Re: "manned missions to Mars to be completed within a mere two months"
"Time dilation. 4 years is not.... 4 years"
From your perspective at lightspeed if it's a one way trip. But if you're planning on coming back you'll find it hard to re-adjust from 'short' trips and from longer trips you might even find this planet unrecognisable. For a clear exposition of the cultural problems, see Larry Niven's short story 'Rammer'.1
Oh, and for really long trips (even one way), given the delay between cosmic events and us seeing them plus the actual trip time2, there's a possibility that the world you'd be aiming for might not even exist any more once you'd reached its nominal vicinity.
1: yes, I know the initial time shift wasn't due to FTL travel, but the cultural principle remains valid
2: you, in your spacecraft may experience time dilation, but cosmic events proceed independently in normal time
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