Calculation of Interstellar Relativistic Spacecraft Collision Probabilities with 'Oumuamua-like Asteroidal Debris

Abstract

On Oct. 19, 2017, Robert Weryk, using the University of Hawaii's PanSTARRS telescope, discovered the first known interstellar asteroid, now officially named 'Oumuamua (from Hawaiian meaning "first visitor from afar." 'Oumuamua comes from another solar system. It was created in a planetary collision which ejected it into the interstellar medium where it has been for the past 400 million years. The discovery implies that interstellar objects are at least 108 times more abundant than models had predicted, and that the interstellar medium has vastly more debris, ranging in size from grains of sand to larger than 'Oumuamua, that results from planetary system formation..The amount of interstellar debris is so large that it may effectively prevent future interstellar spacecraft from traveling at relativistic speeds between the stars. Using the 'Oumuamua discovery as a constraint on the density of interstellar debris, we calculated the probability of various sized spacecraft colliding with specified sizes of debris. We also calculated the energy release of collisions between spacecraft and such debris..We find that collisions between spacecraft and 'Oumuamua sized objects is too small to be significant. However, the collisions between large spacecraft and grain sized objects will be relatively common on collisions between star systems. Such collisions will release enough energy that special shielding, such as water ice tens of meters thick, will be required on interstellar spacecraft. We calculated that the Mean Free Path (MFP) for an object with a radius of 1mm is approximately 8.89 x 1023 light years with a number of density of 'Oumuamua (3.404 x 10-35). With that same radius, at a velocity of 10-4 times the speed of light, the energy release after colliding is approximately 2.119 x 10-4 kilotons. Furthermore, the MFP for an object with a radius of 1cm is approximately 9.49 x 1021 light years with a number density of "Oumuamua. With that same radius, at a velocity of 10-4 times the speed of light, the energy release after colliding is approximately 0.2119 kilotons.