Hippotherapy, riding a horse in the context of rehabilitation, is a medical treatment that successfully has been employed in various fields, e.g. for improving locomotion performance of patients with movement disorders. Robotic systems enable the application of hippotherapy in clinical environments with additional benefits, like adjustable speed and high repeatability. Fundamental for a therapy outcome equivalent to classical hippotherapy is that the trajectory of the robotic system is as realistic as possible. This paper introduces a method for the synthesis of horseback motions using motion capture data of various horse gaits. Based on complete gait cycles, an analytical, time-continuous and periodic motion description is constructed. Measured 3D marker positions are reconstructed with a mean error not exceeding 8.6 mm. If the motion capture data of several gait cycles are considered, a more generalized trajectory is generated. An adjustable time dilatation parameter enables the adaptation of the generated motion according to the physical abilities of the patient or the capabilities of the robotic system. This method allows for motion synthesis with arbitrary time span and time resolution, generating realistic trajectories effectively applicable to robotic systems for riding simulation in general and robotic hippotherapy in particular.