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Secular Perturbations for Asteroids Belonging to Families

Published online by Cambridge University Press:  14 August 2015

Y. Kozai  and
M. Yuasa
Y. Kozai
Affiliation:
Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan 181
M. Yuasa
Affiliation:
Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan 181

Extract

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The first-order theory of secular perturbations for an asteroid indicates that the secular motions of the longitudes of the perihelion and of the ascending node have an equal absolute value with opposite signs, that is, , where b is a function of the semimajor axis and has the disturbing mass as a factor, if the eccentricity and the inclination are sufficiently small so that their squares are of the order of the disturbing mass and if there is no commensurable relation between the mean motions of the asteroid and the disturbing planet. Thus Π + Θ is a stable quantity according to the first-order theory, therefore, the origin of families of asteroids has been discussed by using the data for distribution of Π + Θ as well as those for dispersions of other orbital elements of asteroids belonging to a family.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 81 - 82
Copyright
Copyright © Reidel 1974 

References

Kozai, Y.: 1953, Publ. Astron. Soc. Japan 6, 41–66.Google Scholar
Yuasa, M.: 1973, Publ. Astron. Soc. Japan 25, 399–445.Google Scholar