A World of Bits

A side calculation for Cosmic Communications

Aiming
calculations

How well can we aim?

For grossly macroscopic particles Heisenberg is irrelevant. What matters is random gravitational perturbation en route, from the pull of stars whose placement we do not precisely know.

The angular deflection for a body moving past a large stationary mass M at initial velocity v0, with closest approach y0, is about 2MG/v02y0, where G is the gravitational constant. For a closest approach of 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 of less than 0.001 LY on a 10 kLY 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 10 kLY 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 is also the issue on a long trip of chaotic stellar motion — what you are 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 will leave that particular calculation to my orbital mechanics and dynamics betters.