There have always been people in the fan community whose commitment was so complete that they were compelled to determine the validity of the science portion of science fiction - to do things like calculate whether or not the U.S.S. Enterprise actually could travel the 16.5 light years from Earth to 40 Eridani A in four days* and so on.
For the most part, I haven't been one of those people. I generally give most scientific questions the benefit of the doubt, or attribute any possible discrepancies to creative license. However, I recently ran across the following paragraph in the David Weber/Steve White military SF collaboration In Death Ground, and it made me just a little curious - it was just a bit too glib:
"Fifteen light-seconds," Trang reported. "Coming into - missile launch! Multiple hostile launches! One hundred twenty plus inbound. Impact in two-seven seconds from mark!"
Okay, let's do some math. They're fifteen light seconds away from the ships launching the missiles. Light travels 299,792
kilometers in one second, so that's 4,496,880 kilometers.** Average speed or velocity (v) is calculated by dividing
displacement*** (Δx or x) by time (t) , which gives us a result of 166,551
kilometers/second, which kind of makes sense if you just roughly calculate it - 15 light seconds, 27 seconds travel time, so a little bit faster than half the speed of light.However, that's the average velocity - obviously if you start at zero k/s, you need to accelerate to a higher speed to cover that distance in the same rate as if you had hit the ground running, so to speak. Thanks again to Google™, we find that acceleration (a) = 2x/t2 - 2v0/t, which gives us a constant acceleration of 12,337,119 m/s2 squared (v0 is starting velocity, which in this case is presumably zero - or perhaps a negative value, the starships in question are retreating from their missile-launching enemy).
Final velocity of 333,102.213 km/s - hang on, that's faster than the speed of light, and the book is clear that the tech base for Mr. Trang's space navy doesn't include FTL travel. But this sort of makes sense as a number, obviously your speed at some point has to be higher than the average speed in order to compensate for the fact that you started from zero.
I wasn't completely confident in my results, so I sought out our resident numbers guy, Andrew. (Andrew was hired as a business analyst, but the manipulation of statistics and information is a large part of that, so Andrew is often pulled into discussions regarding math.)
To my astonishment, after I explained the question, he went to the white board in his office and produced the following off the top of his head:
Well, now I know why we hired Andrew.
Ultimately, the moral of the story is that the authors might not have done full due diligence on their math. (Or maybe their drive technology has a very steep acceleration curve.) For me, the real joke is that the missiles are supposed to explode when they hit their target. I'm reasonably certain that if a multi-tonne projectile hits a starship while travelling at the speed of light, an explosion would be redundant. I'll leave it to the curious reader to calculate the amount of energy that would result from such an impact - just leave your answers as comments. The actual weight of the missiles doesn't appear in the book anywhere to the best of my knowledge, so feel free to make your own estimate as to an appropriate weight for a weapon of this sort****. Good luck - and please show your work.
- Sid
* 40 Eridani A is generally considered to be the location of Vulcan. This is one of those things that was never clearly defined in the original series, but when science fiction author James Blish was hired to turn the episodes into short stories for the purposes of novelization, he chose 40 Eridani A as being a likely candidate based on its distance from Earth, and over time this has become accepted as canon.
** To give you some perspective on that number, the Moon at its furthest from earth is 405,696 kilometers away, so eleven times as far as the Moon.
***AKA distance if you're not a mathematician.
**** As a guideline, a fully loaded F16 Falcon fighter weighs in at about 21 metric tonnes.
EDIT: Sadly I've had to close down Comments for this posting, I've had one very enthusiastic but somewhat non-linear commenter who is just getting further and further away from the actual topic at hand. My apologies, Tonyon.
