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The physicochemical mechanism of the formation of planetary systems

HomepageINSTITUTE of Physico-Chemical Problems of EvolutionPhysical Chemistry of Evolution of Planetary SystemsThe physicochemical mechanism of the formation of planetary systems

Institute of Chemical Physics, Academy of Sciences of the U.S.S.R., Moscow, U.S.S.R.
(Received 30 January, 1978)

Abstract. The planets and their satellites are formed in accordance with similar mechanisms as a result of spatially periodic condensation of gaseous matter during the formation of the central body.

Using the diffusion theory one can calculate the age of the planets and explain the nature of the Titius-Bode law.

1. Introduction

There, exist several elaborate hypotheses of the formation of planetary systems, in particular the solar system, in which the decisive role is played by gravitational, magnetic and other forces (references 1, 2, 3 and 4), but there are no quantitative hypotheses taking into account the peculiarities of the kinetics and mechanism of physico-chemical phenomena in the formation of planets and their satellites.

In this paper we present the fundamentals of a diffusion hypothesis, according to which the regular structure of planetary systems can be quantitatively explained as a consequence of spatially periodic condensation of gaseous matter during the formation of the central body.

It will be shown that the planets and their satellites are formed in accordance with similar mechanisms. The present paper is a first attempt to use diffusion theory to explain the solar system's formation. The theory gives the possibility of calculating the time of formation of primary rings of condensed matter and the ages of the planets and the solar system as a whole and then of explaining the nature of the Titius-Bode law.

2. Model Considerations

Let us consider one of thc simplest models. Following well-known concepts, let us assume that the Sun began to take shape from a rotating nebula consisting of gaseous matter and fine-grain dust. Gravitational compression led to the formation of a protosun, surrounded by a nebula (disk) of rarefied matter. Later, matter from the Sun began to escape in the equatorial plane. Owing to subsequent diffusion of the ejected hot matter into the relatively cold nebula consisting of matter in a gaseous state, tliere occurred a spatially periodic condensation of the rarefied gas, leading to the formation of condensed matter from which protoplanets took shape. Protoplanets experienced gravitational compression and then, as in the case of the Sun, lost their gaseous envelopes. Rings were formed, followed by the accumulation of particles and formation of regular satellites.

It can be shown that during diffusion (reference 5) of matter from the protosun or protoplanet into their corresponding nebula (disks) there should form, under certain conditions, periodically condensed rings due to proceeding chemical reactions of formation of nonvolatile compounds. Minute particles of cosmic dust may have served as centers of such a condensation.

A confirmation of the hypothesis under consideration should be the correspondence of the arrangement of the rings being formed to the Titius-Bode rule (references 1, 2,4 and 6), which can be represented in the form

, (1)

where rn is the major semi-axis of the n-th orbit, r0 is a constant and is a constant for the solar system close to 1.7.

Let us consider the mechanism of periodic condensation accompanying chemical processes. Assume that the periodic condensation on cosmic scales is similar to the Liesegang phenomenon (references 5, 7, 8 and 9), which although interpreted variously lead in all models to the same basic result.

We shall consider that matter escaping from the protosun or protoplanet is hotter than the nebula's matter. We shall also assume that, after matter from the central body and nebula has mixed, the multi-component gas exists for a certain time in a supersaturated state. For simplicity, we shall designate the concentration of the escaping reactive multi-component diffusing matter by cs and the concentration of the nebula's reactive matter by cn.

The interaction of matter s and n yields condensed matter. The magnitude of super-saturation may be represented by the product where n' and m' are averaged stoichiometric coefficients. Condensation begins when the value of exceeds a certain critical value. After the formation of condensate, the value cs and cn decrease abruptly, so that close to the critical distance rcr (references 6, 7, 8 and 9) the value of is reduced practically to zero. With increasing distance from the central body, the process described is repeated periodically (references 7,8 and 9).

In considering the posed problem, let us assume that for a certain value of r'n<1, r2,…,rn the motion of particles of matter obey the Fick relation

, (2)

where t is time and Ds,n is the coefficient of diffusion.

The approximate theory does not make it possible to obtain the value rn but, if it is known, one can determine rn+1, which is proportional to rn

, (3) where a is a constant.

Thus we come to the conclusion that rings of condensed matter are arranged in geo-nictrical progression, i.e. as required by the Titius-Bode rule.

Using the simplified one-dimensional model of Liesegang rings formation (reference 9), one can write


for , where is the distance between the rings, , , , K is the constant of supersaturation, and being coefficients of condensed matter, is a dimensionless constant determined (for Ds=Dn) by the ration of initial concentrations

From Equation (4) it follows that =constant arid is determined by the types of chemical processes and peculiarities of condensation.

Moreover, from the same equation it follows that the distance between rings is the greater, the smaller .

We shall show that from the standpoint of the diffusion laws the proposed hypothesis is quite justified. Let us assume that for very rarefied gas (reference 10)

, (5)

with D in (cm2/sec) and T is the temperature (°K), M is the average atomic (molecular) weight of matter, p is the pressure in (atm) and is the average diameter of the particles in (A).

By use of the expression


where is a dimensionless constant determined in the general case (reference 8) by the ratios


one obtains

p(atm) = . (7)

If one assumes that is sufficiently high (e.g. 100 °K and higher, reference 4) and , the time of formation of all "primary rings" is commensurable with the age of the solar system (» 1.4 ґ 1017 sec), then p, calculated from Equation (7), turns out to be such that the overall mass of the nebula is commensurable with (or even significantly exceeds) the mass of the planets of the solar system (reference 11).

Another model assumes diffusion of matter from the periphery of the nebula to a relatively rarefield region which could have formed during gravitational compression. From the standpoint of mathematical description this model is analogous to the model discussed above. Therefore, the overall results obtained are applicable, in principle, to both models.

3. Discussion

The detailed theory of diffusion formation of planets should take into account the fact that the original distances and periods of rotation () around the central body are functions of many parameters

where and are average heats of condensation and of chemical transformation.

One can believe that a consequence of the functional dependence of should be that Equation (1) is more satisfactorily obeyed for systems of regular satellites of large planets than for the planets of the solar system themselves.

The theory presented in the paper affords making some predictions. In particular, it predicts an effect of separation of chemical substances during the formation of the primordial rings of planetary systems and the existence of rings round the young planets of the solar system, for example, Neptune.

Besides, rings and satellites may be formed around large satellites of planets, etc.

It is interesting to apply the hypothesis under consideration to galactic scales.


I should like to thank G.Arrhenius, J.Arnold, S.Benson, W.Chang, V.Budtov, E.Denisov, N.Emanuel, Yu.Ershov, J.Greenstein, J.Kleczek, G.Korolev, M.Kubin, H.Mark, N.Peterson, V.Safronov, H.Urey and Ya.Zeldovich for helpful discussions.

Notes and References

[1] Arrhenjus,G. and Alfven,H.: 1976, Evolution of the Solar System, National Aeronautics and Space Administration, Washington, D.C., 1-599.

[2] Brandt,J.C. and Hodge,P.W.: 1967, Solar System Astrophysics, McCraw-Hill Book Company Inc., New York, 1964; Russian translation, Mir, Moscow, 1-488.

[3] Safronov,V.S.: 1969, Evolution of Pre-Planetary Nebula and Formation of Planets, Nauka, Moscow, 1-244.

[4] Symposium sur l'Origine du Systemes Solaire (Symposium on the Origin of Solar systems) Nice, 3-7 April, 1972, Reeves, Hubert responsable de la publication, Edition du Centre National de la Recherche Scientifique, Paris, 1972. For some interesting aspects of the solar system formation see for instance the papers by W.McCrea, H. Reeves, G.Arrhenius, R.B.Larson, H.C.Urey, E.Anders, J.Lewis and J.Vedder and by some other authors.

[5] At first we talk about diffusion (in a classical sense) of matter into the nebula itself which is along Keplerian orbits; thus the matter of the central body moves according to the diffusion laws.

[6] Nieto,M.M.: 1976, The Titius-Bode Law of Planetary Distances: Its History and Theory, Pergamon Press, Oxford, 1972; Russian translation, Mir. Moscow, 1-190.

[7] Liesegang,R.: 1897,Z. Physik. Chem. 23, 365.

[8] Zeldovich,Ya. and Todes,O.M.; 1949, Zh. Fiz. Khim. 23, 180.

[9] Wagner, C.: 1950, J. Colloid Sci. 5, 85.

[10] Hirschfelder,J.O., Curtiss,C.F. and Bird, R.B.: 1961, Molecular Theory of Gases and Liquids, John Wiley and Sons, New York, 1954; Russian translation, IL, Moscow, 19-29,

[11] We present a numerical example. Combination of Equations (5) and (6) and pV=(m/M)RT gives

If = 1.35ґ 1030 g, = 82.1 cm3 atm/mode °K, = 6ґ 1014 cm, (= 3Е, = 20, =1044 cm, = 6, =200 °K, then =5ґ 109 yr.

We emphasize this this evaluation is semi-quantitative. The gas diffusion leads to a decrease in the distance from the central body of corresponding masses of the nebula (compressing nebula). But this and other effects not taken into account by us do not change the general picture of the phenomenon. For the time being, we also disregard the presence in the nebula and in the protostar matter of "unreactive" ("uncondensing") substances, such as redundant hydrogen and the like.

A more exact solution of the problem assumes the use of the equation of motion of a partially ionized gas in a velocity field provided that the equation takes into account gravitational, Coriolis and electromagnetic forces, temperature and density gradients and other effects.

According to one of the simplest models, the rings of the germs of primary protoplanets and satellites arc formed in general of the iron and silicon compounds. Fe (as other heavy elements) is transported from the central body in the form of the following compounds such as FeH, FcHn(C0)m (Si0)p Halr (the sum of n, m, p, r may change from 1 to 5). Then these compounds may react, for example, with H20 of the protonebula, producing non-volatile compounds.

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