Why exactly does acceleration become difficult?
You know, I've been thinking about it, and it shames me to admit, that I'm at loss as to why it is supposed to be so. After all, the thing that first comes to mind is the relativistic mass increase, that would need more and more force to accelerate it by the same factor. Yet, the mass increase is associated with the frame of reference that is moving, i.e. from the point of view of the ship, it's the planets that are moving. So it's the planets that should gain mass, not the spaceship, no? Somebody help me here.
I'm not so sure about this, but I believe that's a consequence of dilation and not actually lack of acceleration. From your POV, you keep accelerating at the same rate, so you ARE going "faster and faster", but from the external POV you seem to be accelerating less and less. Or is it the other way around? That's why as you approach C, the people inside the ship could perceive a trip to be (near) instant, while people outside will still think you still took 4 or more years to reach the nearest star.
Also, not doing any actual math here, so only the idea counts, not the actual numbers and proportions: let's say you accelerate from 0.90 C to 0.91 C. From an outside POV you just shaved maybe a few days from your (4 year) trip, but inside, it may appears to you that you doubled your speed (because the energy required to do such thing "should" have accelerated you to twice your speed) so what you woul dhave perceived as a (pulling out of my ass number) 3 months, took only month and a half.