Space travel without knowledge of relativity

A civilization has begun its space program without any knowledge of general or special relativity. How would this affect the program? Would this establish any limits on where/how they could travel? Could they make it to the moon or other planets? Would space travel be possible at all? Finally, if this is possible, how helpful would it be in the eventual discovery of relativity?

Edit: Their current understanding of physics is the same as ours just before relativity.

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Space travel without knowledge of relativity

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