Complexity of capture phenomena in the conservative and the dissipative restricted three-body problems

Some dynamical properties of satellite capture in the conservative and the dissipative circular and planar restricted three-body problems are studied. The investigations were performed in the space given by (Jacobi constant) x (initial position) x (capture time). For the conservative case, we identi fy the regions with capture and with noncapture and we associate them with the orbital resonances. The fractal dimensions of their contours also are c omputed. Moreover, it is shown that the rate of capture falls off as a powe r law with time. For the dissipative forces, we study the effect of gas dra g on the structures that are observed in the space of initial conditions. W e inspect how the fractal dimensions of the transition regions (the contour of the capture regions) and the power law associated with the time of capt ure are related to a change in the drag coefficient.