It depends on the context, but I think "so that" is more commonly used this way - "in order..." is more often seen as "in order" to do something, as in "In order to get there faster, she took a shortcut." "so that" X result happens vs. "in order" to do something I believe they are both technically correct, but "...so that astronauts..." does sound better

Personally I would use "so that" I think because its shorter even though only by one word and makes the sentence flow better. I think "so that" is used more commonly than "in order that" the latter seams too rigid to me personally. If I was going to use "in order that" I would have to change it and the sentence "Missions have to be carefully designed in order to keep astronauts safe from take-off to landing." hope I helped :L