Golden Fleece question

First of all, I enjoyed this book, like all of Robert Sawyer's work. Believable characters, etc. But I don't remember noticing physics errors like this in his other books.

(spoiler)

So apparently JASON is killing time by spinning the ship around Sol, out at about 0.5 ly in the Oort cloud. At near light-speed, the centripetal acceleration required to maintain an orbit with that radius is about 19 m/s^2. (as observed in the reference frame of Sol, not the moving ship.)

a=v^2 / r = c^2 / (0.5 * 365 * 24 * 3600sec * c)
a = c^2 / (1.577*10^7sec * c)
a = c / (1.577*10^7sec)
c ~= 3*10^8 m/s
a ~= 19 m/s/s ~= 1.94g

If I recall correctly, the ship was accelerating at 2.6g (from the ship's reference frame). Even discounting special relativity, most of that 25.5 m/s^2 would be needed to keep the ship circling the sun, instead of flying off in an escape trajectory. (Sol's gravitation that far out is negligible).

With relativity, from Sol's reference frame, the ship would have a mass increased by the relativistic gamma factor 1/(sqrt(1-v^2/c^2). So the acceleration achieved by the ship would be 2.6g divided by a lot. At v = 0.9999c, gamma = 70.7. At v = 0.9999786c, gamma = 152.8. (And that speed was before the halfway point of the journey, so it wasn't even JASON's planned top speed).

Or from the ship's reference frame, the circumference of its orbit would shrink by a factor of gamma. (looking towards Sol, perpendicular to the direction of motion, an observer would not see a relativistic change in the distance. Length contraction is observed in the direction of motion. But since the ship is turning to achieve a circular path, the acceleration needed increases with the contraction in circumference.)

As stated in the text, the ship is going so fast that it covers 47 light years in a shipboard day. Going that fast in a circular orbit around Sol at 0.5ly radius means it orbits Sol 15 times per shipboard day. (circumference = 2pi*r) That's a pretty tight circle for a ship going that fast.

So circling in the oort cloud at that high a fraction of light speed requires about 100 times the ship's 2.6g acceleration in the oort cloud just to provide centripetal force.

It just wouldn't work at all.

Another problem is that Bussard ramjets experience drag from the gas they collect, which increases with the relative velocity of the ship through the gas. They can only continue to accelerate if their exhaust speed exceeds the speed of the incoming ions, otherwise the net change in momentum is negative.


Anyway, good book, but not a valid plan for killing lots of real time in only 8 subjective years.

(mega-extra-spoiler-alert)

I also wondered why the AIs didn't bring their predicted nuclear holocaust to the attention of the world's governments, and/or attempt to audit the software they somehow predicted would have a bug-caused problem in a very specific timeframe.

I can forgive the author for this one, as computers were a lot newer in 1990, and programming was less well understood then than it is now. (Being a programmer myself makes it even more odd to think of being able to predict failure due to a bug would happen in 6 to 8 weeks, after disaster-free operation for a couple centuries, without having specific enough info to correct the bug.)

The subject of the book is whether it's better to know the truth, or whether ignorance is bliss. Fortunately, neither of these problems with the book do too much to ruin any of the heart of that philosophical conundrum. Imagine it's an asteroid impact that the computers saw but couldn't prevent, if the buggy-SDI-generated nuclear holocaust is too silly.