The 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.
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
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
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
where t is time and Ds,n is the coefficient
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
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
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
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
is a dimensionless constant determined in the general case (reference 8)
by the ratios
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
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.
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,
Besides, rings and satellites may be formed around large satellites
of planets, etc.
It is interesting to apply the hypothesis under consideration to galactic
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
 Arrhenjus,G. and Alfven,H.:
1976, Evolution of the Solar System, National Aeronautics and Space
Administration, Washington, D.C., 1-599.
 Brandt,J.C. and Hodge,P.W.: 1967, Solar System Astrophysics,
McCraw-Hill Book Company Inc., New York, 1964; Russian translation, Mir,
 Safronov,V.S.: 1969, Evolution of Pre-Planetary Nebula and Formation
of Planets, Nauka, Moscow, 1-244.
 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.
 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.
 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.
 Liesegang,R.: 1897,Z. Physik. Chem. 23, 365.
 Zeldovich,Ya. and Todes,O.M.; 1949, Zh. Fiz. Khim. 23, 180.
 Wagner, C.: 1950, J. Colloid Sci. 5, 85.
 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,
 We present a numerical example. Combination of Equations (5) and
(6) and pV=(m/M)RT gives
1.35ґ 1030 g, =
82.1 cm3 atm/mode °K, =
6ґ 1014 cm, (=
cm, = 6, =200
°K, then =5ґ
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.