Applications in many domains require processing moving object trajectories. In this work, we focus on a trajectory similarity search that finds all trajectories within a given distance of a query trajectory over a time interval, which we call the distance threshold similarity search. We develop three indexing strategies with spatial, temporal and spatiotemporal selectivity for the GPU that differ significantly from indexes suitable for the CPU, and show the conditions under which each index achieves good performance. Furthermore, we show that the GPU implementations outperform multithreaded CPU implementations in a range of experimental scenarios, making the GPU an attractive technology for processing moving object trajectories. We test our implementations on two synthetic and one real-world dataset of a galaxy merger.One motivating application for this work is in the area of astrophysics/astrobiology [10]. Astrobiology is the study the evolution, distribution and future of life in the universe. Biologists study the habitability of the Earth and find that life can exist in a multitude of environments (including extreme environments, such as temperature, pressure, salinity, radiation exposure, and others). The past decade of exoplanet searches implies that the Milky Way, and hence the universe, hosts many rocky, low mass planets that may be capable of supporting complex life (land-based animal life). Given that there are many planets in the Milky Way and given the broad range of conditions in which life is found to thrive on Earth, the notion of the Galactic Habitable Zone has emerged, i.e., the region(s) of the Galaxy that