Modern view on Laplace's problem

Details Modern view on Laplace's problem Modern view on Laplace's problem

Sep 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31...53h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Sept. 1983, p. 53-72.

Mathematics

Probability

4

Comets, Orbital Mechanics, Probability Theory, Solar Orbits, Boundary Value Problems, Elliptical Orbits, Hyperbolic Trajectories, Probability Density Functions, Velocity Distribution

Scientific paper

The problem of the probabilities of the occurrence of elliptical and hyperbolic orbits of comets, first investigated by Laplace (1816), is studied using various distributions of the velocities and variable initial conditions for the comets. It is found that the accepted velocity distribution and maximal velocity range for comets determines the probability of the occurrence of the type of orbit. For distributions with the density concentrated in the neighborhood of zero, elliptic orbits are found to be more prevalent than hyperbolic ones, even for large maximal velocities. For a given distribution, the range of the maximal velocity is shown to determine the approximate probability of a given type of orbit. The probability of hyperbolic orbits is found to increase with increasing maximal velocity, whereas the reverse is true for elliptic orbits.

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