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KRONOS Vol VII, No. 2

ON THE CIRCULARIZATION OF THE ORBIT OF VENUS

RAGNAR FORSHUFVUD

ABSTRACT

After the Saturn nova outburst that caused the Deluge, a flat cloud of hydrogen gas would have been rotating around the Sun. The aerodynamic drag caused by the hydrogen gas may have changed the orbit of Venus substantially in a period of a few hundred years. This is demonstrated by numerical calculations, using a theoretical model for the gas cloud. The effects of the gas on electric and magnetic fields in space are also discussed.

Velikovsky's reconstruction of ancient astronomical events requires that the orbit of Venus, originally elliptic like that of a comet of the Jovian family, became circular in a period of a few thousand years. Most astronomers refuse to believe that such a thing is possible. For a bibliography of works dealing with the problem (1977 and older), see Ref. 1. A more recent contribution to the discussion was written by Sherrerd.(2)

The problem of orbit circularization does not concern catastrophist astronomy only. According to some theorists, several satellites of the large planets are in fact captured asteroids which succeeded, after being captured, in achieving approximately circular orbits. The Moon may also be a captured body no really satisfactory theory has been found for the existence of a satellite to the Earth, the difficulty with the capture theory being the circularization problem.

The extra difficulty which meets the catastrophist is that the time scale is so short. Some of the oldest traditions refer to a time when there was no Moon.(3) This indicates that the Moon was captured comparatively recently. Furthermore, Velikovsky has suggested that the Earth was once a satellite of Saturn. This seems to be the only way to explain certain parts of the oldest myths, but it leaves us with another circularization problem: how did the Earth get its circular orbit, after it had left the gravitational field of Saturn?

In most of the circularization literature, the problem is discussed in general terms without quantitative analysis. An exception is the comprehensive treatment done by Rose and Vaughan.(4) In their interesting article, the authors specified the theoretical problems of Velikovsky's reconstruction: large amounts of energy and angular momentum seem to have disappeared mysteriously from the solar system. They estimated the total loss of energy since Venus left Jupiter at just below 1040 ergs, or 1033 joules, of which about 40 percent was lost before the Exodus, and the rest afterwards. If all this energy had been absorbed and stored by Venus, Earth, and Mars, the average storage requirement would be 10,000 calories per gram of planetary material. Assuming that the average specific heat of these planets is 0.2 cal/gK, the energy would be sufficient for heating each of them to 50,000 degrees Kelvin!

As a possible solution to these problems, the authors suggested that there was once one more body besides the known planets a body which later disappeared, either by a direct collision with Venus, at which the two bodies merged, or by a drastic change of orbit: "Various near-collisions have either propelled it right out of the solar system or else have placed it on a highly eccentric orbit with such a large semimajor axis that it is noticeable now only at its perihelion passages, which may be separated by many centuries." This hypothesis shows that the problem is not insoluble. However, for each orbit to be circularized, the theory requires the right body to be there at the right moment.

Several authors (5, 6, 7) have stressed the fact that our present knowledge of the solar system is incomplete and that forces of an electrical or magnetic nature may play a much greater role than is generally recognized. In 1972, Sherrerd(8) wrote: ". . . if there exist strong electromagnetic forces, attractive or repulsive, between Venus and the Sun, the orbit of Venus would tend to reach circular orbit in less time than expected by gravitational and tidal-dissipation considerations alone." But there is not yet a fully worked-out theory of electromagnetic circularization, and electromagnetic forces do not automatically solve the fundamental problems of energy and angular momentum.

This article was not written in order to rule out the possibility that the orbit of Venus was circularized by electromagnetic forces. Its purpose is to demonstrate that, even without such forces, the circularization of the orbit of Venus can be fully explained on the basis of a simple gas-cloud model. Although no such gas cloud is observed today, neither its creation nor its dissipation is inherently implausible. As we shall see, electromagnetic forces were probably responsible for the scattering of the cloud.

THE GAS CLOUD

When studying ancient catastrophes, Velikovsky found that the Deluge must have been caused by a nova-like outburst within the solar system.(9) He identified the erupting body as Saturn. Tresman and O'Gheoghan,(10) and Cardona(11) have come to the same conclusions. Most of Velikovsky's works on the subject are still unpublished.

The present theory is based upon the assumption that the outburst of Saturn gave rise to a disc-shaped cloud of hydrogen gas, rotating around the Sun. This cloud is assumed to have remained in the solar system for several thousand years, so that it was still there when Venus entered upon the stage.

The idea of the disc-shaped cloud came from the fact that such clouds play an essential part in modern nova theory. Rotating gas clouds, shaped like discs or rings, are assumed to be created whenever a cataclysmic variable has an outburst, regardless of whether this cataclysmic variable is an ordinary nova, a recurrent nova, a dwarf nova or a nova-like variable. In general, it is agreed that a nova consists of at least two bodies. The one with the larger mass is called the primary, and the one with the smaller mass, the secondary. During the outburst, hydrogen-rich material is transferred from the gravitational field of the secondary to that of the primary, forming a disc-shaped cloud rotating around the primary.(12)

Applying the accepted nova model to a hypothetical outburst of Saturn is not without problems. It requires Saturn to have been much larger than now, and much closer to the Sun. There is also another problem, which may seem even worse: existing nova theory says that the primary of a nova binary is always a white dwarf. A white dwarf is a star with a mass comparable to that of the Sun, but a diameter comparable to that of a planet. This description does not fit the Sun very well. However, Warner(13) has pointed out that the evidence for a white dwarf may be a bit shaky: the original evidence must be "relegated", but in the meantime new findings have been made which do indicate an object "the size of a white dwarf". But is this object necessarily the primary? [See Editor's Note at the end of this article]

To understand how a fundamental thing like this can still be under discussion, one must remember that no nova outburst so far has been close enough to allow the observation of details. Not even the disc has ever been watched through a telescope or seen in a photograph it is a part of a theoretical model, based upon results from observational techniques such as spectroscopy, high-time-resolution photometry, radio interferometry, etc.

Summarizing nova research in 1975, Sahade(14) said the following:

". . . I sometimes feel that we are in too much haste to provide models and to reach definite conclusions when the phenomena to be explained are not simple and, in most cases, the amount of available information is too meager even to attempt a simple description of actual facts."

It may be sensible, therefore, not to lean too heavily on existing nova theories. Let us assume that some kind of outburst took place not necessarily similar to anything yet observed by modern astronomers and that hydrogen gas was ejected from Saturn. If we study what has been published of Velikovsky's own words on Saturn and the Flood(15) we find that he mentions the disruption of Saturn as well as the ejection of hydrogen gas. If, as most theorists believe, a large portion of Saturn is hydrogen, a disruption would automatically lead to ejection of hydrogen into space.

A portion of the hydrogen gas probably had sufficient energy for leaving the solar system forever. Gas molecules with sufficient energy to leave the gravitational field of Saturn, but not the gravitational field of the Sun, would circulate in orbits around the Sun, forming a gas cloud similar to the disc-shaped cloud of the accepted nova model, which also rotates around the primary.

The reason why such a cloud assumes a flat shape is that the amount of energy required for giving something an orbit in or near the plane of revolution (corresponding to the ecliptic plane of the solar system) is much smaller than the energy required for giving it an orbit far from this plane, a fact well-known to those who follow space research.

For similar reasons, the direction of the cloud's rotation would coincide with the direction of Saturn's movement around the Sun. A rotation in the opposite direction would require much more energy.

The mass distribution within a cloud of the type described is not governed by aerostatic laws such as those that determine the mass distribution of the terrestrial atmosphere. The gravitational attraction of the Sun cannot pull the cloud inward because of the high velocities within the cloud. (For basically the same reasons the Moon does not fall down upon the Earth.) In each point of the cloud, gas velocity coincides with the velocity of a hypothetical satellite on a circular orbit at the same distance from the Sun. It may be a little misleading to say that the cloud is rotating, as it is not rotating as a solid body. Each particle in the cloud is in fact orbiting the Sun.

The cloud formed by the Saturn nova outburst consisted mainly of hydrogen gas. It certainly contained other things as well, but in what proportions is difficult to say. As the cloud was the cause of the Deluge, it must have contained water unless as Velikovsky suggested as a possibility, the water was the result of an oxidation of hydrogen in the Earth's atmosphere.(16)

My own guess is that the cloud did contain water originally in the form of ice crystals. The ice contained a small proportion of common salt (sodium chloride) and other contaminants (old sources say that the waters of the Deluge were salty(17)). In the heat of the Sun, the ice vaporized with the contaminants forming a dust. The water vapour and the dust remained in the gas and followed the same path around the Sun.

Planets having elliptic orbits met an aerodynamic drag which tended to damp out all movements relative to the cloud, so that the orbits tended to conform to the circular movement of the cloud.

The theory has an attractive feature. If it is correct, the circularization of planetary orbits would not be the result of some rare coincidence. It would be the logical consequence of the damping action of the gas upon any movement relative to the gas.

GRADUAL ENERGY LOSS

Rose and Vaughan(18) worked out three possible sequences of events, all starting with the stage when Venus was still behaving like a comet of the Jovian family and ending up with the present situation. One of these sequences, specified in Table 3 of the cited work, is especially interesting because it is based upon the assumption that energy was lost gradually by the planets, rather than only at those times when near-collisions were in progress. This is exactly what would happen if aerodynamic drag was at work. However, it must be pointed out that Rose and Vaughan assumed that the angular momentum of each planet remained constant between encounters, while aerodynamic drag will generally not leave angular momentum unaffected. This parameter may either increase, decrease, or remain essentially the same, depending on the diameter of the cloud and the mass distribution within it.

Table 1 in this work is a reproduction of the first part of Table 3 in the article by Rose and Vaughan. Only the orbit of Venus is changing between stage 1a and stage 1b. The decrease of the semimajor axis from 3.0 to 2.1 A.U. is accompanied by a decrease of eccentricity from 0.794 to 0.687, which is exactly what is required to keep angular momentum constant. If we allow a decrease in angular momentum, the eccentricity will change less; if we allow an increase, it will change more. Still, both the 1a and the 1b orbits can be considered as typical examples of possible Venus orbits during the first phase of the circularization process, and both will be used here for testing the hypothesis of circularization by aerodynamic drag.


Semi-major Axis Eccentricity Mass Sidereal period Mean Synodic Period* Perihelion Aphelion Minimum velocity Maximum velocity Energy Angular Momentum
Stage 1a










Earth .706 .070 1.012 .593
.656 .755 6.972 8.022 -28.307 5.330
Mars .574 .080 .107 .435 2.748 .528 .620 7.655 8.986 -3.680 .508
Venus 3.000 .794 .870 5.196 1.129 .618 5.382 1.229 10.705 -5.724 5.756
Stage 1b








-37.712 11.594
Earth .706 .070 1.012 .593
.656 .755 6.972 8.022 -28.307 5.330
Mars .574 .080 .107 .435 2.748 .528 .620 7.655 8.986 -3.680 .508
Venus 2.100 .687 .870 3.043 1.242 .657 3.543 1.867 10.067 -8.178 5.756










-40.165 11.594

The energy lost by Venus between stage 1a and stage 1b is 2.454 geobasic energy units, which corresponds to 3.3 x 1032 joules. We shall now investigate whether aerodynamic drag could be responsible for this loss of energy.

A cloud model is presented in Figure 1. The Sun is surrounded by a flattened cloud of circulating gas. The cloud has the shape of an ellipsoid with one minor axis of 0.2 A.U. and two major axes of 4.0 A.U. each. For simplicity we assume the gas density to be constant within the cloud. At each point, the gas velocity equals that of a body in a circular orbit at the same distance from the Sun, which means that the velocity of the gas is inversely proportional to the square root of the distance from the Sun.

For simplicity, the plane of the major axes is assumed to coincide with the plane of the orbit of Venus. A deviation of one degree would shorten Venus' path through the cloud by about 2 percent. The present orbital planes of the planets do in fact deviate slightly from one another. For instance, the angle between the orbit plane of Venus and the orbit plane of Saturn is 2.1 degrees.

Figure 2 shows the initial orbit of Venus. The period of revolution was 5.196 years, and it took Venus 0.690 year to pass through the cloud.

The orbital velocity of Venus reached a maximum each time Venus passed through the perihelion point, which is the point in the orbit closest to the Sun. But to calculate aerodynamic drag we must know the velocity relative to the surrounding gas. At perihelion, Venus and the gas moved in the same direction, which means that the velocity of the gas should be subtracted from the velocity of Venus. This relative velocity had a minimum, not a maximum, at perihelion, as shown in Figure 3.

All the time, the relative velocity was well above that of sound. The velocity of sound in hydrogen is about 1300 m/s at 300K and 1500 m/s at 400K.

[*!* Image] Fig 1. Disc-shaped cloud model.

Fig 2. Rotating gas cloud (stitched contour) and orbit of Venus. The velocity of Venus at perihelion (P) was 51km/s, while at aphelion (A) it was only 5.8km/s. S =Sun. Gas velocity at P: 38km/s. Orbit parameters are those of stage 1a, Table I.

Fig 3. The velocity of Venus relative to the surrounding gas had a minimum at perihelion. Note that the velocity is many times higher than that of sound in the gas, which would be about 1.3km/s at 300K and 1.5km/s at 400K.

Aerodynamic drag at supersonic speed can be calculated from the expression 0.5 [rho] V2 A, where [rho] is the density of the gas, V is the velocity relative to the gas and A is the effective cross section area.

Two parameters have yet to be decided upon: the effective cross section area of Venus and the density of the cloud.

When estimating the effective cross-section area of Venus, we must remember that Venus was once surrounded by an extended atmospheric envelope.

THE EXTENDED ATMOSPHERE

When Venus left Jupiter, as posited by Velikovsky, it brought with it an envelope of gas, dust, and larger particles. It may seem logical that a body moving on an elliptic orbit, like a comet, should also have a cometary tail. This, however, can by no means be taken for granted, and as a matter of fact there are fundamental differences between the tail of a comet and the envelope surrounding Venus.

The mass of an ordinary comet is small. No one knows exactly how small, but even very bright comets have been shown to have masses smaller than 10-6 Earth masses. Consequently, the escape velocity at the surface of the nucleus is also small. As the comet approaches the Sun, material on its surface is vaporized, and the vaporized material immediately leaves the nucleus and is swept away by radiation pressure and the solar wind. Even at moderate temperatures, gas molecules easily exceed the escape velocity. The nucleus may also be rotating, which helps to send material out into space.

With a large body like Venus, things are different. The escape velocity at its surface is about 10 km/s. Enormous amounts of energy are required to accelerate material to this velocity. The present atmosphere, although much more massive than its terrestrial counterpart, is nevertheless just a thin shell surrounding the planet, compressed by gravity to a thickness of less than two percent of the planet's radius.

And yet, some thirty-five centuries ago, the Exodus encounter brought down meteorites, petroleum, and red dust to the Earth from the extended atmosphere of Venus. Physical considerations of this encounter and other types of evidence presented by Velikovsky indicate that the atmosphere and tail of Venus must have been extended indeed. How could this extended atmosphere avoid being compressed by gravity? A possible explanation is that the gas, dust, and larger particles of the extended atmosphere were whirling around Venus at velocities approaching the escape velocity.

Theoretically, gaseous material can circulate (orbit) around a planet at a distance as large as that of any remote satellite. There is a limit, however. At distances where the gravitational force of the planet cannot compete with that of the Sun, no satellite orbits are possible, and no material can stay.

ROCHE LOBE

In celestial mechanics, the region where the gravitation of a planet dominates over that of the Sun is known as the Roche lobe, sometimes called the Lagrangian lobe. The Roche lobe is drop-shaped, with its point directed towards the Sun. Inside the lobe, a satellite will generally follow a stable orbit, but if for some reason it is brought outside the lobe, it is likely to leave the planet, falling into an orbit around the Sun.

To calculate the extension of the Roche lobe is not as simple as it may seem. It is not just a question of comparing gravitational forces; instead, the Roche lobe is calculated as an equipotential surface in a rotating coordinate system, which means that system acceleration must also be taken into account. Tables have been published by Kopal.(19)

In astronomical literature the Roche lobe is occasionally called the "Roche limit". This denomination should be avoided, however, to prevent confusion with another concept for which the same term is used, namely the minimum distance to which a large satellite can approach its mother planet without being torn apart by tidal forces. This Roche limit has no connection with the Roche lobe, except that both are based upon the law of gravitation.

When a body moves on an elliptic orbit, as Venus did in early days, the Roche lobe will grow and shrink synchronously with the distance to the Sun. Each time Venus approached perihelion the lobe contracted. The material that came outside the lobe was left behind, forming the long tail of Venus.

The regular contraction of the lobe had a limiting effect upon the extension of the atmosphere of Venus. When Venus passed close to the Sun for the first time, most of the envelope of gases, dust, and larger particles that Venus had brought with it from Jupiter was stripped off. What remained was principally material that had its orbit inside the minimum extension of the lobe. As shown in Appendix I, the minimum value of the lobe radius was approximately 5.8 x 108 m or 580,000 km in stage 1a, which is about 1.5 times the present Earth-Moon distance.

But the extended atmosphere was not only influenced by gravitation. Dynamic pressure from the interplanetary gas forced the atmosphere backwards, into the rear part of the lobe. It also had an important influence upon the atmosphere's circulation pattern, as indicated in Fig. 4. The outer parts of the atmosphere were streaming backwards because of friction forces from the gas of the interplanetary cloud. Near the central axis, the gas returned forward in a large whirl, attracted by Venus' gravitation. This whirl probably looked like a tornado funnel and is probably the "dragon" of the myths "a writhing, bright, elongated thing".(20)

[*!* Image] Fig 4. When Venus passed through the gas cloud, it's "extended atmosphere" actually a system of circulating gas and dust was pressed backwards into the rear part of the Roche lobe. The dotted contour in the figure is the outline of the Roche lobe.

The strange, circulating gas-and-dust system of Fig. 4 has very little in common with what we would normally call an atmosphere. Still we shall use this denomination for the lack of something better.(21)

It should be noted that the atmosphere's center of gravity was situated well behind the body, so the body attracted the atmosphere and the atmosphere attracted the body. Aerodynamic drag, primarily acting upon the atmosphere, was transferred to the body by gravitation.

This description of the atmosphere of Venus is not necessarily correct in all details. Its sole purpose is to serve as a basis for an estimate of the effective cross-section area of the atmosphere. The characteristics of the atmosphere model are as follows:

Shape approximately spherical
Radius 3 x 108 m
Effective cross-section area 2.83 x 1017 m2
Mass 3 x 1021 kg
Average density 2.65 x 10-5 kg/m3

The mass chosen for this model is greater than the present mass of the atmosphere of Venus, which is 4.8 x 1020 kg. Much of the original atmospheric material is assumed to have left Venus via the long tail. Much material was transferred to the Earth during the Exodus encounter. Much of what was left consisted of dust and larger particles, now settled on the surface of Venus.*

* Editor's Note: Be that as it may, the only two photographs ever taken from the surface of Venus by Veneras 9 and 10 on October 22, 1975 show a rocky surface (see New Scientist, 20 January 1977, pp. 127-129 and Science News, April 16, 1977, pp. 252, 253, 255). These limited data are too fragmentary from which to draw planet-wide conclusions. The dust remains to be found. CLE

THE DENSITY OF THE CLOUD

Estimating the density of the cloud may seem a difficult task. At first glance, it seems that the density could have been almost anything. A closer investigation shows, however, that some clues do exist.

Using data from nova observations, astronomers have tried to estimate disc masses. Warner(22) reports that disc masses can be expected to be of the order of 10-4 solar masses for all cataclysmic variables (these include classical novae, recurrent novae, and dwarf novae). Provided that we have chosen a reasonable value for the volume of the cloud, we can get a rough idea of the density of the cloud simply by dividing mass by volume. The result is 3.6 x 10-8 kg/m3.

Velikovsky came to the conclusion that the material ejected from Saturn was absorbed by Jupiter.(23) If the whole mass were absorbed by Jupiter, the mass of the cloud can obviously not have been greater than the mass of the present Jupiter. This gives us an upper limit for the mass of the cloud: 1.9 x 1027 kg. The corresponding density is 3.4 x 10-7 kg/m3. As Jupiter must have existed before it could start to absorb anything, it can only partly consist of absorbed material. On the other hand, parts of the cloud may have gone elsewhere (for instance, absorption by the Sun cannot be excluded).

Another approach is via the optical properties of the cloud. Although pure hydrogen has a very good transmittance for light, there is always the so-called Rayleigh scattering, a phenomenon that is common for all gases and causes attenuation of light, especially at short wavelengths. Fig. 5 shows the effect of Rayleigh scattering on transmittance of light for three different gas densities, assuming that the gas was 100% hydrogen. If the density of the cloud were as high as 10-6 kg/m3, sunlight would be reduced to a very faint, reddish light. We have no reason to believe that sunlight was quite so attenuated in Middle Kingdom days, although there are good reasons to believe that the cloud had some attenuating effect. (One of these reasons is the following. If, as Velikovsky proposed,(24) the Earth were much closer to the Sun in pre-Exodus days, one would have expected the climate to have been terribly hot. However, the available evidence suggests that this was not the case. While certain problems may remain, it seems clear that attenuation of the Sun's radiation by the cloud would have provided some reduction in the amount of heat reaching Earth.)

We can conclude from Fig. 5 that the cloud density was probably not as high as 10-6 kg/m3. Unfortunately, this is the only conclusion we can draw, because the cloud probably contained not only hydrogen, but also minor portions of substances that are much more efficient absorbers of radiation, such as ozone (absorbing UV radiation), water vapour (absorbing IR radiation), and dust (which absorbs and scatters all kinds of radiation).

[*!* Image] Fig 5. Light transmission through the hydrogen gas of three densities at a distance of 0.81 A.U. (=pre-Exodus distance Sun-Earth according to Refs. 25 and 26).

Based upon the above considerations, the density 10-7 kg/m3 was selected for the model. For comparison, the density of the terrestrial atmosphere at sea level is approximately 1.2 kg/m3, while at 110 km altitude it is only about 10-7 kg/m3. The density of the interplanetary plasma is of the order of 10-20 kg/m3 near the orbit of the Earth.

The parameters of the gas cloud model are summarized in Table II.

Table II: Parameters of Gas Cloud Model .

Shape rotational ellipsoid
Major axes 4 A.U.
Minor axis 0.2 A.U.
Volume 5.61 x 1033 m3
Density 10-7 kg/m3
Mass 5.61 x 1026 kg (94 Earth masses)

TESTING THE MODEL

The energy lost by Venus between stages 1a and 1b was 3.30 x 1032 joules (J). Using the computer program of Appendix II, one can calculate the energy loss per revolution as Venus moved through the gas cloud, and from this the average loss per year, as shown in Table III. The result is an average loss of 5.94 x 1029 J per year, which means that the time required for Venus to lose 3.30 x 1032 J of energy in our gas cloud model is approximately 556 years.

Table III: Energy lost by Venus

Joules per rev. Joules per year (average)
Stage 1a 2.84 x 1030 5.47 x 1029
Stage 1b 1.95 x 1030 6.41 x 1029
Average 5.94 x 1029

These are modern years. Pre-Exodus years were almost certainly shorter. Using a pre-Exodus year of 266.3 modern days, as suggested by Ransom and Hoffee,(25) would give us 762 pre-Exodus years between stages 1a and 1b. Rose and Vaughan assumed a pre-Exodus year of 0.593 modern years,(27) which would make the time between 1a and 1b equal to 937 pre-Exodus years.

And how much time actually elapsed between stages 1a and 1b? Unfortunately, we have no exact figure. Stage1b is the Exodus stage, about 1450 B.C. Stage 1a is the stage when Venus had just left the gravitational field of Jupiter. Velikovsky seems to have been uncertain about the date for this event. He only stated that it took place after the Deluge, "maybe hundreds or thousands of years later".(28) If the Deluge took place as late as 3400 to 3200 B.C. (a "possible" date according to Mullen(29)), the period between stages 1a and 1b could not have lasted more than 2000 years.

The calculated results are well within that limit. If future research should show that the 1a-1b period was shorter, it may become necessary to adjust the model so as to increase the energy loss per revolution. This could be accomplished by increasing the gas density somewhat. Thus the 1a-1b period could be brought down by a factor of three, but not much more.

THE SHOCK WAVE

A body traveling through gas at supersonic speed will give rise to one or more shock waves in the gas.

Aircraft and missiles designed for supersonic speeds have pointed noses. When they fly at supersonic speed, shock waves extend from points and edges, as shown in Fig. 6. But if an aircraft with a blunt nose is operated at supersonic speed, a curved shock wave is formed ahead of the object, as shown in Fig. 7. The shock wave that preceded Venus must have been similar in shape.

[*!* Image] Fig. 6. Flow about a body streamlined for supersonic speed. After Ref. 30.

Fig. 7. When a body streamlined for subsonic speed is traveling at supersonic speed, a shock wave is formed ahead of the body. After Ref. 30.

The temperature of a shock wave may reach several thousand degrees Kelvin, which is more than enough to make the gas incandescent. Hydrogen does not emit very much visible light when heated, but if there are sodium-chloride particles in the gas, it makes a great difference; sodium is known for emitting an intense yellow light when heated.

It seems likely that the ancients saw a luminous shock wave preceding the planet Venus. Many ancient gods had attributes of different kinds, some of which could be explained as attempts to describe a shock wave (e.g., the shield of Athene and the bow of Artemis). It also seems likely that the Greeks partly understood the nature of the shock wave, which resembled the bow wave of a ship, and that this was the reason why they thought that space was filled by a medium which they called aether. They were right the medium consisted mainly of hydrogen gas.

When a body moves through gas at supersonic speed, a large portion of the energy lost by the body is dissipated in the shock wave. This fact is utilized for bringing space travellers back to earth without frying them. A re-entry capsule has an enormous kinetic energy when it enters the atmosphere of the Earth. According to one source, "careful vehicle design can result in more than 99% of this energy remaining in the air".(31) Thus it is not so strange as it may seem that nearly 1040 ergs (1033 joules) of energy could be dissipated without heating the planets to many thousand degrees Kelvin. Most of the energy remained in the hydrogen gas.

Today each planet, including the Earth, has a bow shock wave in the solar wind. These waves are not visible.

THE ELECTROMAGNETIC EFFECTS OF THE GAS CLOUD

The solar wind, or the continuous flow of plasma (ionized gas) out from the Sun, was mentioned earlier in terms of its effect on comets. One might think that the solar wind would soon sweep interplanetary space free from gas, thus removing the gas cloud, but the dynamic pressure of the solar wind is too low for that. Instead, the gas impeded the solar wind. For some period of time, probably a few thousand years, the solar wind ceased to blow through interplanetary space.

The gas cloud must have brought about a drastic reduction of electrical conductivity in interplanetary space, partly because of the reduction of the mean free path (by many orders of magnitude), partly because of the reduced degree of ionization wherever the Sun's radiation was attenuated by the gas.

Mainly from traditional evidence, Velikovsky inferred that electrical discharges took place between celestial bodies in the past. Electrical discharges require electric fields. Among astrophysicists it is generally agreed that electric fields in space are negligible because of the high conductivity of plasmas. But the gas had a relatively low electrical conductivity, especially in those parts of the gas cloud where the general radiation level was low. Thus the gas cloud takes away another theoretical problem.

Even more interesting is the effect that the cloud may have had on the magnetic field in interplanetary space. Today this field is comparatively weak. At the Earth's orbit, 30 microgauss is a typical value.

Many stars are surrounded by magnetic fields of several thousand gauss. The Sun's magnetic field reaches only 0.5 to 1 gauss at the poles. Still, many theorists think that the Sun has a strong internal field. If so, the reason the external field is so weak is that electric currents in the surrounding plasma outbalance the magnetic field from the Sun almost completely. It is interesting to note that the same explanation has been offered for the fact that no magnetosphere has been observed around Venus.(32)

According to a model by M. A. White, published in the Handbook of Geophysics and Space Environments, the Sun's magnetic dipole moment is 8.8 x 1043 cgs units.(33) From this we can calculate the flux density at the Earth's orbit, had there been no plasma currents. The result is 260,000 gauss! This is a purely hypothetical figure. Even in a low-conductivity medium, electric currents will flow and reduce the magnetic field, although it will not be as completely neutralized as in a high-conductivity medium.

It is possible, perhaps even probable, that one result of the reduction of the electrical conductivity in interplanetary space was a relatively strong interplanetary magnetic field, extending from the Sun. Conversely, if we could prove that the magnetic flux density in interplanetary space was once much larger than it is now, it would be a strong indication that something had happened to the electrical conductivity in interplanetary space.

Apart from these theoretical considerations, do we have any support for the idea that a strong interplanetary field existed a few thousand years ago? Is it possible that the effects of such a field would still be noticeable?

The ability of ferromagnetic materials to become magnetized and thus "remember" a magnetic field is well-known. Less well-known is the fact that any object with a certain electrical conductivity can retain a magnetic field for a limited period of time. The field is then sustained by eddy currents in the object, in accordance with Lenz' law. As the magnetic energy is dissipated by the eddy currents, the field keeps decreasing until it is no longer measurable. For a small metal object, like a copper coin, this occurs within a few milliseconds after the removal of the external field, but large objects may retain a field for a very long time. The lifetime of the field is proportional to the square of the body's radius multiplied by its electrical conductivity. For the Earth, the half-life is of the order of a few thousand years. One source indicates that "electric currents in the earth's core can last for about 10,000 years without having to be regenerated",(34) while Barnes(35) points out that the presently observed decay (5% per 100 years) corresponds to a half-life of only about 1400 years.

If there were a strong magnetic field in interplanetary space a few thousand years ago, eddy currents would still be circulating inside the Earth. We would then have an attractive explanation for the present geomagnetic field, in fact a much better explanation than the so called "dynamo theory".

As pointed out by Barnes,(36) the dynamo theory is questionable, to put it mildly. Barnes has also shown that no dynamo theory is required to explain the circulating current that causes the Earth's magnetic field. "There is no more need for a dynamo in the earth's core to keep the current flowing than, by analogy, there is a need for a motor to keep the earth spinning."

Some of Barnes' conclusions were criticized by Milsom.(37) Still, there seems to be nothing wrong with the main lines of Barnes' reasoning. If there is a large current circulating in a conducting body, there is only one probable cause for this: the magnetic flux through the body is changing, either increasing or decreasing. We know that the Earth's total magnetic flux is decreasing at a rate of about 5% per 100 years. The decrease explains the current, and the current explains the field. The only thing that remains to be explained is how the field was acquired in the beginning. There must have been an external cause. What could it have been but a magnetic field in space?

Barnes' theory of a recent origin of the Earth's field implies that the field has been declining ever since it was created. When Milsom criticized Barnes' theory he objected that the field has been decreasing only for the last 2000 years. A paleomagnetic compilation by J. A. Cox(38) shows a maximum about 1500 years ago, as shown in Fig. 8.

[*!* Image] Fig. 8. The variation of the Earth's magnetic field during 9000 years, according to Ref. 38.

[*!* Image] Fig. 9. Apparent precessing movement of interplanetary field. The angle [delta] is the inclination of the Earth's axis (presently 23.45 degrees).

Fig .10. A rotating magnetic sphere (would not work today).

Before that there was a period of about 4000 years when the field was building up. Further back in time, the field was declining at a rate comparable to the average decline over the last 1500 years. Such a decline of the field is to be expected when the interplanetary field is weak. The magnetic energy is then slowly dissipated by electric currents in the interior of the Earth. The intermediate building-up period can be explained if we assume the existence of a strong interplanetary field during this period. This would mean that the measured field intensities from this period are really the sum of two fields: the external, interplanetary field and the field from electric currents in the Earth.

In a reconstruction of the field's time variation compiled by Bucha(39) the field minimum is roughly 1500 years earlier than in the reconstruction by Cox. This reflects the general uncertainty in the dating of prehistoric objects. There is a corresponding uncertainty in the dating of the Flood, which according to the theory presented here should be roughly contemporary with the geomagnetic field minimum.

ROTATING SPHERES

Because of the inclination of the Earth's axis, an interplanetary field would precess in an earthbound coordinate system, completing one turn per sidereal day, as shown in Fig. 9. This apparent movement of the field would make it possible to construct rotating magnets. A magnetized ball, pivoted as indicated in Fig. 10, would rotate one turn per sidereal day, provided friction was low enough. It is a remarkable fact that Petrus Peregrinus, who wrote his famous "Epistola de Magnete" in 1269, maintained that it was possible to pivot a sphere of magnetite in such a way that it rotated one turn per sidereal day.(40) This was probably no longer true in his days. He was probably just echoing an older tradition. Silvanus Thompson, commenting on the work of Peregrinus, said: "Possibly all this is only an echo of an old tradition that Archimedes constructed a sphere which reproduced the motions of the heavenly bodies doubtless a mere model."(41)

This "mere model" was in fact quite famous and is often mentioned in ancient literature. Archimedes, who usually did not describe his own mechanical inventions, made an exception for this one, describing it in a work called "On Sphere Making" ([Greek text]), unfortunately no longer extant. From Cicero we know that Archimedes made at least two spheres, one of which was placed in the temple of Virtus by Marcus Marcellus after the capture of Syracuse.(42) According to Cicero, the first sphere of the kind had been made by Thales of Miletus. The same Thales, who lived in the sixth century B.C., is the first European known to have described magnetism. The sphere of Thales was a simple solid sphere. Archimedes improved the invention, adding a gear to indicate the positions of the Sun, the Moon, and the five known planets. Hultsch(43) conjectured that the sphere was driven by water. We cannot prove that the sphere was driven magnetically, but otherwise where did Petrus Peregrinus get his strange idea?

A probable order of magnitude for the interplanetary field at Earth's orbit is 1 gauss. If it had been much weaker, it could not have turned Archimedes' sphere around. It could not have been much stronger, either, at least not for a long period of time, without leaving paleomagnetic traces.

WHAT HAPPENED TO THE CLOUD?

We have shown that a gas cloud provides a unified explanation for various phenomena. However, as there is no interplanetary gas cloud rotating around the Sun today, we are faced with the problem of explaining how it could disappear in the 3500 years that have passed since the Exodus. To move the gas cloud from its place near the Sun to a remote location (e.g., the orbit of Jupiter, where the gas could be collected and absorbed by this planet) would require something like 2 x 1035 J of energy, or 2 x 1042 ergs. Thus the whole hypothesis may seem like an attempt to drive out the Devil with Beelzebub. First, in order to explain the disappearance of 1040 ergs from the solar system, we assume the former existence of an interplanetary gas cloud. Then we need 2 x 1042 ergs to get rid of the cloud! This problem may seem to be a serious one, but there is a solution to it.

Theoretically, a rotating gas cloud like that of our model could linger for a very long time. It would gradually get flatter because of internal collisions and would ultimately look like Saturn's rings, very flat, with circular concentric orbits. But it would stay for millions of years, unless there were some more efficient scattering mechanism than thermal diffusion and radiation pressure.

Such a mechanism exists. We may call it "the magnetic centrifuge". If the central body has a magnetic field and is rotating, the magnetic field will also be rotating. This rotating magnetic field will interact electromagnetically with the gas, provided that the gas contains ions, which it normally does. The circular motion of the cloud will be accelerated and the gas will migrate outwards. Possibly, this is a normal process after a nova outburst. From modern nova observations, Warner draws the interesting conclusion that "evidence exists for a stream of material leaving the disc".(44) He then lists the evidence, most of which is hard to understand for anyone except the professional astronomer.

By the magnetic-centrifuge process, both energy and angular momentum would be transferred to the cloud, the source being the Sun's rotational energy and angular momentum.

The present interplanetary field is too weak for transferring the required energy to the cloud in less than 3500 years. If we adhered to the uniformitarian view that conditions in interplanetary space have remained unchanged for the last few million years, we would have a theoretical problem. Fortunately, we have seen indications that only 2000 years ago the interplanetary magnetic field was much larger than it is now.

The former existence and sudden dissipation 25 centuries ago of a strong magnetic field in space has been suggested before by Sherrerd.(45) He noted that a substantial circularization effect upon planetary orbits would require field strengths many orders of magnitude larger than those known to exist today. Much weaker magnetic fields would be sufficient, however, for scattering the gas cloud in a few thousand years, mainly because of the low density and large area of the cloud. As shown in Appendix III, a field of the order of 1 gauss should be enough.

From magnetic bodies like the Earth and Jupiter, rotational energy is transferred to the surrounding plasma. Space research has revealed regions of corotating plasma in the magnetospheres of both these bodies.(46)

CONCLUSION

The circularization of the orbit of Venus and the nova-like outburst of Saturn are two separate parts of Velikovsky's reconstruction. Both rest mainly on the evidence of human traditions. The theory presented here shows that one can be explained if the other is true.

In the author's opinion, the fact that the nova hypothesis turns out to support the circularization hypothesis strongly indicates that both are correct.

Editor's Note: Warner's use of "relegated" is not clear. While the quote is accurate, Warner should have followed "relegated" with a phrase such as "to lesser status" or simply used a different verb such as "discounted". Warner's text, which Forshufvud is characterizing, follows: "The evidence for a white dwarf primary was originally based on the presence of a hot continuum in stars of low luminosity (Section 6), evidence which must be relegated because the bright spot is in general the dominant light source, and on the presence of apparent extreme pressure-broadening in the absorption spectra of WZ Sge and DI Lac, evidence which we dispute in Section 7. However, the emission lines with wings out to several thousand km s-l (section 7) and the existence of brightness oscillations with periods ~20 s (Section 12) both indicate objects of the size of white dwarfs." CLE

* * *

APPENDIX I: THE EXTENSION OF THE ROCHE LOBE

Although the Roche lobe is not spherical, a sphere with the same volume is a good approximation. The radius of such a sphere can be calculated from the following formula with an accuracy of about 2%, provided M2 < 0.5M1, where M1 is the mass of the primary and M2 is the mass of the secondary.(47)

R2/a = 0.462 (q/(a+q)1/3
where R2 = radius of sphere.
a = distance between bodies.
q = M2/M1

R2 as given by the formula above is 0.67 times the distance from the body to the point of the drop-shaped lobe (the inner Lagrangian point).

In a strict mathematical sense, the Roche lobe is defined only for the circular case, where a is a constant. However, if for a we substitute the instantaneous distance between Venus and the Sun, the result will not be too far from the truth. The smallest distance occurred in stage 1a(perihelion = 0.618 A.U.). The formula gives us the minimum value of R2: 5.8 x 108 m.

APPENDIX II: COMPUTER PROGRAM FOR CALCULATING ENERGY LOSS PER REVOLUTION

Definitions (see also Fig 11)

AR Effective cross-section area of Venus
RO Density of gas cloud
E Eccentricity of Venus orbit
A Semimajor axis of Venus orbit
R Radial coordinate of Venus in heliocentric system
f (FI) Angular coordinate of Venus in heliocentric system
fo (FIO) Value of f where Venus passed out of the cloud
T Orbital period of Venus
V Velocity of Venus
VR Radial component of V
VA Azimuthal component of V
VG Gas velocity at radius R
VF Velocity of Venus relative to gas
F Aerodynamic drag force on Venus
a (ALPHA) Angle between VA vector and V vector
b (BETA) Angle between VA vector and VF vector

[*!* Image] Fig. 11. Some of the variables of the computer program. VQ is Venus' azimuthal velocity relative to the gas and equals VA-VG. It is positive in counter-clockwise directions and thus negative in the figure.

Computer Program. Language: FORTRAN. Units: SI

	AR=2.83E17
	RO=1E-7
	E=0.794
	A=3.0*1.496E11
	FIO=+2.167
	DFI=0.2167
	FI= -FIO -DFI/2
	SDW=0
	N=0
	T=3.16E7*(A/1.496E11)**1.5
	C=6.283*A*A*SQRT(1. -E*E)/T
100	FI=FI+DFI
	R=A*(1. -E*E)/(1.+E*COS(FI))
	VA= -C/R
	VR=6.283*A*E*SIN(FI)/(T*SQRT(1. -E*E))
	VG=2.98E4*SQRT(1.496E11/R)
	VF=SQRT((VA -VG)**2+VR**2)
	F=0.5*AR*RO*VF**2
	ALPHA=ATAN2(VR,VA)
	BETA=ATAN2(VR,(VA -VG))
	DW=F*R*DFI*COS(BETA -ALPHA)/COS(ALPHA)
	SDW=SDW+DW
	N=N+1
	IF(N.GT.30.) GO TO 999
	WRITE(20, 2000) FI, R, VA, VR, VG, VF, F, BETA, ALPHA, DW, SDW
2000	FORMAT(1X, F6.3, E10.3, E10.3, E10.3, E10.3, E10.3, E10.3,
	&F7.3, F7.3, E10.3, E10.3)
	IF(FI.LT.(FIO -DFI)) GO TO 100
	WRITE(20, 3000)SDW
3000	FORMAT(//1X,"LOSS PER REVOLUTION",E10.3)
999	STOP
	END

APPENDIX III: FLUX DENSITY AND MAXIMUM ACCELERATING POWER

Alfvén(48) has described what happens when the Sun's dipole field is rotating in the surrounding plasma, while this is flowing outwards (the solar wind). As always when there is relative movement between a magnetic field and a plasma, an electric field acts upon the plasma, giving rise to electric currents. Alfvén found that the radial electric current induced in this way amounts to ca. 3 x 109 A. The current flows in a current sheet in the equatorial plane. The return current goes via axial currents emerging from the poles, and via a curved current sheet at a large distance from the Sun. Alfvén pointed out that this current system may transfer rotational energy from the Sun to the plasma.

The interplanetary plasma is such a good conductor that the current is not limited by resistivity. The limit is set by the secondary field produced by the current. This would be true even if the resistivity were higher by several orders of magnitude. It seems probable that it was true also in the hydrogen gas cloud. Conductivity in a gas results from ionization. Ionization agents in space are UV, X-ray, and particle emissions from the Sun, as well as cosmic radiation from outer space.

As a rule, the intensity of the secondary field will not exceed that of the primary field, that which produced the current. The man-made dynamo, which is an exception from the rule, proves that it cannot be a principle of universal validity. Experience shows, however, that it generally holds for natural phenomena (although those who believe in the geomagnetic dynamo theory think that there is another exception inside the Earth).

If we assume that the flux density at the Earth's orbit is B, without putting any restrictions upon the field in other parts of the cloud, then the induced radial current would probably not exceed

I = 2 R B / mo

where R is the distance Earth-Sun and mo the permeability of vacuum. This is the current that would produce a secondary flux density B (perpendicular to the primary field). With B = 10-4 T (= 1 gauss) the maximum total current would be 7.5 x 1013 A

A conductor carrying a current I through a magnetic field will be subjected to a force B x I per unit of length, where B is the component of the field perpendicular to the current. At the Earth's orbit, the model's mass per unit length in a radial direction is 2 R h [r], where h is the thickness of the cloud at the Earth's orbit (h = 0.173 A.U.), and [rho] is the density of the gas. From this we can derive the maximum force per unit mass:

F / m = B 2 / (r mo h )

For B = 10-4 T the force is 3.1 x 10-6 N/kg.

The direction of the force coincides with the cloud's direction of movement. The work done per unit time by the force is F V g, where V g is the velocity of the gas. At the Earth's orbit, V g = 30 km/s. The accelerating power is then 0.092 W/kg.

Using a rather rough approximation, which can only give us a ball-park estimate, we now assume that the calculated value is an average for the whole cloud. Multiplying by the mass of the model, 5.6 x 1026 kg, gives us a total accelerating power of 5.1 x 1025 W Each kg requires an energy of 4.3 x 108 J for its transportation to Jupiter, so the material could be sent off at a rate of 1.2 x 1017 kg/s, theoretically. It should be noted that this is only a ball-park estimate of a theoretical upper limit. There is no reason to think that the "magnetic centrifuge" really operated at the limit of its capacity. But even if the rate of transportation were only 1016 kg/s, interplanetary space would still be cleared in about 1600 years.

REFERENCES

1. R. E. Juergens: "Sagan's Ten Plagues", KRONOS III:2 (Winter 1977), p. 77.
2. C. S. Sherrerd: "The Electromagnetic Circularization of Planetary Orbits", KRONOS IV:4 (Summer 1979), pp. 55-58.
3. I. Velikovsky: "Earth Without a Moon", Pensée IVR III (Winter 1973), p. 25.
4. L. E. Rose, R. C. Vaughan: "Velikovsky and the Sequence of Planetary Orbits", Pensée IVR VIII (Summer 1974), pp. 27-34. Reprinted in Velikovsky Reconsidered (Doubleday, 1976), pp. 110-132.
5. R. E. Juergens: "Reconciling Celestial Mechanics and Velikovskian Catastrophism", Pensée IVR II (Fall 1972), pp. 6-12.
6. E. R. Milton: "The Not So Stable Sun", KRONOS V:1 (Fall 1979), pp. 64-78.
7. C. E. R. Bruce: Successful Predictions of the Electrical Discharge Theory. E. R. A. report 5275 (The Electrical Research Association, Leatherhead, Surrey, 1968).
8. C. S. Sherrerd: "Venus' Circular Orbit", Pensée IVR I (May 1972), p. 43.
9. I. Velikovsky: "On Saturn and the Flood", KRONOS V: 1 (Fall 1979), pp. 3-11.
10. H. Tresman, B. O'Gheoghan: "The Primordial Light?", SIS Review II:2 (Dec. 1977), pp. 3540.
11. D. Cardona: "Let There Be Light", KRONOS III:3 (Spring 1978), pp. 34-55.
12. S. Starrfield, et al.: "The Cause of the Nova Outburst", in P. Eggleton, et al. (eds.): Structure and Evolution of Close Binary Systems (IAU Symposium No. 73, published Dordrecht/Boston, 1976), p. 155.
13. B. Warner: "Observations of Dwarf Novae", in P. Eggleton, et al. (eds.): Structure and Evolution of Close Binary Systems (IAU Symposium No. 73, published Dordrecht/Boston, 1976), p. 100.
14. J. Sahade: "Introductory Address", in P. Eggleton, et al. (eds.): Structure and Evolution of Close Binary Systems (IAU Symposium No. 73, published Dordrecht/Boston, 1976), p. 2.
15. I. Velikovsky, op. cit. (Ref. 9), pp. 6-7. 16. Ibid., p. 7.
17. H. Tresman, B. O'Gheoghan, op. cit., p. 38.
18. L. E. Rose, R. C. Vaughan, op. cit., pp. 29 ff.
19. Z. Kopal: Close Binary Systems (London, 1959), pp. 133 ff.
20. C. Sutherland: "China's Dragon",Pensée IVR VI (Winter 1973-74), pp. 47-50.
21. Assurbanipal, quoted by Velikovsky in Worlds in Collision, speaks of Ishtar-Venus "who is clothed with fire and bears aloft a crown of awful splendor . . ." (WiC, Part I, ' Worship of the Morning Star"). Figure 4 was based upon physical considerations. Still, when it was finished, it struck the author that there was something familiar with it. It makes one think of a king's crown. On top of the most common type of royal crown, you will still find a ball with a cross the old Venus symbol. The long red tail of Venus may well have resembled a king's mantle. Perhaps the original idea behind the traditional royal dress was to make the king look like the comet Venus, with its atmosphere and tail.
[*!* Image]
22. B.Warner, op. cit., p. 110.
23. I. Velikovsky: "The Birth of Venus from Jupiter", KRONOS II:1 (1976), pp. 3-7.
24. I. Velikovsky: "Changes in the Times and the Seasons", Worlds in Collision (N.Y., 1950), Part I, Chapter V.
25. C. J. Ransom, L. H. Hoffee: "The Orbits of Venus", Pensée IVR III (Winter 1973), pp. 22-25. The length of the pre-Exodus year used by these authors was based upon orbit parameters suggested by Rose and Vaughan, Ref. 26.
26. L. E. Rose, R. C. Vaughan: "The Orbits of Mars, Earth and Venus", Pensée IVR I (May 1972), p. 43.
27. L. E. Rose, R. C. Vaughan, op. cit. (Ref. 4), p. 30. See also L. E. Rose: "The Lengths of the Year", Pensée IVR VIII (Summer 1974), pp. 35-36.
28. I. Velikovsky, op. cit. (Ref. 24), p. 5.
29. W. Mullen: "A Reading of the Pyramid Texts",Pensée IVR III (Winter 1973), pp. 10-16.
30. A. G. Hansen: "Streamlining", in McGraw-Hill Encyclopedia of Science and Technology, 4th ed. (1977), Vol. 13, p. 197.
31. M. E. Tauber: "Entry, atmospheric", in McGraw-Hill Encyclopedia of Science and Technology, 4th ed. (1977), Vol. 5, p. 11.
32. V. A. Firsoff: "On Some Problems of Venus", KRONOS V.2 (Winter 1980), pp. 5745 (Reprinted from J. Brit. Astron. Assoc.).
33. M. A. White: "Interplanetary Space and the Solar Atmosphere", in S. L. Valley (ed.): Handbook of Geophysics and Space Environments (N.Y., 1965).
34. C. R. Carrigan, D. Gubbins: "The Source of the Earth's Magnetic Field", Scientific American, Vol. 240 (Feb. 1979), pp. 118-130.
35. Th. Barnes: "Recent Origin and Decay of the Earth's Magnetic Field", SIS Review II:2 (Dec. 1977), pp. 4246.
36. Ibid., p. 43.
37. J. Milsom: "A Commentary on Barnes' Magnetic Decay", SIS Review II:2 (Dec. 1977), p. 46.
38. A. Cox: "Geomagnetic Reversals", Science 163 (1969), pp. 237-245.
39. V. Bucha, et al.: "Geomagnetic Intensity: Changes during the Past 3000 Years in the Western Hemisphere", Science 168 (1970), pp. 111-114; also see V. Bucha, "Changes of the Earth's Magnetic Moment and Radiocarbon Dating", Nature 224 (1969), pp. 681-682.
40. P. Peregrinus de Maricourt: "Epistola de Magnete". Printed as No. 10 in the series Rara Magnetica, editor G. Hellman (Berlin, 1898). For a summary in English, see Ref. 41.
41. S. P. Thompson: Petrus Peregrinus de Maricourt and his Epistola de Magnete (London, 1906), p. 11.
42. M. T. Cicero: De Re Publica I, paragraphs 21-22.
43. Hultsch, Zeitschrift f. Math. u. Physik (hist. litt. Abth.), XXII (1877), pp. 106 ff.
44. B. Warner, op. cit., p. 121.
45. C. S. Sherrerd, op. cit. (Ref. 2), p. 55.
46. S. W. H. Cowley: "Jupiter's Magnetosphere", Nature 287 (1980), pp. 775-776.
47. B. Warner, op. cit., p. 98.
48. H. Alfvén: "Electric Current Structure of the Magnetosphere", in Hultqvist and Stenflo (eds.): Physics of the Hot Plasma in the Magnetosphere (N.Y., 1975).

ACKNOWLEDGEMENT

I wish to thank those who have read and commented on earlier versions of this manuscript, especially Raymond C. Vaughan for stimulating suggestions and constructive criticism; and Earl R. Milton for extensive theoretical comments.

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