I'm currently working on an analysis of the technology of E. E. Smith's classic "Lensman" space opera books, and could do with some help with the maths involved (my own mathematical abilities being too close to "zero" for my own liking :P ). If anyone's able to help with the following I'd be most grateful: 1) In the last book of the series ("Masters of the Vortex" for those interested), an analog computer is developed that can predict the activity of a self-sustaining (and very chaotic) atomic fireball (surface temperature usually around 25,000 kelvin) up to 3.6 seconds in advance (what can I say, this is sci-fi :P ). The fireballs appear to be fairly small - I'd estimate no more than a few metres across in most cases. The thing is, how many calculations per second would a computer need to do predict something like this? Obviously I know that we're dealing with rather vague things here and for that I apologise - but if anyone could hazard a guess as to the sort of computer power necessary (I'm expecting a pretty large range given the lack of hard figures in the books) I'd be very grateful. 2) In an earlier book, an energy beam (think in terms of lasers here) is used to simultaneously melt the surfaces of half a dozen mobile planets in an attacking fleet in about a second. This thankfully should be easier as we can get some proper figures: i) Six planets caught in the beam simultaneously. I'd imagine only half their surfaces are thus hit. For simplicity's sake I'm going for 6 Earth-like planets. ii) Damage involves the crust being melted, mountains collapsing as lava flows, oceans vaporised and so on, so at the very least the beam can turn water to steam at a depth of several kilometres. iii) Don't forget the atmospheres - surely they must absorb a fair bit of energy? Also the atmosphere from the other side of the planet would absorb some of the energy from the parts of the beam that don't hit the surface of the planet and continue on through the atmosphere. iv) A lot of energy must surely be wasted in empty space. The planets were most likely in an octahedron formation given that they formed the centre of a fleet in a spherical formation. Using Roche's Limit to work out the distances between the planets, how wide would the beam have to be to strike all of them? Ideally I'd like to see a figure / range giving the energy required to do something like this, although again I realise that the answer will be far from perfect given the lack of information from the books. So, thank you in advance for any help you're able to give with these questions :) . I realise that this isn't the sort of thing you'll usually encounter here, and that the original material is rather vague when it comes to the figures, but it would be a great help if anyone could help me out here.