In Vernor Vinge's new novel The Children Of The Sky, humans are preparing for a confrontation with the Blight fleet some 30 lightyears away from the Tines' world. The book takes place over 10 years, but there are two "zone temblors" during which the Blight fleet could achieve speeds above light speed. The first is 10 milliseconds (p.19) and the second is 193 seconds (p.249). If the Blight is travelling as fast as it possibly can during all ten years, how far did it travel?
I think I've figured this out and I was a bit taken aback by the answer. I would appreciate someone checking my math!
- The Blight didn't make any superluminal travel during the first temblor. p.247 mentions that it took Oobii "less than ten seconds" to switch to standard mode. Thus, I assume that 10 milliseconds was not enough time for the Blight to shift to superluminal flight.
- A linear drop-off from 50 lightyears/hour to 1 lightyear/year.
- The Blight can somehow travel at light speed in the slow zone. This is unlikely - 30%-70% of light speed is probably a more reasonable estimate - but we'll hand wave this one.
I converted everything to light hours and hours for my calculations. So:
- 50 lightyears/hour = 438300 lighthours/hour
- 193 seconds = 0.0536 hours
Since we're assuming a base speed of c, we assume the Blight travelled a distance 0.0536 lighthours for starters. We need to subtract 1 lighthour/hour (base speed) from the maximum speed to compensate. So we end up with 438299 lighthours/hour above the base speed of 1 lightyear/hour. Since we are assuming a linear dropoff of speed, the area under the curve is just triangle, which means we can avoid the use of integrals and calculate the area of a triangle instead (A=0.5*b*h).
- 0.5 * 0.0536 * 438299 = 11748.88 lighthours traveled above lightspeed
Now we need to add in the distance traveled at lightspeed (0.0536)
- 11748.88 + 0.0536 = 11748.93 light hours or...
1.34 lightyears travelled during the major zone temblor. This number alone surprised me. Now we add in 10 lightyears for the total length of time the Blight was travelling and we get (approximately):
That's the maximum distance the Blight could have traveled over the ten years of the novel.