Laplace's problem in mathematical aspect

In this paper we consider the mathematical aspect of Laplace's problem pertaining to the occurrence probability of elliptical and hyperbolical orbits for comets. We show that, among other things, if we use arbitrary velocity distributions in Laplace's problem, we may obtain an arbitrarily small probability for elliptical orbits and a probability neighbouring around one for hyperbolic orbits, or conversely. Our theorems hold, even for the variable initial conditions. The aspect presented here permits us to describe easily studies of Laplace's problem.Dedicated to my teacher, Professor W. Orlicz, on the occasion of 80th birthday.