Von Weizsäcker Forms His Quantitative Theory of Planetary Formation

Carl Friedrich von Weizsäcker put forward a quantitative theory of planetary formation, based on contemporary theories of high-temperature turbulence and stellar formation, in which planets evolved from the same raw materials—and in roughly the same fashion—as did the stars they orbited.

Summary of Event

In contrast to many theories proposing the sudden “catastrophic” creation of Earth, the earliest scientific (“evolutionary”) hypotheses of planetary formation were those of René Descartes Descartes, René (1644), Immanuel Kant Kant, Immanuel (1755), and Pierre-Simon Laplace Laplace, Pierre-Simon (1796). All these nebular (gas cloud) theories Nebular theories of planetary formation postulated that the universe, then not known beyond the Sun and five planets, was filled by gas and dustlike particles of matter. Astronomy;planetary formation Planetary formation "On the Formation of Planetary Systems" (Weizsäcker)[On the Formation of Planetary Systems] [kw]Von Weizsäcker Forms His Quantitative Theory of Planetary Formation (1943)[Vonweizsäcker Forms His Quantitative Theory of Planetary Formation] [kw]Quantitative Theory of Planetary Formation, Von Weizsäcker Forms His (1943) [kw]Planetary Formation, Von Weizsäcker Forms His Quantitative Theory of (1943) Astronomy;planetary formation Planetary formation "On the Formation of Planetary Systems" (Weizsäcker)[On the Formation of Planetary Systems] [g]Europe;1943: Von Weizsäcker Forms His Quantitative Theory of Planetary Formation[00710] [g]Germany;1943: Von Weizsäcker Forms His Quantitative Theory of Planetary Formation[00710] [c]Astronomy;1943: Von Weizsäcker Forms His Quantitative Theory of Planetary Formation[00710] [c]Science and technology;1943: Von Weizsäcker Forms His Quantitative Theory of Planetary Formation[00710] Weizsäcker, Carl Friedrich von

Descartes pictured a large primary gas vortex of circular shape, surrounded by still smaller eddies, from which, respectively, the Sun, major planets, and their satellites were to have formed by an unspecified process of turbulent collision and condensation. Likewise, Kant, in his Allgemeine Naturgeschichte und Theorie des Himmels Universal Natural History and Theories of the Heavens (Kant) (1755; Universal Natural History and Theories of the Heavens, 1900), proposed a large rotating gas and dust cloud, which increased rotational speed and flattened to a disk as it progressively contracted because of gravitational attraction. From this disk, the remaining matter was supposed to condense to form the sun and planets. Laplace modified Kant’s theory by assuming that as the disk-shaped cloud’s rotation increased, centrifugal force at its edge also increased until it exceeded gravitational forces toward the center, thereafter separating into concentric rings, each subsequently condensing to form a planet.

Nebular hypotheses for the next sixty years essentially remained fallow, resulting from the absence of both observational evidence and a more quantitative basis in physics. Only after the 1870’s were significant observations of the solar system and stellar nebulas obtained that could begin to confirm or constrain further development of planetary theories. As a result, a number of particular problems with extant nebular hypotheses were examined by several English scientists. A major objection was that nebular hypotheses did not explain the skewed distribution of angular momentum observed between the sun (2 percent) and the planets having the most momentum. If the nebula increased rotational speed as it contracted, the sun should be rotating much faster than it does, and thereby have the bulk of the solar systems’ angular momentum.

James Clerk Maxwell Maxwell, James Clerk further argued that Laplace’s rings would not coalesce directly into planets but would first have to be collected into rings of smaller planetoids, or planetesimals. In a series of papers around 1900, American geologist and astronomer T. C. Chamberlain Chamberlain, T. C. and F. R. Moulton Moulton, F. R. argued strenuously against the nebular hypothesis and, reviving Comte de Buffon’s (1745) idea of a catastrophic star-sun encounter, presented their tidal-collisional planetesimal model. The solar system was said to have developed from material ejected by huge solar tides raised in a glancing collision of another star or comet. English physicist and geophysicist Sir James Jeans Jeans, Sir James and Sir Harold Jeffreys Jeffreys, Sir Harold later proposed a similar theory, in which a close encounter withdrew solar gas filaments, coalescing into beadlike strings of protoplanets.

Within two decades, several problems arose with collision accounts of planetary origins. For one, the statistical frequency of interstellar encounters was far too low to make this a probable mechanism. Also, no collision hypothesis could ensure the current angular momentum distribution. In 1939, American astrophysicist Lyman Spitzer Spitzer, Lyman showed that gases torn from the sun or passing star/comet would disperse before being able to cool sufficiently for condensation.

During the 1930’s and early 1940’s, a new group of neonebular hypotheses was proposed as a consequence of the developments in atomic, nuclear, and plasma physics and of quantitive physical-chemical observations of the sun and nearby stars. Kristian Birkeland Birkeland, Kristian (1912) and Hannes Alvén Alvén, Hannes (1942) suggested that the sun acquired a nebular gas cloud, the electrically charged atoms of which condensed into gas rings, grains, globules, and planets, controlled not only by the sun’s gravity but also by its electromagnetic fields. Stanley Jaki’s Planets and Planetarians Planets and Planetarians (Jaki) (1977) revived nebular theories.

In mid-1943, at the University of Strassburg in Germany, nuclear astrophysicist Carl Friedrich von Weizsäcker was completing his own more detailed and comprehensive nebular theory. Associated with aspects of the German nuclear fission project, his paper “On the Formation of Planetary Systems” was prepared as a primary technical contribution to the memorial volume of the Zeitschrift für Astrophysik for the seventy-fifth birthday of German atomic physicist Arnold Sommerfeid. Sommerfeld had long insisted on real connections between quantified angular momenta of electrons in atomic structure and the planetary-solar system.

After initially synopsizing the history of prior nebular hypotheses, the first technical question addressed whether and how the sun’s original mass was distributed within the boundaries of the present solar system. This raised again the old question of an apparent hundredfold decrease in solar mass needed to account for its presently low angular momentum. Von Weizsäcker reintroduced the circumsolar gas envelope (nebula) as the earliest common origin of both the sun and planets. He assumed that by the laws of momentum and energy conservation, a portion of the original gas nebula would fall into the cloud’s center, the liberated energy carrying off most of the sun’s angular momentum.

Von Weizsäcker next discussed whether and how it was possible for particles in the rotating disk to form systematic and stable patterns. This was feasible in his view if one assumed that the predominant interparticle interactions were almost exclusively gravitational. The next stage, his theory’s core, derived a set of five concentric lenticular-shaped rings around the sun, each ring, in turn, encompassing five internal vortices of similar shape. The corresponding diagram of this system was eventually reprinted in many textbooks and publications.

This nebula figure was ingeniously derived from particle dynamics, wherein particle trajectories moving in elliptical orbits of small eccentricity viewed from a rotating solar reference would appear increasingly lenticular with increasing eccentricity. More important, the plasma physics of developing mutually stable vortices demanded a vortex upper size limit. A major consequence of this quintic arrangement was that ratios of the radii of successive preplanetary rings is approximately defined by the well-known Titius-Bode law Titius-Bode law[Titius Bode law] of 1772, an empirical formula. The result was seen as a major internal consistency check and plausibility argument.

An eddy is a transient thermodynamic condition generally sustained only long enough for its gas to travel a distance roughly equaling its own diameter. Turbulence, or turbulent fluid flow, has a high complex velocity and pressure distribution typically characterized by random spatial and temporal fluctuations. The location of planetary formation within this turbulent system was therefore proposed to be the low-friction “roller bearing” areas formed by three touching adjacent vortices. From theoretical considerations, turbulence at these locations seemed sufficiently high to facilitate formation of planetesimals from disk gas and dust, by way of intermediate-sized globules sufficiently large that their rate of accretional buildup by gravity exceeded their volatilization rate through collision. As von Weizsäcker explicitly noted, these thermohydrodynamic assumptions were the most uncertain aspects of his theory. Specifically, strong analogies exist between hierarchical spatial relations in the preplanetary disk and gas particle patterns; these analogies were not yet a definite physical-causal connection.

Significance

Although most immediate discussions of von Weizsäcker’s theory were delayed by World War II, almost all initial published reactions to his theory were positive. In the spring of 1945, nuclear physicist George Gamow and cosmologist J. A. Hynek published a short review (“A New Theory by C. F. von Weizsäcker on the Origin of the Planetary System”) in the Astrophysical Journal. In their estimate, the theory “allowed an interpretation of the Bode-Titus law of planetary distances” and explained “all the principal features of the solar system,” notably the common revolution plane, small orbital eccentricities, common rotational direction, and lower material densities of the larger planets. The single criticism was difficulty in visualizing the details of a single planet forming from five planetesimals, an issue von Weizsäcker subsequently addressed. Several astronomers have argued that one reason for von Weizsäcker’s theory’s popularity was its extraterrestrialist implication for universal planetary formation.

The theory received further attention when in 1946 noted astrophysicist Subrahmanyan Chandrasekhar published a favorable account in the Reviews of Modern Physics. Nevertheless, German astronomer Friedrich Nölke and Dutch astrophysicist D. ter Haar Haar, D. ter in 1948 independently published detailed criticisms of von Weizsäcker’s theory, based on rigorous and extensive hydrodynamic considerations of energy transport by nebular eddies. Nölke showed that serious difficulties remained in the angular momentum problem.

According to ter Haar, if the Sun’s presently slow rate of rotation was caused by absorption of material from the nebular disk, there still existed a discrepancy of a factor of one thousand between actual and predicted solar mass. Dutch American astronomer Gerard Peter Kuiper Kuiper, Gerard Peter from 1949 to 1951 likewise rejected von Weizsäcker’s regular vortices, but redeveloped the nebular theory, proposing formation of random turbulent eddies in the nebular disk as a natural consequence of binary star formation. Kuiper argued that vortex stability required high-mass density in the cloud, such that the resulting gravitational attraction equals or exceeds the Sun’s gravity.

Later theories incorporated the ideas of turbulence, magnetic fields, and planetesimals, maintaining that supersonically turbulent nebular clouds break up into chaotic swarms of “floccules,” continually dispersing and reforming according to statistical laws governing plasma interaction. Despite increases in empirical and theoretical astrophysics, von Weizsäcker’s theory of planetary formation remains, among some scientists, a partial source and exemplary model for future planetesimal theories. Astronomy;planetary formation Planetary formation "On the Formation of Planetary Systems" (Weizsäcker)[On the Formation of Planetary Systems]

Von Weizsäcker Forms His Quantitative Theory of Planetary Formation Summary