Origin of Tektites

Abstract

RECENT communications in Nature ¹, defending the lunar origin of the tektites, appear to do so on somewhat questionable grounds, and their reasoning could easily be misunderstood. Thus the fact that Varsavsky (op. cit.) apparently succeeded in constructing admissible mass-particle trajectories connecting the Moon and the Earth does not, by any means, prove the lunar origin of the tektites or even make it probable; for any point on the Earth can be so reached from an arbitrary point of lunar surface, provided only that the initial velocity-components are appropriately chosen. As is well known, such space trajectories are governed by three simultaneous differential equations of second order ; and, hence, six boundary conditions are required for complete specification. If three are set apart to specify the position of an arbitrary point of ejection on lunar surface, the remaining three can be committed to specify an arbitrary point of impact on the Earth : the initial velocity-components are then uniquely determined; but owing to the non-linearity of the underlying dynamical problem they cannot be solved for directly in terms of the selected space co-ordinates at both ends, and must be established numerically by trial and error.