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 Serie 8 78 (1985), fasc. n.6, p. 268-277, (Italian)
Seguito di RLINA_1985_8_78_4_138_0 | pdf (1.08 MB), djvu (1.16 MB). | MR 0919019 | Zbl 0641.70010
Sunto
With reference to Nota I, the hypothesis that the cluster $\mathcal{U}$ is spherical is substituted by the hypothesis that it has an isotropic behaviour with respect to a given frame of reference $\mathcal{I}_{O}$ with origin in an element $O$ internal to $\mathcal{U}$. The kinematical behaviour of $\mathcal{U}$ during the collapse with respect to the frames of reference with origin in the elements of $\mathcal{U}$ and in translatory motion with respect to $\mathcal{I}_{O}$ 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 $\mathcal{U}$ 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 $\mathcal{U}$ is necessarily spherical.
Referenze Bibliografiche
[1]
GALLETTO D. (
1982) -
Un teorema di inversione nella teoria del campo di attrazione newtoniano, «
Atti Accad. Sci. Torino»,
116, 349-356. |
MR 840732 |
Zbl 0606.35067[3]
GALLETTO D. e
BARBERIS B. (
1984) -
Sulla legge di gravitazione universale. I, «
Atti Accad. Naz. Lincei Rend.», Ser. VIII,
76, 359-366. |
MR 863497 |
Zbl 0603.70006[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. |
MR 919016 |
Zbl 0641.70009