That's what I thought, too. I think the energy examples were supposed to scare me, and if he'd said something like total output of the sun, ever, they would have. But total power output of current civilization for five days garnered more of a "sounds doable" response from me.
Yeah I don't think it's impossible to build a bomb that big, as far as I understand it, no one felt like building bigger bombs than tsar bomba because it becomes useless, if I'm not mistaken after 400 megaton or so, most of the energy will just be sent to space.
From the Tsar Bomba article on wikipedia: "Since 50 Mt is 2.1×1017 joules, the average power produced during the entire fission-fusion process, lasting around 39 nanoseconds[citation needed], was about 5.4×1024 watts or 5.4 yottawatts (5.4 septillion watts). This is equivalent to approximately 1.4% of the power output of the Sun.[8]"
That's a lot of power right there. Now to harness that :)
You wouldn't build one huge bomb, but instead use lots and lots of tiny bombs in an Orion-type spacecraft. That way you get a better utilisation of your energy.
Doesn't that make it even easier? But then again I think 400 megaton isn't enough. Last time I calculated it ( I probably made a ton of mistakes ;p) it was in the the 10s of thousands or something like that.
Accelerating the space shuttle to 0.10c :
(2,030 t * (0.10c)(0.10*c))/210 PJ = 8700 (wolfram alpha)
2,030 mass of space shuttle in metric tons
210PJ the energy from tsar bomba.
But then you have to add in the weight of the bombs too.
since they are each 27,000kg and then you have to sum it up to get to something that can approach 0.10c (and I don't remmember how I had figured that one out)
And what says once you get to the other planet you can't fill the tank with nuclear materials over there for the return trip?
Yeah, it didn't seem like an absolute impossibility to me either (in the distant future). That much energy (9x10^17 Joules) translates to about 400kg of lithium deuteride in a 100% efficient fusion reactor. We're not even close to being able to burn that fuel efficiently at all but it's theoretically possible and I would hesitate to say that we'll never figure it out.