How much Earth time passes over a 1000 lightyear journey? Ok, so I'm writing a sci-fi novel featuring a lot of interstellar travel. I was wondering how much time would pass, from an Earth-based perspective, if I were to travel 1000 lightyears from Earth, and then back again. I assume it's 2000 Earth years, right?
I've been getting twisted in knots over relativity recently (writing this thing), and I just wanted to be certain I'm not going insane.
I also gleaned, from the movie Interstellar, that you can 'buy back' years by skimming around the event horizon of a black hole; I know it's a separate question, but it is sort of related; can anyone clarify that effect for me?
 A: The fastest you can go 1000 ly and then return (from the Earth perspective) is 2000 years. This corresponds to travelling at lightspeed. There is no slowest limit, of course: you can spend as long as you want to slowly get to the destination. It is the speed, rather than the distance, that matters.
From Earth's perspective, if you travel at constant velocity $v$ you will arrive at your destination after $1000 (c/v)$ Earth-years, and return at Earth-year $2000 (c/v)$.
From the traveller perspective the trip was quicker, only taking $2000 (c/v) \sqrt{1-(v/c)^2}$ ship-years. where the square root factor is due to the time dilation. A very slow ship will give rise to a long trip (and a time measurement close to the Earth measurement), while a near $c$ trip can be experienced as very short. You still need to travel faster than 70% of $c$ to get a ship-time smaller than 2000 years.

A: The pace of time is for everyone the same. It is only when you compare these paces that differences occur.
If you compare clocks when meeting another person, it depends on your histories of space travels what the outcome of this comparison is.
If your interstellar travelers journey 1000 light-years away with high speed and return to Earth with high speed, the clocks of the travelers will show that less time has passed for them. This is because light has a finite speed that is the same for everyone.
The travelers see those on Earth travel fast just the same. But they have experienced acceleration. To go away and to return. During the trip you will see their clocks go slower (like their movements) as they will see yours. When the accelerate to go back to Earth and move home with same high velocity they have to accelerate one last time. It's then that on Earth you'll see that their clocks actually are way behind yours. Possibly close to 2000 years, but in that case they must have traveled very close to the speed of light and have accelerated in short time to achieve this speed.
So they, upon coming near to Earth, see that your clock goes forward fast, so it points to 2000 years.
If Earth had accelerated to them instead, in the same way they took off, and then both of you start moving symmetrically towards each other, your clock would show no difference.
You could make your travelers orbit a huge black hole, like Gargantuan in interstellar. Time moves slower there. Do you remember the doctor who they left behind in his spaceship? The planet was closer to Gargantuan than he was. Causing 23(?) Years of difference... Strange, but it could be. The nearer you orbit a black hole the slower time goes relative to orbits further away. That's curvature of time, accompanying curvature of space. Together they form curvature of spacetime.
