In the novel Dragon's Egg, the human crew use one asteroid to swing other asteroids in place to counter the gravity of the neutron star. I understood that it was similar to a gravity sling shot, but I wasn't able to fully get how the crew were able to move the smaller asteroids in place using the big one. Can anyone explain that further?
Answer
I know nothing of this book, but I do know a little about N-body gravitational interactions. When N >= 3, you can do just about anything you want with a little propulsion, but it may take a very long time. This has been proposed by NASA (good approximate for hard SF) as a way of sending probes to the outer solar system: http://en.wikipedia.org/wiki/Interplanetary_Transport_Network
As far as the stability questions, it is known that you can put 7 or 8 equal-mass objects on a stable circular orbit around their center of mass: http://adsabs.harvard.edu/abs/1988A%26A...205..309S
After introducing an external mass and its accompanying tidal forces, I imagine there is still some stability regime, which could be pretty close to the NS, especially if the "asteroids" have WD density, their constellation could be on the order of 1km, while the NS radius is probably closer to 15km.
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