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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Improbability of collisions in Newtonian gravitational systems. II


Author: Donald G. Saari
Journal: Trans. Amer. Math. Soc. 181 (1973), 351-368
MSC: Primary 70.28
DOI: https://doi.org/10.1090/S0002-9947-1973-0321386-0
MathSciNet review: 0321386
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Abstract: It is shown that the set of initial conditions leading to collision in the inverse square force law has measure zero. For the inverse $ q$ force law the behavior of binary collisions for $ 1 < q < 3$ and the behavior of any collision for $ q = 1$ is developed. This information is used to show that collisions are improbable in the inverse $ q$ force law where $ q < 17/7$ and that binary collisions are improbable for $ q < 3$.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0321386-0
Keywords: $ n$-body problem, gravitational systems, collision, measure preserving, singularities, celestial mechanics
Article copyright: © Copyright 1973 American Mathematical Society

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