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Oops? Tripping over a math problem.

Just finished reading Variable Star, a book written by Spider Robinson from a partial story outline found recently in Robert Heinlein's papers.

Have to admit to a bit of confusion here. Both Heinlein and Robinson are among my favorite authors, but I would never have tagged Robinson as "the new Heinlein". (Then again, my interest in "science fiction" has much diminished over the years.) The book works out to a very decent Spider Robinson story with overtones of Heinlein.

There is one part of the story where the math strikes me as badly wrong. Given the list of credits given at the end, I do not know how this could have been missed by other reviewers. Maybe I'm dead wrong. Will try to setup the problem without giving away too much of the plot. (Might be a silly concern. At this point in time, is there anyone likely to read this article before reading the book?)

Given two ships: One large, traveling at near the speed of light, and unable to slow or stop. One small and capable of traveling at ~20 times light-speed. The larger ship is on-course and provisioned for a destination many light-years away. The larger ship is designed for and carries ~50 times as many folk as the smaller ship.

How long would it take the smaller ship to off-load passengers from the larger? The answer in the book is many years of continuous shuttling, and I am pretty sure that is wrong.

To take a first-order guess at the answer, assume that minimum round trip time for the smaller ship is one day - when the larger ship is passing the destination at minimum distance. A ship designed for 10 passengers on long trips can probably handle twice as many for short trips (a very rough guess), so figure 20 passengers per trip (for short trips). After 20 days the larger ship will be about 20 light-days from the destination, so the smaller ship will add about a day to it's travel time. We can (very roughly) average the travel time, and say that over that 20 day period round trips by the smaller ship between the larger ship and the destination take about 1.5 days. Over 21 days you could make about 14 round trips. Assuming the same logic applies when the larger ship is both approaching and just past the destination (another massive assumption) then in 42 days the smaller ship could make 28 round trips, and off-load 560 passengers.

Would be pretty tedious for the pilot(s), but it looks as though you could off-load the larger ship in a few months (with room for large error in either direction, of course) - and almost certainly in less than a year. The trick is you do most of the shuttling when the larger ship is close to the destination.

I can understand why this problem was not looked at too closely - but without giving away plot, I cannot say more here. :)