  This paper presents an analytical study of the behavior of radial
free-geodesics in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime
within the Lambda Cold Dark Matter ({\Lambda}CDM) model. Using the radial free
motion solutions, we provide two methods for characterizing the geodesics and
defines a general formula that encapsulates all possible solutions, determined
by two initial conditions. We show that the past light cone, event horizon, and
particle horizon, can be considered as special cases of this overarching
formula. Furthermore, the paper explores the free geodesics within the
currently accepted cosmological model based on the recent Planck results,
thoroughly examining the various possible geodesic scenarios.
