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Specifically, I'm curious about 2 key points in time.
And if you want a bonus question: Was the Puppeteer's exodus detectable during the Fringe war?
At the time of the first expedition (2851), the Fleet of Worlds was a little more than two light-years from the Ringworld. This is given on chapter 7 ("Stepping Discs"):
They were in hyperdrive for a week, covering a little more than two light years. When they dropped back into Einsteinian space they were within the system of the ringed G2 star; and the foreboding was still with Louis Wu.
The Fringe War takes place forty-one years later, by 2892. The Fleet of Worlds had been accelerating steadily for more than 200 years at the time of the first expedition. According to chapter 8 ("Ringworld") of the first novel it was already at near-lightspeed at that time:
The puppeteer worlds had been moving at nearly lightspeed along galactic north.
Having travelled at near-lightspeed for forty-one years, the Fleet should be somewhere between about 39 to 43 light-years away from the Ringworld when the Fringe War takes place.
I think not. The Fleet has no sun, and the artificial suns that are used in its place are not very bright because they're very close to their worlds. We first see the Fleet on chapter 5 ("Rosette"), and we're given the following description:
Five dim stars, in a regular pentagon. They were a fifth of a light year distant and quite invisible to the naked eye. At present scope magnification they would have to be full sized planets. In the scope screen one was faintly less blue, faintly dimmer than the others.
At a fifth of a light-year, the Fleet cannot be seen with the naked eye, and Louis Wu's scope can only resolve them to what looks like five dim stars. The participants in the Fringe War would be receiving the light sent when the Fleet was approximately twenty light-years away. That is one hundred times farther away, which should make the Fleet pretty much undetectable.
We know that the Puppeteer homeworld achieved 3% of the speed of light in 8 years, according to Juggler of Worlds. Assuming that same acceleration, not taking into account relativity, the speed would be:
(200/8)*0.03=0.75c
The speed at the Fringe war would be:
(240/8)*0.03=0.90c
Of course, relativity dictates that the effective mass increases as the speed increases (The reason for the speed of light being the universal speed limit). Of course, that would not have much of an affect until the speed was very high. I'm too lazy to do the math myself, but I suspect that the speed would likely be in the range of 0.7-0.8c during the previously mentioned periods of time.
Given that there was 40 years between the two events, that means the Puppeteers would be around 30 Light Years distance.
