In an attempt to explain the apparent absence of satellites of the planet's satellites we have investigated two kinds of hypothesis formally independent of each other. The analysis, though qualitative, suggest that the same parameter links the examined hypothesis.Asociación Argentina de Astronomía (AAA

Lavagnino, Carlos J.

English

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ABOUT THE SIZE OP THE C03MICAL SYSTEMS
Carlos J . Lavagnino 
(Observatorio Astronómico, La Plata)
In an attempt to explain the apparent absence o f sa te llite s  o f the pla­
nets* sa te llite s  we have investigated two kinds o f hypothesis formally in­
dependent o f each other* The analysis, though qualitative, suggest that the 
same parameter links the examined hypothesis.
We are describing here in a very qualitative way an attempt to  link  two 
lin es of thought of contemporary cosmogony that mutually remain rather ex­
traneous* The idea arose seven years ago in an unsatisfactory e ffo r t  to ex­
plain the apparent absence o f s a te llite s  o f the planets* sa te llites*  We do 
not know i f  th is question was formulated before 1954, But no doubt i t  would 
have reached us i f  i t  had been considered interesting* We thought that the 
solution  to th is problem would be a contribution to  the knowledge o f the 
structure and evolution of cosmical system in general* Por, we may well 
suppose (ccsmogonical hypothesis) that the formation o f a planetary system 
is  an aspect or event in the evolution os a star, or on the contrary we may 
suppose (cosmological hypothesis) that the formation o f a planetary o f a 
planetary system is  ruled by very general laws that must be fu l f i l l e d  when­
ever discrete masses are formed from diffuse masses* These two types of 
hypothesis are apparently so very unlike each other, that i t  would have 
seemed curious that the existence o f a moon o f the Moon should be approved 
(cr  vetoed) by cosmological reasons and, simultaneously, by cosmogonical 
reasons*
To deal with the problem from a cosmological point of view we have made 
use o f Lambert's idea, as la ter  developed by Charlier, o f a universe struc­
tured in systems o f d ifferent orders. I t  is  easy to see that Charlier*s in­
equality is  ver ified  in the planetary system, and thus the size o f the great­
est orbits of the s a te ll ite s ' moons can be deduced, in case they exist* So 
i t  follow s that Jupiter's most massive sa te llite s  would not always have room 
fo r  their moons, but our Moon would. I f  instead we apply Eigenson's c r ite r ia ,
58
i t  follows that no sa te llite  can have moons, and thus i t  becomes clear that 
the probable number of systems forming a system of k + 1 order, is  enough 
to decide the existence of k-order systems.
Regarding the cosmogonical treatment of the problem, we have combined a 
turbulence process with the sta b ility  critérium due to Pesenkov, and have 
obtained that, at le a st , conditions could have been favourable for the form­
ation of a moon of Titan, The reality of th is process depends fundamentally 
on the existence of turbulence. For this purpose we have investigated Jas— 
chek's empirical law relative to the else of the planets' sa te llite s  systems 
and, after having discussed i t s  numerical significance, we have found that 
fo r  dimensional reasons the distribution of the kinetic arergy in tbe origi­
nal turbulence fie ld  leads to a potential law such as t£e mass-oize empirical 
law found by Jaschek; the only requisite to be observed is that the laborato­
ry measures concerning Prandtl's law and Reynolds number may be extrapolated 
to cosmioal conditions, i . e . ,  that Prandti A coefficient should be negative. 
Should that happen,a turbulence fie ld  would he the straightest ( rplanation 
ftu- the so called hierarchy of systems, because this would correspond to the 
original turbulence spectrum; moreover i t  would force us to anticipate a l i ­
mit to t : a nume^jcal valid ity  of Jaechek's relation, of which on the other 
hand, we may have a glimpse when applying the relation to globular clusters 
and galaxies. Regarding this we may connect the behaviour of A, of the Ray­
leigh coefficien t, and of the mean free path, with the si*/e of the system, 
and conjecture that, for a given cosmical energy distribution, the turbulence 
eddies must have received and ti msferred enei'gy sums dependent on the scale 
of each le v e l. That is  why i t  becomes interesting to compare the energy va­
lues corresponding to the different structural orders already known. The dis­
cussion of such numbers is  under way.
The paper in fu ll  w ill he published, elsewhere.
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About the size of the cosmical systems

http://sedici.unlp.edu.ar/bitstream/handle/10915/80940/Documento_completo.pdf?sequence=4

About the size of the cosmical systems

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