Statistics – Computation
Scientific paper
Jan 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998lpico.957r..45t&link_type=abstract
Origin of the Earth and Moon, Proceedings of the Conference held 1-3 December, 1998 in Monterey, California. LPI Contribution N
Statistics
Computation
Gravitational Effects, Mathematical Models, Lunar Evolution, Collisions, Protoplanets, Vapor Jets, Boundary Value Problems, Solar System Evolution
Scientific paper
The theory of origin of the Moon due to giant impact of protoplanets proposed is generally recognized. Further investigations showed that different aspects of such impact should be studied in more detail for a complete understanding of the phenomenon. However, up to now, not all answers have been found to the questions related to this problem. As it is impossible to organize a full-scale natural experiment, we have to rely on complex mathematical modeling. A high -velocity, high-temperature jet, consisting of vapors of colliding bodies and of fragments in condensed state, is formed due to the giant impact. The initial fields of velocities of vaporous and condensed components are supposed to be the same. The ratio fo masses of components in jet can be determined from the specific thermal energy, under the assumption that their temperatures are equal. Granulometric composition of fragments can be described by known statistical distributions. Based on the supposition that fragments have a magnitude of the specific of fragments make the fields of velocities of the components different. This, in its turn, leads to their force interaction. One of the most important factors in the process of ejecta cloud formation is gravitation. In calculations an account of force of gravity was performed only in the supposition of central symmetry of gravitational field, constant in time and space, which was created by the target protoplanet. Later a new model was developed, which takes into account gravitational interaction of substances distributed in space, including the discrete condensed fraction. For this purpose in the computational area, a boundary-value problem for the equation Delta(u) = r(pi gamma rho(x,y,z)) of the potential of the field is solved in the supposition of absence of external sources. This allows one to describe correctly not only the initial stage of ejecta jet formation, but also its further evolution, assuming outflow of substances from the area under consideration is negligible.
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