Moving asteroids is not that big of a deal, we could do it with hardtech, but the fuel cost would be insane if you want it done quickly. luckly that doesn't apply to handwavium, and asteroids don't need to be that close together, considering racers will be going a fairly significant % of c.
When you go at 1% lightspeed it doesn't matter if the asteroids are tens of thousands kilometers apart, you'll still reach one every few seconds. But the 'racetrack' will have to be prepared, and some back of the napkin calculations show that there should be an asteroid roughly every 20'000 kilometers, so not that much shifting is required.
As for who's going to build it, well someone need to organize the race, much like there are people organizing NASCAR, and building/maintaining racetracks for that too.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."
When you go at 1% lightspeed it doesn't matter if the asteroids are tens of thousands kilometers apart, you'll still reach one every few seconds. But the 'racetrack' will have to be prepared, and some back of the napkin calculations show that there should be an asteroid roughly every 20'000 kilometers, so not that much shifting is required.
As for who's going to build it, well someone need to organize the race, much like there are people organizing NASCAR, and building/maintaining racetracks for that too.
E: "Did they... did they just endorse the combination of the JSDF and US Army by showing them as two lesbian lolicons moving in together and holding hands and talking about how 'intimate' they were?"
B: "Have you forgotten so soon? They're phasing out Don't Ask, Don't Tell."