Sul collasso di un ammasso di materia disgregata. Nota II

Galletto, Dionigi

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 78 (1985) no. 6, pp. 268-277

Résumé

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.