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How big would a manned ascent stage for Mars need to be? assumes 3 astronauts. That question appears to draw inspiration from the Apollo programme, and the Soyuz evolution. Part of the rationale behind the 3-count is mentioned in Why have so many space missions had a crew of 3?

Yet a manned mission to Mars, or any celestial body other than Earth's Moon would probably be significantly different from the Apollo Program; if only because of the time-scale involved given contemporary technology.

How would one come up with an optimal team-size for a manned mission from Earth to a celestial body other than Earth's Moon?

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This question boils down to the objective and length of the specific mission. If the mission consisted of 30 days on the surface and the primary objective was simply to get there and lay the framework for future missions, three or four crew members would suffice. But if you are opting for a longer mission with specific scientific objectives, you are going to need more people. Just how many "more" depends. To come up with this number, you must decide first what all you need people to do. List everything that will need to be completed by a human on the mission. From there, you can delegate how many people and -- more importantly -- what each person will do (Hint: cross-training is a magnificent resource saver.) I hope this was helpful.

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