We model accelerated trips at high velocity aboard light sails (beam-powered propulsion in general) and radiation rockets (thrust by anisotropic emission of radiation) in terms of Kinnersley's solution of general relativity and its associated geodesics. The analysis of radiation rockets relativistic kinematics shows that the true problem of interstellar travel is not really the amount of propellant nor the duration of the trip but rather its tremendous energy cost. Indeed, a flyby of Proxima Centauri with an ultralight gram-scale laser sail would require the energy produced by a 1 GW power plant during about one day, while more than 15 times the current world energy production would be required for sending a 100 tons radiation rocket to the nearest star system. The deformation of the local celestial sphere aboard radiation rockets is obtained through the null geodesics of Kinnersley's spacetime in the Hamiltonian formulation. It is shown how relativistic aberration and the Doppler effect for the accelerated traveler differ from their description in special relativity for motion at constant velocity. We also show how our results could interestingly be extended to extremely luminous events like the large amount of gravitational waves emitted by binary black hole mergers.