Some Completely Unnecessary Math

When I read Andy Weir's The Martian, I realized there was a whole genre of science fiction that took the science part seriously. It's interesting that the original genre of science fiction was just that - fiction extrapolated from science. Sure, I know there's a hard science fiction genre, but Weir started at Bill-Nye-Science-Guy-level and turned it up to eleven. 

Even if you're not a hard science fiction fan, there's the puzzle appeal. You'll find it in movies like Apollo 13. Everyone remembers the square-peg-in-a-round-hole brainstorming scene. Or MacGyver, a fellow who literally saved himself and everyone else each episode with science.

Now that it's Christmas, it makes me think of the meme where someone calculates how fast Santa's sleigh would need to go to traverse the world overnight, and what would happen if it did. There's some nerdiness in us all.

I'd read that Weir actually calculated the orbital mechanics of the Hermes in the Martian. I remember thinking he could have just said the NASA guys worked it out in the story and I would've taken his word for it, but, at the same time, it's the sort of thing I do in my stories. If it takes twenty-six days for the Aristarchus to get from the outer system to Earth, I've actually done the math. At times it's been my bane. Simple things like flying from Saturn to Cassini Station (just outside Saturn's rings) in Erebus takes hours of flight time. Space is big. Saturn is really big.

Recently I was watching one of my favorite sci-fi movies of all time, Star Trek II: The Wrath of Khan. I can't say how many times I've seen it. At the end there's the dramatic escape when Khan activates the Genesis device and Kirk says, "Scotty, I need warp speed in three minutes or we're all dead!". Mid-scene we hear that the Enterprise's distance to the Reliant is 4000 km. Sulu says, "We're not going to make it, are we?". David shakes his head. Great stuff.

So, here's where the nerd in me perks up. I know the Enterprise has been shot up and is operating under impulse engines or thrusters. However, it's always struck me that 4000 km is not very far for a starship.  If you pay attention, Kirk provides a time and distance in the clip:

Kirk: "Time?"

Saavik: "Three minutes, thirty seconds."

Kirk: "Distance from Reliant?"

Chekov: "Four thousand kilometers."

I'm going to make an assumption the Enterprise was accelerating that entire time. Which would make sense if they're using thrusters. I have no idea how Star Trek's impulse drive works, but if it's a space-bending-continuous-speed thingy, then the math is just distance over time:

4000 km / 3 minutes 30 seconds = 19 kilometers per second

This is fast, but slower than most asteroids. As an aside, not even Star Trek seems to know how its impulse drive works. In some movies they use impulse drive while in space dock, which, you know, seems like a bad idea.

Now if the Enterprise is accelerating at a constant rate from a standstill, the math is a little harder:

distance = 1/2 acceleration * time (squared)

If you solve for acceleration, the Enterprise is accelerating at 18 g

Presumably Star Trek's inertial dampeners keep everyone from getting squished. On the plus side, this is faster than I thought. 18 g acceleration will get you from Earth to the Sun in a speedy 16 hours.  Unfortunately the (albeit damaged) impulse drive doesn't work out so well in the long run in this case. Traveling a continuous 19 kps will take 91 days to get from Earth to the Sun. So, stick with the thrusters.

Anyway, this is what happens when I have a day off. Enjoy the geekiness.