Orbital dynamics of a simple solar photon thruster.
Starting from the considerations developed in [4], it is shown that the only forces at a distance exerted among the elements of an isolated spherical cluster of incoherent matter which, preserving homogeneity, is collapsing are those expressed by Newton's law of gravitation and those of the elastic type. Furthermore the reverse is shown, that is if the forces at a distance are of these two types during the collapse the homogeneity is preserved.
With reference to Nota I, the hypothesis that the cluster is spherical is substituted by the hypothesis that it has an isotropic behaviour with respect to a given frame of reference with origin in an element internal to . The kinematical behaviour of during the collapse with respect to the frames of reference with origin in the elements of and in translatory motion with respect to is studied. This behaviour is the same with respect to each of such frames, which are in translatory motion...
We consider the classical three-dimensional motion in a potential which is the sum of attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the centres, we find a universal behaviour for all energies above a positive threshold. Whereas for there are no bounded orbits, and for there is just one closed orbit, for the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....