Space mission complexity is constantly increasing, therefore there is a growing demand for highly accurate and fast trajectory design and simulation tools. Some astrodynamics applications, such as planetary protection simulations, require millions of total simulated years to quantify certain probabilities with a high confidence level. It is hoped that by efficient programming, calculations executed in parallel on a GPU (Graphics Processing Unit) can bring significant speedups compared to traditional sequential CPU (Central Processing Unit) execution, therefore GPU utilization for massively parallelized trajectory propagations was investigated. A powerful software was developed in CUDA C++ which is able to propagate the trajectories of many samples in parallel on a CUDA-capable GPU. After an extensive optimization procedure, up to two orders of magnitude speedups were achieved using different test applications compared to single core CPU execution of the same software. Numerous test cases were shown to be able to identify which one of them is the most suitable for GPU executions. Three examples were presented which intended to show the robustness of the tool when it is applied for real mission cases. The studies included the upper stage disposal of the BepiColombo mission, the Lunar Ascent Element disposal of the HERACLES mission, and the mirror cover disposal of the ATHENA X-ray telescope. Significant speedups were achieved compared to software that are being used by the Mission Analysis Section of the European Space Operations Centre (ESOC) for current and future mission designs.