Final answer:
The provided materials do not give a specific duration for a manned Orion mission to Mars. However, it's estimated that a round trip to Mars, including time spent on the planet, would take just under 3 years.
Step-by-step explanation:
The proposed duration of the manned trip to Mars using the Orion spacecraft is not explicitly stated in the provided reference materials. However, in practice, the duration of a manned mission to Mars, including the journey there and back plus the time spent on the Martian surface, is estimated to take just under 3 years. This total duration accounts for the voyage to Mars, the time spent on the Martian surface, and the return trip to Earth. The trip to Mars alone would take several months; NASA's current plans estimate that the journey to Mars could take approximately 6-8 months one-way, depending on the alignment of Earth and Mars and the specific trajectory used. As technology and mission plans are still developing, the exact duration of the Orion missions to Mars is subject to future planning and optimization based on the various factors of space travel.