Sul collasso di un ammasso di materia disgregata. Nota II

Dionigi Galletto

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1985)

  • Volume: 78, Issue: 6, page 268-277
  • ISSN: 1120-6330

Abstract

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With reference to Nota I, the hypothesis that the cluster 𝒰 is spherical is substituted by the hypothesis that it has an isotropic behaviour with respect to a given frame of reference ℐ O with origin in an element O internal to 𝒰 . The kinematical behaviour of 𝒰 during the collapse with respect to the frames of reference with origin in the elements of 𝒰 and in translatory motion with respect to ℐ O is studied. This behaviour is the same with respect to each of such frames, which are in translatory motion with respect to inertial frames. With the hypotheses that the forces at a distance depend on masses and distances only (see [3], 2), the integral equation which such forces must satisfy and in which also the shape of the cluster is unknown is determined. It is proved that if the forces at a distance are those expressed by Newton's law of gravitation the shape of the cluster is necessarily spherical, with the consequence that if it is not spherical 𝒰 cannot have an isotropic behaviour during the collapse. Finally, under suitable hypotheses it is proved that the forces at a distance are necessarily expressed by Newton's law of gravitation and that, at least under such hypotheses, the shape of 𝒰 is necessarily spherical.

How to cite

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Galletto, Dionigi. "Sul collasso di un ammasso di materia disgregata. Nota II." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 78.6 (1985): 268-277. <http://eudml.org/doc/287216>.

@article{Galletto1985,
author = {Galletto, Dionigi},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {isotropic behaviour; collapse; translatory motion; inertial frames; Newton's law of gravitation},
language = {ita},
month = {6},
number = {6},
pages = {268-277},
publisher = {Accademia Nazionale dei Lincei},
title = {Sul collasso di un ammasso di materia disgregata. Nota II},
url = {http://eudml.org/doc/287216},
volume = {78},
year = {1985},
}

TY - JOUR
AU - Galletto, Dionigi
TI - Sul collasso di un ammasso di materia disgregata. Nota II
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1985/6//
PB - Accademia Nazionale dei Lincei
VL - 78
IS - 6
SP - 268
EP - 277
LA - ita
KW - isotropic behaviour; collapse; translatory motion; inertial frames; Newton's law of gravitation
UR - http://eudml.org/doc/287216
ER -

References

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  1. GALLETTO, D. (1982) - Un teorema di inversione nella teoria del campo di attrazione newtoniano, «Atti Accad. Sci. Torino», 116, 349-356. Zbl0606.35067MR840732
  2. GALLETTO, D. (1983) - Some Converse Theorems in Newtonian Field Theory and Their Applications, «Applicable Anal.», 15, 313-337. Zbl0507.31002MR710197DOI10.1080/00036818308839453
  3. GALLETTO, D. e BARBERIS, B. (1984) - Sulla legge di gravitazione universale. I, «Atti Accad. Naz. Lincei Rend.», Ser. VIII, 76, 359-366. Zbl0603.70006MR863497
  4. GALLETTO, D. e BARBERIS, B. (1985) - Sul collasso di un ammasso di materia disgregata. I, «Atti Accad. Naz. Lincei Rend.», Ser. VIII, 78, 138-147. Zbl0641.70009MR919016

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