Abstract Radiation pressure exerted by solar photon output is salient to the motion of primary neutral hydrogen atoms streaming into the inner heliosphere directly from the local interstellar medium. The action of a time-dependent radiation pressure force, when coupled with the usual gravitational force, changes the characteristic velocities, and therefore energies, of the atoms when they reach regions in which explorer probes are present. A study is presented that uses a 2D code to backtrace neutral hydrogen trajectories from representative target points located 1 au from the Sun. It makes use of both a radiation pressure function and a function for the photoionization rate at 1 au that both oscillate with time based on measurements over a typical solar cycle, as well as a time-independent charge exchange ionization rate at 1 au. Assuming a Maxwellian distribution in the distant upwind direction, phase space data is calculated at the target points, at different moments in time. The dependence of the force on the radial particle velocity has been omitted in the analysis, such that the emphasis is on the effects of the global solar UV intensity variations through the solar cycle. This process allows for the analysis of direct and indirect Maxwellian components through time and space in the time-dependent force environment. Additionally, pseudo-bound orbits caused by energy losses associated with this force environment are observed, and their properties are evaluated with the aim of determining their effects on potential measurements by explorer probes.