AC is only 4.5 years away. If we really wanted to go there we could most definitely build something that can travel at 0.5c and get there at, say, 6 to 7 years. It's not hard to keep accelerating and decelerating for 1m/s for 15 years with current tech.
> It's not hard to keep accelerating and decelerating for 1m/s for 15 years with current tech.
Just to put some numbers to this, I went to my go-to quick reference for these types of problems is the Usenet Physics FAQ article on the equations for relativistic rockets:
The key numbers are the trip time T according to the ship's clocks, the trip time t according to clocks on Earth or Alpha Centauri, the maximum velocity v achieved by the ship, and the mass ratio M, or kg of fuel needed per kg of payload. Assuming that we accelerate for half the distance and then turn around and decelerate for the other half, and that we use an ideal rocket that converts fuel to energy at 100% efficiency and exhausts all that energy out the back with perfect collimation (so it all goes into changing the rocket's momentum and not into heat or some other waste product), the formulas for these are:
T = 2 (c/a) arccosh (ad/2c^2 + 1),
t = sqrt((d/c)^2 + 2d/a),
v = at/2 sqrt(1 + (at/2c)^2)
MR = exp(aT/c) - 1,
where a is the acceleration, d is the total distance traveled, and c is the speed of light. The equation for T, assuming that we accelerate halfway, then turn around and decelerate to arrive at the destination at rest, is
Plugging in a = 1m/s^2, d = the distance to Alpha Centauri, or about 4 x 10^16 meters, and c = 3 x 10^8 m/s, we get
T = 3.9 x 10^8 s, or about 12.7 years,
t = 4.2 x 10^8 s, or about 13.6 years,
v = 1.7 x 10^8 m/s, or about 0.57 c,
MR = 2.7
This is a pretty small mass ratio, but of course it was derived using highly idealized assumptions. More realistic assumptions would result in a much larger mass ratio. Also, a maximum speed of more than half the speed of light would create huge radiation issues requiring heavy shielding, so the payload mass would be very large.
Yeah, hard is clearly an understatement. However, if it were critical to the human race, and the top 20 economies put a trillion dollars and some of their best scientists behind it starting today, there is absolutely zero question that a ship capable of that could be built and launched within 20 or 30 years.
Alternatively, Bezos will probably have $100 billion to play with in the next 12 to 24 months or so ($61 billion today, most projections have Amazon climbing quite a bit higher yet, new price targets have it at $1,000 per share; whether it takes a year or six years, it'll very likely get there). He just sold off $671 million worth of shares the other day, I'd expect his sales will continue as the price climbs. So maybe he'll fund it by himself in the coming two decades.
