@Phemox, you can only feel a change in velocity, and thus the accleration would be the only problem. But whose to say you have to accelerate to the speed of light so fast that it is harmful to you? It doesn't matter as long as you get there.

@Capanno, pretty much what Dan said, but also the fact that this is supported mathematically, so it's no real surprise that the clocks were different.

@EX Citer, the speed that the planets move is nearly irrelevent compared to the speed of light. Similiarly, the difference in the speed of the sun and the speed of the planets is also quite irrelevent in comparison to the speed of light. (299,792,458 meters/sec) Still, time does move slower for us than for the sun, but the difference is so small that it's pretty much unnoticable.

Also, I forgot to mention, the process of time travel I stated above is known as time dialation, for anyone interested in further reading.