Laplace's problem in mathematical aspect

Details Laplace's problem in mathematical aspect Laplace's problem in mathematical aspect

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33...71s&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 33, May 1984, p. 71-84.

Mathematics

Probability

2

Celestial Mechanics, Comets, Elliptical Orbits, Hyperbolic Trajectories, Laplace Equation, Boundary Value Problems, Interstellar Space, Probability Density Functions, Solar Orbits, Velocity Distribution

Scientific paper

The author considers the mathematical aspect of Laplace's problem pertaining to the occurrence probability of elliptical and hyperbolical orbits for comets. He shows that, among other things, if arbitrary velocity distributions in Laplace's problem are used, it is possible to obtain an arbitrarily small probability for elliptical orbits and a probability neighbouring around one for hyperbolic orbits, or conversely. The theorems hold even for the variable initial conditions. The aspect presented here permits to describe easily studies of Laplace's problem.

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