If we want to travel into the future, we just need to go fast. Really fast. And I think the only way we're ever likely to do that is by going into space. The fastest manned vehicle in history was Apollo 10. It reached 25,000mph. But to travel in time we'll have to go more than 2,000 times faster. And to do that we'd need a much bigger ship, a truly enormous machine. The ship would have to be big enough to carry a huge amount of fuel, enough to accelerate it to nearly the speed of light. Getting to just beneath the cosmic speed limit would require six whole years at full power...Hawking estimates that it'd take 80 years to reach the edge of the galaxy. But here's where this method of time travel loses out to a much more plausible (and probably much more affordable) option. Consider that during those 80 years, you'd age at a normal rate--unless, like in a lot of Sci-Fi-let's-travel-to-the-edge-of-the-universe flicks, you were somehow sleeping away the time in suspended animation.
After two years it would reach half-light speed and be far outside our solar system. Two years later it would be travelling at 90 per cent of the speed of light. Around 30 trillion miles away from Earth, and four years after launch, the ship would begin to travel in time. For every hour of time on the ship, two would pass on Earth. A similar situation to the spaceship that orbited the massive black hole.
After another two years of full thrust the ship would reach its top speed, 99 per cent of the speed of light. At this speed, a single day on board is a whole year of Earth time. Our ship would be truly flying into the future.
And that's the key. After all, if your only goal is to wake up 150 years in the future without having aged, why travel anywhere? What we need is a Rip Van Winkle technology, not a monstrous spaceship, if we really want to travel in time. The trick isn't to go faster, but to slow down.