The angular deflection for a body moving past
a large stationary mass M at initial velocity v_{0} with
closest approach y_{0} is about 2MG/v_{0}^{2} y_{0} where G is the gravitational constant. For a closest approach
of about y_{0}=0.001 LY, v_{0} = 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/v_{0}^{2}. 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.

Back to previous page.