In this paper we present the results of a theoretical study of the trajectories of massive particles in the K¨ottler metric in view of the cosmological constant Λ. For both negative and positive signs of Λ a classification of trajectories is proposed, with entries based on different solutions of the trajectory equation, obtained by the expansion of the corresponding algebraic curve in Puiseux series. We also provide some specific types of trajectories which correspond to different values of the cosmological constant. In the case of negative values of the cosmological constant its upper limit is estimated from the galaxy rotation curves.