature (absolute) of heating source
DELTMO, time increment for calculation of heating
TMO, total time interval for heating
SINK, temperature (absolute) of cooling sink
STFBLT, Stefan-Boltzmann constant
DELT, time increment for calculation of cooling
FINTIM, total time interval for cooling
TPRINT time between printed outputs, for cooling;
(DELT <= TPRINT <= FINTIM).
NOTE: DELTMO and DELT call be set to a value less than one-tenth of the thermal time constant. but only values every TPRINT will occur as outputs.
PROGRAM FOR FINDING THE TEMPERATURE PROFILES OF RADIATING MASSES (SEE USAGE RULES TO FOLLOW)
READ(5,1)EM,CP,A,FE,FA,TZRO 1 FORMAT(6E12.5) READ(5,2)T,DELTMO,TMO,B,SINK 2 FORMAT(5E12.5) READ(5,8)STFBLT,DELT,FINTIM 8 FORMAT(3E12.5) READ(5,111)TPRINT 111 FORMAT(E12.5) PRINT=TPRINT FACTOR=STFBLT*FE*FA*A*DELT FLAG=l.0 CTIME=0.0 9 QIN=STFBLT*FE*FA*B*DELTMO*(T**4-TZRO**4) TZRO=TZRO+QIN/(EM*CP) CTIME=CTIME+DELTMO WRITE(6,10)CTIME,TZRO 10 FORMAT(4X,'RISE TIME',2X,E12.5,2X,'TEMPERATURE',2X,E12.5) IF(CTIME-TMO)9,9,6 6 IF(FLAG.NE.l.O)GO TO 3 TIME=O.O WRITE(6,4)TIME,TZRO 4 FORMAT(4X,'INITIAL TIME',2X,E12.5,2X,'INITIAL TEMP',2X,E12.5) FLAG=O.O 3 QRAD=FACTOR*(TZRO**4-SINK**4) TZRO=TZRO-QRAD/(EM*CP) TIME=TIME+DELT IF(TIME-PRINT)112,113,113 113 WRITE(6,5)TIME,TZRO 5 FORMAT(4X,'TIME',2X,E12.5,2X,'TEMP',2X,E12.5) PRINT=PRINT+TPRINT 112 IF(TIME-FINTIM)6,6,7 7 CONTINUE END
1. Read in all parameters.
2. Compute temperature versus time for heating:
^ | QIN=STFBLT*FE*FA*B*DELTMO*(T**4-TZRO**4) | v TZRO=TZRO+QIN/(EM*CP)
In a (relatively) small time increment, an amount of heat QIN enters the mass and raises its temperature from TZRO to a new TZRO. At most, TZRO will equal T. For a very large mass, the heating rate will be very slow, and to approach T will take a long time. The heating algorithm works by letting each newly formed TZRO go back to find a new QIN until the sum of DELTMO values equals TMO, at which time heating ceases. The plot of TZRO with time gives the "heating curve" or table.
3. Compute temperature versus time for cooling:
^ | QRAD=STFBLT*FE*FA*A*DELT*(TZRO**4-SINK**4) | v XTZRO=TZRO-QRAD/(EM*CP)
In a (relatively) small time increment, an amount of heat QRAD leaves the mass and lowers its temperature from TZRO to a new TZRO. At its minimum, TZRO will equal SINK. For a very large mass of relatively small area (as with spheres), the cooling rate will be very slow, and to approach SINK will take a long time. The cooling algorithm works by letting each newly formed TZRO go back to find a new QRAD until the sum of DELT values equals FINTIM, at which time cooling ceases. The plot of TZRO with time gives the "cooling curve" or table.
FUNDAMENTAL RULES OF USAGE
(a) For small solid masses, as in the cases of our alumina and plastic spheres, the algorithm is reasonably accurate.
(b) For small or large fluid masses, where fluid communicates with a radiating surface by forced convection, the algorithm is accurate.
(c)The algorithm loses accuracy as the temperature of the radiating surface departs radically from the mixed mean temperature of the entire body. For example, the algorithm would not be accurate where a molten fluid core communicates its heat by conduction only through a very thick billion-year old rock layer leading to the surface. One would not use the algorithm for terrestrial gradients.
(d)The algorithm does not take into account other radiative; heat loads (e.g., sunlight); it would apply mainly to a body experiencing ample forced convective heat transfer by circulating magma and lava, having a surface temperature akin to its mixed mean temperature, and shielded from solar energy by a 200°K filter of thick clouds. If a significant contribution to the body's heat load is ongoing solar radiation, then the algorithm would have to be modified.
Enclosure (4): Venusian SphereVenusian Mass : 4.83 x 1027 grams
Specific Heat : 9.1872 x 10 watt second/gram °K/
Surface Area : 5.0034 x 1018 cm2
Initial Temperature : 2000°K
Heating Source Temperature: 6000°K
Time Increment, Heating : 60 seconds
Heating Time : 3000 seconds
Sink Temperature, Cooling : 200°K
Time Increment, Cooling: 3.1536 x 107 seconds (one year)
Cooling Time : 1.1038 x 1011 seconds (3500 years)
Emissivity = 1.0 (black body)
Enclose (4): Venusian Sphere (Concluded)
3500-YEAR TEMPERATURE HISTORY AT 500-YEAR INTERVALS, USING INITIAL TEMPERATURES FROM 1500K to 6000K
Note: See the alternative tabulation on the following page.
3500-YEAR TEMPERATURE HISTORY AT 500-YEAR INTERVALS, USING INITIAL TEMPERATURES FROM 1500K TO 6000K, AND DATA SHOWN AT TABLE BASE
VENUS MASS = 4.87 x 1027 grams