When Mission of Gravity was finished in late 1952, I had a perfectly honest degree in astronomy. I nevertheless made a few mistakes, including one in basic physics; I said, somewhere in the story, that the Bree would sail faster with the wind behind her. Predictably, a sailor caught that one.
More seriously, I erroneously took for granted that the figure of rotation which was Mesklin would be an oblate spheroid, and did all the gravity calculation (on a slide rule) assuming that most of its mass was degenerate matter very close to the center. John Campbell told me when he accepted the story that a mathematician had told him that Euler must be spinning in his grave, but I still don’t know what theorem I violated.
More usefully, a few years after the story was published, members of the M.I.T. Science Fiction Society (MITSFS) managed to get enough computer time to figure out more nearly what the planet’s shape would be. They were presumably right; all I could console myself with was the realization that I had written the story to give pleasure to people even if that wasn’t quite the specific pleasure I’d had in mind.
I eventually did get a computer, wrote a relevant program in BASIC6, and came up with an object looking more like the discus used in field and track sports—an object fairly sharply curved at the poles, much flatter in the midlatitudes, and coming almost to a real edge at the equator. With arbitrarily chosen three g’s at the equator, the polar gravity came out to only about 275, as I recall.
I assume that readers with appropriate background knowledge and computer hardware will want to check this. Maybe someone will want to write a book on the things that minor differences in the basic assumptions will do to Mesklin’s shape.
Personally, I wound up doing forty years of high school teaching instead of being an astronomer essentially because of my mathematical weaknesses.