Aiming Calculations

The angular deflection for a body moving past a large stationary mass M at initial velocity v0 with closest approach y0 is about 2MG/v02 y0 where G is the gravitational constant. For a closest approach of about y0=0.001 LY, v0 = c/1000, and M one solar mass, the angular deflection is about 0.0003 radians. Furthermore, the probability of having a closest approach less than 0.001 LY on a 10kLY trip is about 0.0008 at Milky Way disk stellar densities. So all told, one would not expect fast moving packages to be deflected by terribly much.

A Monte Carlo simulation (with every deflecting mass assumed as large as our sun) showed an average 0.14 LY miss over a 10kLY trip. For a more reasonable distribution of solar masses (our sun is largish on average, it turns out), the mean miss distance is about 0.08 LY. And given that the package already has to have some means of deceleration in the vicinity of the target, correcting for such small ballistic miss distances will almost certainly not add appreciably to the overall energy budget.

Of course, for slower moving packages, gravitational perturbation could become appreciable since the angular deflection goes as 1/v02. Furthermore, there's also the issue on a long trip of chaotic stellar motion -- what you're aiming at moves out of the way in an effectively random fashion. So it might be tough to target a given solar system -- but I'll leave that particular calculation to my orbital mechanics/dynamics betters.

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