Binary and Multiple Stars
The prevalence of binary and multiple systems is one of the most striking facts that has emerged from the astronomers observations of the stars, but they have not been able thus far to find an explanation for the existence of these star systems that is plausible enough to attain general acceptance. A number of different types of theories have been proposed, but all are subject to serious difficulties. As one astronomy textbook describes the situation:
In view of this embarrassing lack of understanding of one of the most prominent features of stellar existence, it is significant that the development of the theory of the universe of motion provides a detailed account of the origin of these binary and multiple systems, not as something of a separate nature, but as an integral part of the explanation of the stellar evolutionary process. Furthermore, this explanation of the origin of these systems carries with it an explanation of the diversity of the components, another item that has hitherto puzzled the investigators. A half century ago, James Jeans made the following comment about this situation, an observation that is equally appropriate today:
The existence of two distinct products of the supernova explosions, with speeds in different ranges, is the piece of the puzzle that has been missing. On the basis of the theory of the Type I supernovae outlined in Chapters 4 and 6, every star that has been through one such expansion is now a star system consisting of two components: an A component on or above the main sequence, and a B component on or below the main sequence. This means that the seemingly incongruous associations of stars of very different types that are so common are perfectly normal developments. Combinations of giant and dwarf stars, for example, are not freaks or accidents; they are the natural initial products of the process that produces the second-generation stars.
The significance of the term star system introduced earlier should now be apparent. A star system, in this sense, consists of two or more stars or aggregates of sub-stellar size that have been produced by subdivision of a single star. Inasmuch as the constituents of such a system have originated inside the gravitational limit of the original star, they are gravitationally connected, rather than having a net outward motion away from each other, as is true of the individual stars.
The term binary is frequently used by astronomers in an inclusive sense to cover all systems with more than one component, but for the purposes of this present work it will be restricted to the double systems. The star systems with more than two components will be called multiple systems.
In the early stages the pairing varies with the evolutionary age of the system. Immediately after the explosion the A component is merely a cloud of dust and gas which appears as nebulosity surrounding the white dwarf B component. Later the cloud develops into a pre-stellar aggregate, and then into a giant infrared star. Since these aggregates are invisible, except under special circumstances, the white dwarf appears to be alone during this phase. When the giant star gets into the high luminosity range this situation is likely to be reversed, as the bright star then overpowers its relatively faint companion. Further progress eventually brings the giant down to the main sequence. The development of the white dwarf is slower, and there is usually a stage in which a main sequence star (the former giant) is paired with a white dwarf, as in Sirius and Procyon.
Finally the white dwarf, too, reaches the main sequence, and thereafter both components progress upward along the same path. The upper (more advanced) portions of the main sequence therefore contain no associations of dissimilar stars. Many of these stars are binaries, but they are pairs of the same or closely related types. There are some differences in composition. The white dwarf gets the lion's share of the heavy elements in the supernova process, and even though it accretes the same kind of matter as the giants, it has a larger content of metals in the main sequence stage.
The Wolf-Rayet stars appear to reflect this difference. Their distribution and relative size indicate (on the basis of the theory discussed in Chapter 4 ) that they are former white dwarfs. They are less massive than the O and B stars with which they are associated.74 As noted earlier, they are probably rich in nickel, a white dwarf characteristic, and they are closely confined to the plane of the Galaxy, 75 indicating that they are stars of Class 2 or later. No Wolf-Rayet stars have been found in the Orion Nebula, where O and B stars of Class 1 are plentiful.74
This suspected pairing with O type stars, reported by an astronomy textbook, is fully in accord with our theoretical findings. The O star is the A component of the binary system, the former giant, while the Wolf-Rayet star is the B component, the former white dwarf.
The astronomers have been unable to arrive at any explanation as to why so many stars are binary, and they are even more at a loss to explain the frequent occurrence of pairs of a very dissimilar nature. The pairing of these dissimilar objects is an anomaly in the context of conventional astronomical theory, which pictures the two stars in a binary system as following the same evolutionary path, and therefore occupying very different locations on that path if they are stars of different types. This presumed difference in evolutionary status is hard to reconcile with the rather obvious probability that the two stars of such a system have a common origin. The fact that the white dwarf is normally (probably always) the less massive of the two stars exacerbates this problem.
Dean B. McLaughlin makes this comment on a specific situation:
From the standpoint of the findings of this work, there is nothing at all curious about this situation. Nor is it a strange circumstance that the more massive star is on the main sequence. The seeming anomaly is actually an observational repudiation of current astronomical theory. It exposes the Falsity of the assumption upon which the current theory is based: the assumption that all stars follow the same evolutionary course, and that the main sequence stars precede the white dwarf stars on this course. Our finding is that the two constituents of a binary system follow totally different paths, and at any specific time they are equally far advanced on their respective paths. The path back to the main sequence is, however, somewhat longer for the white dwarfs, which accounts for the variety of the combinations. Because of the nature of the process by which they were formed, all of the stars of the white dwarf class, including the novae and related variables, are accompanied by stars or pre-stellar aggregates on or above the main sequence, These companions are not always visible, particularly if they are still in the pre-stellar stage, but if they are observable, they are either giants, sub-giants, or main sequence stars,
It is true that some of the observed double stars do not fit into this evolutionary picture on the basis of their reported composition, For example Capella is said to be a pair of giants, Neither of these stars can qualify as the B component of a binary, On the basis of the theory of the universe of motion, we must therefore conclude that Capella is actually a multiple system rather than a double star, and that it has two unseen white dwarf or faint main sequence components, The Algol type stars, in which the main sequence star is paired with a sub-giant of a somewhat smaller mass, are similarly indicated as multiple systems. The main sequence star cannot be the B component because it is the larger of the two units and has already attained the equilibrium status, while the sub-giant cannot be the B component because it is above the main sequence. We must therefore conclude that at least one of these stars has undergone a second explosion, and that a faint B companion accompanies it. This assessment of the situation is supported by the fact that in Algol itself at least one, and possibly two, small B components have been located observationally.
The second explosive event attributed to such stars as Capella and Algol is a normal development that can be expected to occur in any star system of an advanced evolutionary age, if it is in an appropriate environment. Chronological age alone will not produce this result, as there is no progress up the main sequence unless sufficient material is available for accretion. But where there is an adequate supply of food, in the environment, the stars continue moving around the cycle until their life span is terminated by a process that will be discussed in Chapter 15.
Each passage of a single star through the explosive stage of the cycle results in the production of a binary system (unless the B component is below stellar size, a possibility that we will examine shortly), The number of stars in the system thus continues to increase with age, as long as sufficient material for accretion is available, Systems with as many as six components are found within the present observational range, and considerations that will be discussed later indicate that even larger systems may exist in the older regions of large spiral and spheroidal galaxies. The status of these multiple systems as combinations of separately produced binaries is clearly indicated by their structures.
The local star group, the concentration of stars in the immediate vicinity of the sun, is composed mainly of Class B stars, those of the main sequence, and since there is ample evidence, such as that contributed by their heavy element content, that these are second generation products, Class 2B, they should be largely binaries. This theoretical conclusion is confirmed by observation. Single stars are a minority.80 Most of the recognized binary systems have main sequence stars in both positions, but there are some main sequence-white dwarf combinations. Few, if any, giant-white dwarf systems are recognized in this region, but this is probably due to the effect of the time factor on the number of stars in each part of the cycle, as the interval during which the giant stars are visible is of short duration compared to the time spent by the white dwarfs in their evolutionary development.
It should be noted in this connection that this local group is representative only of a particular evolutionary stage, not of stellar systems in general, and the proportions in which the various types of stars occur in this local region are not indicative of the composition of the stellar population as a whole, The white dwarf, for instance, is an explosion product, a star of the second or later generation, and stars of this type are almost totally absent from stellar systems such as the globular clusters, which are composed almost exclusively of first generation stars, those which have not yet passed through the explosion phase of the cycle. It should not be assumed, therefore, that the high proportion of white dwarfs in the local region indicates a similar high proportion throughout the universe, or even throughout the Galaxy.
The same caveat should be applied to the estimate, quoted in Chapter 4, that 95 percent of all stars are located on the main sequence. This estimate does not give sufficient consideration to the fact that few of the early type stars, those of the globular clusters and the early elliptical galaxies, have reached this evolutionary stage. These aggregates, which constitute the great majority of stellar systems (although they do not necessarily contain the majority of all stars), are composed almost entirely of Class 1A stars, those that have not yet reached the main sequence. The number of stars of the later classes in these aggregates is no more than can be explained on the basis of the strays, the scattered remnants of disintegrated older structures.
The observers recognize the almost complete absence of the various types of binary stars from these young aggregates, but it remains unexplained in current thought. Burnham, for instance, comments that For some reason not fully understood, eclipsing binaries appear to be very rare in globular star clusters. 81 Likewise novae are scarce. There are only two cases of novae in globular star clusters, 82 he says. The search for binaries in the center of globular clusters has been totally unsuccessful,83 reports Bart J. Bok. Shklovsky concedes that for Population 11 stars in general, multiplicity is fairly rare. 84
No reason for this near absence of binaries from Population 11 (Class 1A) stars is given in the astronomical literature. Nor is much support given to the rather half-hearted efforts to explain the origin of the double and multiple systems. The sad fact is that the astronomers are trapped by their upside down evolutionary sequence. The striking difference in the abundance of binaries between two groups of stars that admittedly differ primarily in age shows that this must be an evolutionary effect. But since the astronomers regard the group with almost no binaries as the older, they have to find one process by means of which the binaries are produced in the original star formation, or very soon thereafter, and another process whereby the combinations are uncoupled at some later evolutionary stage. Even the origin of the binaries is without any explanation that is taken seriously, and no explanation at all has been advanced to account for the uncoupling.
When the correct evolutionary direction is recognized, one half of this problem disappears. Only one process remains to be explained: the production of binary systems at some stage of the evolutionary development. In the context of the theory of the universe of motion, this is seen to be a necessary consequence of the division between motion in space and motion in time that takes place in the products of extremely violent explosions. Here, then, this theory provides a complete and consistent explanation of an important feature of the astronomical universe that is without any explanation in terms of conventional astronomical theory.
The clarification of the situation that is accomplished by the new theory does not end at this point Because of the lack of understanding of the basic principles that are involved, the astronomers are unable to distinguish between cause and effect in these phenomena. For example, Shklovsky expresses the current astronomical opinion in this statement:
As the points brought out in the preceding discussion demonstrate, this view of the situation is upside down, like so many other aspects of currently accepted theory. Instead of the doubling of the star determining its evolution, the evolutionary development of the star results in the doubling. The conventional view expressed by Shklovsky really does not explain anything; it merely replaces one question with another. The question as to what causes the evolution becomes a question as to what causes the doubling. On the other hand, the answer derived from the theory of the universe of motion is complete. This theory explains why stars evolve, why this evolution terminates in an explosive event, and how the doubling of the star results from the explosion.
In a statement quoted in the first volume of the present series, Richard Feynman commented that Today our theories of physics, the laws of physics, are a multitude of different parts and pieces that do not fit together very well. 86 This description is even more appropriate in application to the theories of astronomy.
The binary star theory is one of the individual parts and pieces, that has little connection with anything else. The existence of binaries is simply taken as given, and a set of conclusions with respect to some of the observed binary phenomena is then drawn from this existence, without fitting these conclusions, and the phenomena to which they refer, into the rest of astronomical theory. This comment is not intended as a criticism; it is simply a statement of one of the aspects of astronomy, as it now exists, that needs to be taken into consideration in order to understand why the theoretical development in this series of volumes arrives at so many conclusions that differ radically from the prevailing astronomical thought. Inasmuch as the astronomers have no general structure of theory, either in physics or in astronomy, with which to work, they have had no option but to proceed on this piecemeal basis. Actually, they have made impressive progress in identifying and clarifying the multitude of different parts and pieces. What is now needed is to put these parts and pieces together, turning them right side up where necessary, and fitting them together in the correct manner. This is the task that the general physical theory derived from the postulates that define the universe of motion is now prepared to handle.
With the benefit of, the information supplied by this new theoretical system, it can now be seen that the behavior characteristics of the binary star systems are inherent in the stars themselves. There is no need to invent processes that call for interaction between the components. Hypothetical processes of this nature are the current orthodoxy.
In many binary systems the separation between the stars is relatively sma1l, and some interaction between them is a definite possibility (although it should be remembered that where one of the two stars is a white dwarf, there is a separation in time as well as in space, and the stars are not actually as close to each other as they appear to be). But the current tendency is to use the hypothesis of mass transfer from one member of a binary system to the other as a kind of catch-all, to explain away any aspect of binary star behavior that is not accounted for in any other way. The remarkable extent to which this hypothetical mass transfer process is currently being stretched is well illustrated by the purported resolution of what is called the Algol paradox. As noted earlier in this chapter, the two principal components of Algol are a relatively large and hot main sequence star and a less massive, cooler subgiant.
Very little is actually known about the conditions that exist in these binary systems, and still less is known about the events that have taken place earlier in the lives of these stars. Thus, at the present level of instrumentation and techniques there is no way of disproving a hypothesis about these binaries, and the astronomers have taken full advantage of the freedom for invention, Theoretical studies have resolved the paradox", Hartmann says, It is simply assumed that the smaller star was originally the larger, and that after having achieved the more advanced status, it obligingly transferred most of its mass to its companion. In other binary star situations, such as in the cataclysmic variables, the transfer explanation can be used only if the movement is in the opposite direction, So it is cheerfully assumed, in this case, that the transfer is reversed. As Shklovsky explains;
Of course, we have to keep in mind the difficulties under which the astronomers carry on their work, but nevertheless, there are limits to what can legitimately be classified as scientific. Acceptance of untestable ad hoc assumptions as the resolution of problems, or giving them any status other than that of highly tentative suggestions for study, is incompatible with good scientific practice, It inevitably leads to wrong answers. The correct answer to Hartmann's question is, Yes, there is a fundamental mistake in current ideas of stellar evolution. The so-called paradoxes are actually observational contradictions of a theory that has no foundation in fact.
In addition to the binaries, we also observe a considerable number of stars in the local region, which appear to be single. Some of these may actually be single stars that have drifted in as a result of the mixing process that occurs by reason of the rotational motion of the Galaxy, but others are double stars in which one of the components is unobservable. We have already noted that the A component of a binary is invisible during a portion of the early evolutionary stage, and all we see under these conditions is a 1one white dwarf. The components of the white dwarfs are not dispersed in space, and these stars do not participate in this kind of a retreat into obscurity, but they become invisible for other reasons. As we will find in Chapter II, they cannot be seen at all until they cool down to a certain critical temperature. Later a bright giant or main sequence companion may overpower them, or they may simply be too dim to be observable at any considerable distance.
Inasmuch as the maximum speed produced by the supernova explosions that we are considering is less—usually considerably less—than two units, the distribution of speeds above and below unity is asymmetric, with the greater part of the mass taking the lower speeds. For this reason, even though some of the matter ejected into space escapes from the gravitational control of the remnants of the star, the amount of retained slow speed material still exceeds the inward-moving mass in most, and probably ail, cases. The giant member of the binary system therefore has the greater mass. In Sirius, for example, the main sequence star, originally the giant, has more than twice the mass of the dwarf. Since even the smallest star is subject to a Type II supernova explosion at the age limit, it is evident that in many instances the mass of the dwarf component is below the minimum required for a star, in which case the final product is a single star with one or more relatively small and cool attendants: a planetary system,
In the supernova explosion the material near the center of the star is obviously the part of the mass that acquires greater-than-unit speed, and disperses into time. The remainder of the stellar material is dispersed outward into space. In view of the segregation of heavy and light components which necessarily takes place in a fluid aggregate under the influence of gravitational forces, the chemical composition of the two components of the explosion products differs widely, Most of the lighter elements will have been concentrated in the outer portions of the star before the explosion, those heavier than the nickel-iron group will have been converted to energy, except for the stray atoms mixed in with other material, and the recent acquisitions that had not had time to sink to the center, while the central portions of the star contained a high concentration of the iron group elements.
When the explosion occurs, the outward moving material, which we will call Substance A, consists mainly of light elements, with only a relatively small proportion of high density matter. It can be deduced that the composition of Substance B. the matter of the inward-moving component, is subject to a considerable amount of variation. The exploding stars differ in their chemical composition No doubt there are also differences in some of their physical properties—rotational speed, for example. Because of these differences in the stars from which they originate, the size and composition of the white dwarf components of the explosion products is also variable. If this component is small, it can be expected to be composed almost entirely of the iron group elements. The large white dwarfs contain a greater proportion of the lighter materials.
In each of the two products of the stellar explosions that we are now considering the primary gravitational forces are directed radially toward the center of the mass of the dispersed material Hence, unless outside agencies intervene, it is to be expected that any capture of one subsidiary aggregate by another will result in consolidation the formation of a binary or multiple system being ruled out by the absence of non-radial motions. Ultimately, then, the greater part of the matter of the larger of the two components, the material dispersed in space, will be collected into one unit. The smaller component then acquires orbital motion around the larger, consolidation being unlikely in this case, as neither unit will be moving directly toward the other unless by pure chance The ultimate result is a system in which a mass, or a number of masses, composed primarily of Substance B is moving in an orbit, or orbits, around a central star of Substance A If the B component is of stellar size, the system is a binary star; if it is smaller the product is a planet, or a planetary system Because of interaction during the final stages of the formation process, some of the unconsolidated fragments may take up independent orbital positions, constiturting planetary satellites.
This provides an explanation of, the origin of the solar system, a matter that has been the subject of much speculation among the members of the human race, who occupy a planet of that system. On the foregoing basis we may conclude that at the beginning of the formative period of the solar system, after the gravitational forces had almost completed the task of aggregating the masses dispersed by the supernova explosion. A large mass of Substance A, with some small subsidiary aggregates and consider-able dispersed matter not yet incorporated into the central mass was approaching a much smaller and less consolidated mass of Substance B When the combination of the two systems took place under the influence of the mutual gravitational attraction, the major aggregates of the B component acquired orbital motion around the large central mass of the A component In the process of assuming their positions. These newly constituted planets encountered local aggregates of Substance A which had not yet been drawn into the central star, and under appropriate conditions these aggregates were captured, becoming satellites of the planets At the end of this phase all major units had been incorporated into a stable system in which planets composed of Substance B were revolving around a star composed of Substance A, and smaller aggregates of Substance A were similarly in orbit as planetary satellites
Small fragments are subject to being pulled out of their normal paths by the gravitational forces of the larger masses which they may approach, and while orbital motion of these fragments is entirely possible, the chances of being drawn into one of the larger masses increase as the size decreases We may therefore deduce that during the latter part of the formative period all of the larger members of the system increased their masses substantially by accretion of fragments of Substance A in various sizes from planetesimals down to atoms and sub-atomic particles Some smaller amounts of Substance B. in assorted sizes, were also accreted. After the situation had stabilized, the central star, the sun, consisted primarily of Substance A, with a small amount of Substance B derived from the heavy portions of the original Substance A mix and the accretions of Substance B. Each planet consisted of a core of Substance B and an outer zone of Substance A. the surface layer of which contained some minor amounts of Substance B acquired by capture of small fragments.
The planetary satellites, which had comparatively little opportunity to capture material from the surroundings because of their small masses and the proximity of their larger neighbors, were composed of Substance A with only a small dilution of Substance B. It can also be deduced that after the formative period ended, further accretion took place at a slower rate from the remains of the original material. From newly produced matter, and from matter entering the system out of interstellar space, but the general effect of these subsequent additions did not differ greatly from that of the accretions during the formative period, and did not change the nature of the result
This is the theoretical picture as it can be drawn from the information developed in the earlier pages. Now let us look at the physical evidence to see how well this picture agrees with observation. The crucial issue is, of course, the existence of distinct Substances A and B. Both the deduction as to the method of formation of the planetary systems and the underlying deduction as to the termination of the dense phase of the stellar cycle at the destructive limit would he seriously weakened if no evidence of a segregation of this kind could be found. Actually, however, there is no doubt on this score. Many of the fragments currently being captured by the earth reach the surface in such a condition that they can be observed and analyzed. These meteorites definitely fall into two distinct classes. The irons and the stones, together with mixtures, the stony-irons.
The approximate average composition is as follows:
The composition of the iron meteorites is in full agreement with the conclusion that these are fragments of pure Substance B. The stony meteorites have obviously be en unable to retain any volatile constituents, and when due allowance is made for this fact their composition is entirely consistent with a status as Substance A. The existence of the mixed structures, the stony-irons, is easily explained on the basis of the previous deductions as to the composition of the various sizes of white dwarfs,
It is also reported that the iron meteorites contain practically no uranium or thorium, whereas stony meteorites do.91 This is another piece of information that fits in with the theoretical picture. The energy generation process exhausted the supply of very heavy elements in the central regions of the stars, from which the iron meteorites (Substance B) are derived, before the supernova explosion occurred. But the outer regions of these stars, the source of the stony meteorites (Substance A), contained portions of the heavy element content of the accreted matter that had not yet made their way down to the center. The evidence from the meteorites thus gives very strong support to those aspects of the theory that require the existence of two distinct explosion products, Substances A and B.
There is no proof that the meteorites actually originated contemporaneously with the planets in the manner described, but this is immaterial so far as the present issue is concerned. The theoretical process that has been outlined is not peculiar to the solar system; it is applicable to any system reconstituted after a supernova explosion, and the existence of distinct stony and iron meteorites is just as valid proof of the existence of distinct Substances A and B whether the fragments originated within the solar system, or have drifted in from some other system that, according to the theory, originated in the same manner. The support given to the theory by the composition of the meteorites is all the more impressive because the segregation of the fragmentary material into two distinct types on such a major scale has been very difficult to explain oh the basis of previous theories,
Additional corroboration of the theoretical deductions is provided by the spectra of novae. Since these are stars of the white dwarf class, they are composed of Substance B as originally formed. However, the white dwarfs accrete matter from the surroundings in the same manner as other stars, and within a relatively short time the original star is covered by a layer of Substance A. This material is essentially the same as that in the outer regions of stars of other types, and the composition of the stellar interior is therefore not revealed by the spectra obtained during the pre-nova and post-nova stages. But when the nova explosion occurs, some of the Substance B from the interior of the star forces its way out, and the radiation from this material can be observed along with the spectrum from the exterior, As would be expected from theoretical considerations, the explosion spectra often show strong indications of highly ionized iron.92
Another theoretical deduction that can be compared with the evidence from observation is the nature of the distribution of Substances A and B in the planetary system, The sun has a relatively low density, and we can undoubtedly say that it consists primarily of Substance A, as required by the theory. Whether or not it actually contains the predicted small amount of Substance B cannot be determined on the basis of the information now available. The planet that is most accessible to observation, the earth, definitely conforms to the theoretical requirement that it should consist of a core of Substance B with an overlying mantle of Substance A. The observed densities of the other inner planets, together with such other pertinent information as is available, likewise make it practically certain that they are similarly constituted.
The prevailing astronomical opinion is that the differentiation which produced the iron cores occurred after the formation of the planets. This necessitates the assumption that these aggregates passed through a molten, or semi-molten stage, during which the iron drained into metallic cores. 93 Although this theory is still the one that appears most frequently in the astronomical literature, it received what is probably a fatal blow from the results of the Mariner 10 mission to Mercury. A report of these results reads in part as follows:
These observations indicating that the core formation preceded the acquisition of the lighter material are fully in accord with the theory of planetary formation derived in the foregoing pages, a theory which places the differention of the iron from the lighter elements in the pre-supernova star, rather than in the planets.
The observational situation with respect to the major planets is less clearly defined. The densities of these planets are much lower than those of the earth and its neighbors, but this is to be expected, since they have been able, by reason of greater size and lower temperature, to retain the lighter elements, particularly hydrogen, that have been lost by the inner planets. The observations indicate that the outer regions of these major planets are composed largely of these light elements. This eaves the internal composition an open question. It seems, however, that there must have been some kind of a gravitationally stable nucleus in each case to initiate the build-up of the light material, and it is entirely possible that this original mass, which is now the core of the planet, is composed of Substance B. Jupiter has a total mass 317 times that of the earth, and even if the core represents only a small fraction of the total mass, it could still be many times as large as the earth's core.
We may thus conclude that, although the observational data on the outer planets do not definitely confirm the theoretical deduction that they have inner cores of Substance B. the observed properties are consistent with that finding. Since it is highly probable that all of the planets have the same basic structure, this lack of any definite conflict between theory and observation is significant.
The satellites present a similar picture. The verdict with respect to the distant satellites, like that with respect to the distant planets, is favorable to the theory, but not conclusive. The available evidence is consistent with the theory that the inner cores of these satellites, as well as their outer regions, are composed of Substance A, but it does not definitely exclude other possibilities. The satellites that we know best, like the planet that we know best, gives us an unequivocal answer. The moon is definitely composed of materials similar to the stony meteorites and the earth's crust; that is, it is practically pure Substance A, as it theoretically should be.
It is appropriate to point out that this theory of planetary origin derived by extension of the development of the consequences of the fundamental postulates of the Reciprocal System is independent of the temperature limitations that have constituted such formidable obstacles to most of the previous efforts to account for the existing distribution of material. The fact that the primary segregation of Substance A from Substance B antedated the formation of the soar system explains the existence of distinct core and mantle compositions without the necessity of postulating either a liquid condition during the formative period, or any highly speculative mechanism whereby solid iron can sink through solid rock.
This explanation of the formation of the system also accounts for the near coincidence of the orbital planes of the planets, and for the distribution of the planetary orbits in distance from the sun. It has been recognized for two hundred years that the planets are not distributed haphazardly, but occupy positions at distances that are mathematically related in a regular sequence.
This relation, called Bode's Law (although discovered by Titius), has never been explained, and since present-day scientists are reluctant to concede that there are answers which they are unable to find, the present tendency is to regard it as a mere curiosity. It is probable that the law is no more than an interesting relation of a coincidental nature. 95 says one textbook.
The basic principles governing this situation were explained in Chapter 6. The white dwarf is moving in time, and the speeds of its constituents are distributed in the range between one and two units. Increments of speed above the unit level are limited to unit values, but since the motion in the intermediate speed range is distributed over the full three dimensions of time, the applicable units are the three-dimensional units. As we saw earlier, the two linear units from zero to the one-dimensional limit correspond to eight three-dimensional units. The constituents of the white dwarf are thus distributed to a number of distinct speed levels, with a maximum of seven. The distances in equivalent space at the point of maximum expansion are similarly distributed. In the subsequent contraction back to the equilibrium condition these separations are maintained unchanged although the individual constituents move from one level to the next lower whenever they lose a unit of speed.
During the contraction in time (equivalent to a reexpansion in space) there are two processes in operation. The gravitational force of the aggregate as a whole is pulling the particles in toward the center of mass, Coincidentally, each of the subdivisions of this aggregate defined by the different speed levels is individually consolidating, since all particles in each subdivision are moving at the same speed, and are therefore at rest relative to each other, aside from their mutual gravitational motion. The rate at which each process takes place depends mainly on the mass that is involved and the distance through which the constituents have to travel. If the total mass is relatively large, the central aggregation proceeds rapidly, and the local concentrations are pulled in to the center before they have a chance to develop very far. Where the total mass is relatively small the distances involved are about the same, and the central force is therefore weaker. In this case the subsidiary aggregates have time to form, and the consolidation of these aggregates into one central mass may not be complete by the time the white dwarf becomes subject to the gravitational effect of its companion in the binary system.
Up to this point the subsidiary aggregates are all in a straight line spatially, They are distributed over three dimensions of time, but the spatial equivalent of this time is a scalar quantity, and it appears in the spatial reference system in linear form. When the white dwarf reaches the vicinity of its giant or main sequence companion, and is pulled out of its original line of travel by the gravitational force of the companion, the various subsidiary aggregates go into orbit at distances from the companion that reflect their separations, as well as the amount by which the line of movement of the white dwarf is offset from a direct central impact on its companion.
Bode's Law reproduces these distances, as they appear in the solar system, as far as the planet Uranus. It provides no explanation as to where its elements come from, but it does correctly identify these elements as two fixed quantities and one variable. The fixed quantities are properties of the particular star system (the soar system), and therefore have to be obtained empirically; they cannot be calculated from theoretical premises. The first of these represents the distance in actual space between the A component and the closest of the planetary masses at the time the orbital motion was established. It is the same for all planets, and has the vague 0.4 in terms of the astronomical unit, the mean radius of the earth's orbit, Our finding confirms the vague that appears in Bode's Law, The second constant is related to factors such as the masses of the two components of the binary system, and the magnitude of the explosion in which they were produced, In Bode's Law it has the vague 0.3. We arrive at a somewhat lower value, 0.267.
The variable in the distance relation is the speed level of the motion in time. There are several factors involved in this relation that make it more complex than the simple sequence in Bode's Law. Two of these factors enter into the values in the first half of the group of planets. There is a 1½ step in the numerical sequence that does not appear in Bode's Law. As we have seen in the earlier volumes, this vague frequently appears in such a sequence where the quantity involved is complex, so that it is feasible to have a combination of one-unit and two-unit components, Apparently the big jump from one to two (a one hundred percent increase) favors such an intermediate vague which is relatively rare at the higher levels, The second special factor that enters into the situation we are now considering is that, for reasons explained in Volume I, all magnitudes in equivalent space appear in the spatial reference system as second powers of the original quantities, The distances below n = 4 can thus be expressed by the relation d = 0.267 n² + 0.4 In this lower range the results obtained from this expression are practically identical with those obtained from Bode's Law, as indicated in Table I, where the observed distances are compared with those calculated from the two equations.
In this half of the total distance range, the increments of distance add directly, even though they are the results of increments of motion in time (equivalent space), because they correspond to the first half of the eight-unit speed range, which is on the spatial side of the neutral point. Beyond this point, on the temporal side, the relations are inverted. The n values (number of units from the appropriate zero) move back down, and the distances in (equivalent space, expressed in spatial terms, are inversely related to the value of n², Furthermore, the transition from space to time at the midpoint involves a change in the gravitational effect from one positive unit (gravitation in space) to one negative unit (gravitation in time), a net change of two units. On this basis, the neutral point is one unit (0.267) above the 4.7 distance corresponding to n = 4 on the space side. One more such unit brings the distance to 5.2. This is 4.8 plus the 0.4 initial vague. For the more distant planets, the 4.8 applicable to n = 4 is increased in inverse proportion to n², resulting in the values shown in the table. The applicable equation is d = 76.8/n² + 0.4.
The agreement between the observed and calculated distances is not as close for these outer planets as for the inner group, but it is probably as close as can be expected, except in the case of Pluto. Bode's Law could have a place for Pluto, but only at the expense of omitting Neptune. This is not acceptable, as Neptune is a giant planet, while Pluto is a small object of uncertain status, It appears likely that the inverse speed range corresponding to n = 1½ is the maximum that was reached by the parent white dwarf, and that both Neptune and Pluto condensed in this relatively wide distance range, This would account for the fact that the calculated value for n = 1½ falls between the observed distances of the two planets.
This explanation of the interplanetary distances implies that almost all-small stars of the second generation or later have similar planetary systems in orbit, a point that we will consider in another connection later. Otherwise, the clarification of the distance situation is not of any special importance in itself, It is significant, however, that when we put together the different properties that the motion of the white dwarf constituent of a small binary system must possess, according to the theory of the universe of motion, we arrive at a series of interplanetary distances that are almost identical with the observed values. This numerical agreement between theory and measurement is a substantial addition to the evidence supporting the theoretical conclusions as to the nature of motion in the upper speed ranges. The white dwarf is the only object with component speeds greater than the speed of light that is involved in the astronomical phenomena thus far discussed in this volume, the phenomena that take up about 80 percent of a standard astronomy textbook. But the remainder of this work will be concerned mainly with objects whose components, and often the objects themselves, are moving at upper range speeds. A full understanding of the nature and properties of the white dwarf will contribute materially to clarification of the more complex phenomena of the intermediate and ultra high-speed ranges that will be discussed in the pages that follow.
The smaller components of the solar system include interplanetary dust and gas, meteorites, asteroids, and comets. The asteroids are aggregates of Substance B. from l 000 km in diameter downward, which were never captured by planets, and did not accrete enough material to become planets in their own right. Most of the large asteroids are located in the asteroid belt between Mars and Jupiter, and represent the core of a potential planet that failed to complete its consolidation because of the gravitational effect of nearby Jupiter. The orbits of the asteroids are subject to modification by the gravitational forces of the planets, and occasionally one is deflected into an orbit that results in capture by the earth. Those that reach the earth intact, or in fragmentary form, are the previously mentioned iron, or stony-iron, meteorites. Stray aggregates of Substance A similarly captured are the stony meteorites. Most of these latter objects, like the asteroids, date from the original formation of the solar system.
Comets are relatively small aggregates of material drawn in by the sun from distant locations within its gravitational limit, Unless the incoming material happens to make a direct hit, it goes into a very elongated orbit on the first approach. At each return it loses part of its mass and reduces the size of its orbit. Eventually its entire contents are either absorbed by one of the larger bodies of the solar system or distributed in the space surrounding those bodies. The earth participates in this process in a relatively small way, capturing both individual particles (sporadic meteors) and meteor swarms, which are portions of the detached cometary material that follow previous orbits of their parent comets.
The current view is that there must be a reservoir of cornets at some relatively large distance from the sun in a sense, this is true, as the long period comets spend the greater part of their lives in the outer portions of their orbits. But this reservoir is merely a storage location, not a source. There is a certain residual amount of dust and gas within the gravitational limit of the sun, some inflow of diffuse matter from interstellar space, and a small, but continuous, formation of new matter from the incoming cosmic rays. Thus new cometary matter is constantly being made available. The number of comets in the system is probably now at an equilibrium level where the rate of formation is equal to the rate of loss due to evaporation from the comets and eventual capture of the remnants.
The contents of this chapter identify some of the factors that have a bearing on the question as to where planets are likely to exist, a question that excites a great deal of interest because it is a key element in any assessment of the possibility of the existence of 1ife—particularly intelligent life—elsewhere in the universe. The B component of a binary system is either a star or a planetary system, not both. This eliminates all binary stars, and since all Class 1 stars are automatically excluded, it confines the possibility of planets to single Class 2 stars (such as the sun), or to single components of multiple systems Class 3 and later). Inasmuch as a long period of reasonably stable conditions is probably required for the development of life certainly for the emergence of any of the higher forms of life—the Class C stars of the second and later cycles, and the stars high on the main sequence, all of which are subject to relatively rapid change, can also be crossed off the list.
This wholesale exclusion of so many different classes of stars may seem to limit the possibility of the existence of extra-terrestrial life very drastically, but in fact, these conspicuous and well-publicized stars constitute only a minor part of the total galactic population. The great majority of the stars of the Galaxy are small, and relatively cool, stars in the lower sections of the main sequence. As we will see in Chapter l2, there is a lower limit to the mass of a white dwarf star, and when the B component of a system is below this limit it cannot attain stellar status. This implies the existence of an immense number of planets among the smaller systems. Of course, there are requirements as to size, temperature, etc., that a planet must meet in order to be available as an abode for life, but there is a zone in each system within which a planet of an appropriate size is quite likely to meet the other requirements. Since Bode's Law (as revised) is applicable to all systems in which the conditions are favorable for planet formation (the small systems), it is probable that all of these systems have at least one planet in the habitable zone.
The findings of this work thus increase the probability that there are a very large number of habitable planets earth-like planets, let us say—in our own galaxy, as well as in other spiral galaxies. There are few, if any in the galaxies smaller than the spirals—the ellipticals and the small irregulars—because they are composed almost entirely of Class l stars. The situation in the giant spheroidals is not yet clear. There are multitudes of lower main sequence systems in these giants and these can be expected to have the usual proportion of planetary systems. However, the intense activity that, as we will see later' is taking place in the interior zones of these giants no doubt rules out the existence of life. Whether enough of this activity carries over into the outer parts of these galaxies to exclude life in these areas as well is uncertain. The oldest of these giants are probably lifeless. As we will find in Chapter 19, there is a strong X-ray emission from these mature galaxies and this is probably lethal. So far as we know at present, however there may be outlying regions in some of the younger galaxies of this class in which the conditions are just as favorable for life as in the spirals.
In today's science fiction, where life in other worlds is a favorite motif, the habitations of the alien civilizations are identified with familiar names, for reasons that are understandable. The thrilling action that the authors of these works describe takes place on planets that circle Sirius, or Areturus, or some other well-known star. But according to our findings, few, if any, of these familiar stars are capable of having a habitable planet in orbit, and are also old enough to have developed complex forms of life. Sirius, for instance, has a white dwarf companion instead of a planetary system. Arcturus is a young Class C star. The astronomers do not make the mistake of identifying the environments of these stars as the abode of life, but they avoid it by making a different mistake. In selecting the target of their first systematic attempt at interplanetary communication (1974) they were misled by their current view of the evolutionary direction of the stars. This initial effort was directed at the globular cluster M 13, on the assumption that it is a very old structure in which the processes that lead to life have had ample time in which to operate. We now find that the globular clusters are relatively young structures which, aside from a few stray stars that have been picked up from the environment, are composed entirely of Class l stars. These cluster stars have not been through the explosion process and therefore have no planetary companions at all.
As matters now stand the available information indicates that habitable planets are plentiful, but that the planets on which life probably exists are not located in any systems that we can call by name. The stars that they are orbiting are undistinguished anonymous, and with few, if any, exceptions unseen stars of the lower main sequence.