Science and Science Fiction: Star Dragon

July 30th, 2009

The other day someone emailed me with a question about a passage in my novel Star Dragon that bothered them.   They were right to be bothered and I’m going to just say that we all goof from time to time, even over things we know pretty well, and in the spirit of Obama I’m going to take this opportunity and treat it as a teachable moment.   Anyway, here’s the email:

I am three-quarters through Star Dragon, which is excellent so far, and I would like to applaud you for some really interesting concepts. I did have one concern, however, in that I did not understand what was going on between pages 135 and 136, when “The rotation rate was set to provide one earth gravity for the radius of the fore bulb, but accelerative force was inversely proportional to the radius. The taper made things spin fast, made things heavier.” Now, granting that this is a minor point in the grand scheme of the book, it left me confused and sure that I had misunderstood your explanation of the ships structure. It seemed that Dr. Fisher was climbing “uphill” and thus to a section of the ship with a smaller radius, relative to the central axis of rotation. Shouldn’t then, the centripetal acceleration have been less, thereby providing less artificial gravity? I was imagining a cone, spinning along an axis running from its point to the center of its base. Similarly to two points on a record, the point on the outside that must travel a longer circumference in the same rotational period as a point near the center travelling a smaller circumference must travel at greater speed, thereby increasing the centripetal acceleration at the edge. Thus, the “accelerative force” would be directly proportional to the radius, wouldn’t it? The larger the radius, the further a person standing on the deck would travel in the same amount of time, thus more acceleration. So I thought that I must have misunderstood ship’s structure and its orientation to the axis of rotation. This confusion distracted me from the story, and damaged my suspension of disbelief (or weakened my ability to immediately accept your science), so I was simply looking for some sort of clarification to put my mind at ease. Again, I am enjoying the book, and I look forward to picking up a copy of Spider Star at some point. Thank you for your time, and for the excellent story.

Well, he’s totally right.   I just blew it.   Here’s the exact passage:

He made the tube between rings and followed it, ever so slowly, past all the fore rings, toward the tapered rear of the ship. The missiles were kept there, in one of the holds, away from the inhabited portions of the ship.

Because of the taper down to the smaller rear bulb, the effective gravity increased as he climbed the slope. Because they had cut the wormdrive and their deceleration to arrive early, they rotated the ship around its central axis so that centrifugal forces now defined “down.” Although portions of the ship could twist to accommodate the shift in the gravity vector, the ship rotated as a solid body. The rotation rate was set to provide one Earth gravity for the radius of the fore bulb, but accelerative force was inversely proportional to the radius. The taper made things spin fast, made them heavier.

He climbed up the white hill, his body spiraling as he went. One point one gravities, one point two, one point three gravities. A steep climb indeed. How would the extra weight slow a fish?

So there’s a context here, with Sam Fisher trying to move through the starship undetected, using software to cover his tracks from the monitoring AI, but needing not to make anomalies too large to hide.

But as he climbs the hill, he should get lighter, not heavier.   Just as in Armageddon, the crews meeting at the center of the rotating space station should be weightless (instead they seem to be at an Earth gravity and being pulled in a stupid direction).   With solid body rotation like this, the velocity gets smaller as you approach the spin axis.   The gravity is proportional to the radius, not inversely proportional.

All I can do is apologize for the error and suggest that I was getting angular momentum conservation mixed in with what I know about artificial gravity.   I think I had some stupid idea about a skater pulling in her arms and spinning faster.   This is a related, but very different, concept.   I must have read that passage a half dozen times or more, and I know a bunch of physicists and astronomers read it, and no one ever mentioned it before.   Maybe a few noticed and moved on, but I feel bad about it.

Anyway, here’s the wiki article about artificial gravity which gets things right.

Thanks, Zak, for providing an educational opportunity.

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