Guys, it's a tad more complex than "you can't go to the Moon in 2 hours, that's silly". While the responses here are applicable and correct in one way or another, getting to the Moon in 2 hours is physically possible, but it's just very, very hard to do, and not at all practical unless you have some seriously futuristic technology.
Firstly, we know the Moon has an average distance from Earth of around 384 399 000 meters. And we want to get there within 2 hours, or 7200 seconds.
The following equation is from the
Atomic Rockets Torchship page.
A = (4 * D) / T^2
A = Acceleration.
D = Distance.
T= Time.
If I calculated correctly, that is a required acceleration of 29.66 m/s^2. Earth's gravity is 9.806m/s^2, so that is roughly 3 Gs.
Now that we know the acceleration that our ship and crew will have to endure, we must calculate the dV as well.
transitDeltaV = 2 * sqrt[ D * A ]
A = Acceleration.
D = Distance.
transitDeltaV= Delta V requirement.
Which gives a required dV of 213 550 m/s. Lunar orbital velocity is 1 000 m/s and we need to match that, so 214 550 m/s (214.5 km/s).
Which is a lot. No current rocket engine has a high enough exhaust velocity to reach that DeltaV at an achievable mass ratio. An engine with an exhaust velocity of 100-200 km/s could achieve that DeltaV with a mass ratio of 8.54 to 2.92, respectively.
We do however have theoretical drive systems that could have that performance. That sort of exhaust velocity is achievable by a fusion drive, but is over what can be achieved by a nuclear gas or solid core design.
The problem is, we can't build a drive like that yet. We have yet to build a fusion powerplant that can achieve breakeven; even a fusion rocket with a thrust of a few kilonewtons is impossible currently. And the drive needed to accelerate this spacecraft will certainly have a thrust level above a few kilonewtons; to accelerate a 100 ton spacecraft, the 200 km/s engine will need a thrust of 12 meganewtons; the 100 km/s engine will need a thrust of 28 meganewtons.
Now, that amount of thrust is relatively easy to achieve with a chemical rocket with an exhaust velocity of 3-4km/s, but for a fusion rocket with an exhaust velocity of 100-200 km/s, it is a different story. The 200 km/s, 12 meganewton engine would have an output power of 1.2 terawatts; the 100 km/s, 28 meganewton engine would have an output power of 1.4 terawatts.
In comparison, the Saturn V's first stage had an output power of 0.115 terawatts, or 115 gigawatts. A terawatt is a lot of power; the entirely of human civilisation, as of 2010, uses 16 terawatts of power. And large output powers present waste heat problems as well; this means large, heavy engines and radiators.
The velocity problems are compounded by the acceleration problem; 3 Gs is quite a high acceleration, and higher accelerations means more spacecraft mass (lest it crumple in on itself once the engine switches on). And of course, more mass, equals more fuel, equals more total mass for the engine to propel, equals a more powerful engine... it is a nasty vicious cycle.
And from a point of crew comfort 3 G is pretty bad as well... I mean, sure astronauts can handle that sort of acceleration during launch, for a few minutes, but this is a far longer period of time. It might be
survivable if the crew was strapped horizontally into seats, but it would still be highly uncomfortable.
So physically possible, yes. Technologically possible, not at present, but potentially in future. Practical? I seriously doubt it.
