At the end of Arthur C. Clarke’s “2010”, all those little monoliths start growing on Jupiter, to the point where it becomes massive enough to become a little star of its own. He mentions that on earth, there is no longer any night, and nocturnal animals are having problems with it. What I’m asking is this: Is Jupiter in a geosynchronous orbit? I think it would have to be in order for all night to disappear from earth, rather than just skipping a few now and then. Is there something further on in the series that clarifies this? Has someone discussed this already and I could’t find it? Inquiring minds want to know.
Jupiter is not in geosynch. I think Clarke was using shorthand for the fact that at least 6 months of the year the new star would eliminate night. Clearly, when Earth and Jupiter are on opposite sides of the sun, there is no effect.
So, Clarke doesn’t seem to be suggesting that there would never be a time without either the Sun or Lucifer (Jupiter) in the sky, only that there would be lengthy periods where one or the other would be up practically all the time.
From the 2001 (how appropriate) World Almanac:
For major parts of the year, the periods of real darkness would certainly be much, much shorter and more interrupted.
So what you’re saying is yes, I was missing something? 
I’ve always wondered what would happen when you suddenly increase the gravity well some thirty times, in a matter of moments. Wouldn’t the moons’ orbits radically change? Wouldn’t it affect the orbits of other planets? (I’m thinking in particular about Mars) Would it be enough to capture comets and such, eventually creating its own a miniature Oort cloud?