How fast can we go? Realistically and theoretically, we cannot exceed the speed of light. Not yet at least. The interwebs have been all abuzz about new theories of how we can achieve a real Star Trek style warp drive. Call me maybe, but I’m not so confident that it will work. Mass is what bends space-time, so you would still need to push a huge mass in front of your spacecraft in order to effectively shrink the space in front of your ship if you wanted to make a jump. (I’m not a theoretical physicist, though, so that may be completely wrong)
So theoretically, without warp speed, how long would it take to get to one of the planets we have discovered that may have liquid water?
Let’s assume we want to go to Gliese 581 g. It’s 22 light years away, and using a speed limit of c, you would expect the trip to take 22 years. Unfortunately, if you started with a velocity of 0, and instantly accelerated to c, you would not survive the journey. “Bug on a windshield” doesn’t even begin to describe the effects that would have on your brain, or your organs, or the molecular structure of all of your cells.
We need to accelerate and then decelerate at a reasonable rate if we want to make it. But what is reasonable for acceleration? The space shuttle
launches used to launch at 3 g. X2, an extremely fun roller coaster, hits 4 g. The human body should be able to reasonably handle being subjected to 10 g for a while, but is probably a bit much for the length of a trip to the store, and would probably not work for a trip to another solar system. We need to compromise somewhere.
Gliese 581 g is estimated to have a mass of 3.1 to 4.3 times that of Earth. If we want to have a colony there, we better be prepared to walk around in its gravity. We can pretty safely assume that the local gravitational pull of Gliese 581 g to be around 4 g or less. In order to prepare ourselves to live there, we will accelerate and decelerate at 4 g for the duration of our flight.
So how long does it take to accelerate to the speed of light at 4 g?
The speed of light is 2.99×108 m/s. Local acceleration at or near the surface of Earth is 9.81 m/s2. Applying kinematics, it would take 2.99×108 / (4 x 9.81) = 7,640,000 s = 88.4 days.
Over that time, we will have traveled 1/2 (4 x 9.81) (7.64×106) 2 = 1.145×1015 m, which would have taken 1.145×1015 / 2.99×108 = 3.82×106 s = 44.2 days at the speed of light.
Of course, this completely ignores the fact that running into minute particles of space dust at the speed of light would cause the ship to explode into a nuclear fireball, so cruising along at 1 c still isn’t really very practical.
The point is, when planning your big trip to Gliese 581 g, pack an extra three months worth of sandwiches for the road.