Permanent capture into the solar system

In this note, an interesting region about the Sun in phase space is described where the permanent capture of an object, P, of small mass from interstellar space can occur, under the gravitational perturbation of the resultant mass of the Galaxy. P is never ejected back into interstellar space and would not collide with the Sun. It cycles about the Sun for all time, asymptotically approaching the capture set. In addition to being permanently captured, P is also weakly captured. A recent result in Belbruno (CMDA, 2024) describes this region in general. It has a fractal structure. A capture cross section and the probability of permanent weak capture are estimated. This is applied to the permanent capture of rogue planets and other objects from interstellar space