2008, Vol.11, No.2, pp.177-183
The three body problem in celestial mechanics is unfortunately in
general not integrable, but since more than 200 years we know that
there are stable configurations. One is a solution, where the
three bodies are on the vertices of an equilateral triangle for
all times, the other one is an aligned configuration of the three
bodies involved. We discuss analytically a simpler version of the
general three body problem, namely the restricted three body
problem, where one body has an infinitesimally small mass, such
that the two primary bodies have unperturbed motions around their
common barycenter. This model is also astronomically interesting
because close to the equilateral Lagrange points of Jupiter,
always around 60o ahead and 60o behind this planet
there are two 'clouds' of asteroids, called Trojans. After an
extended discussion of the stability of these 'Lagrangian
equilibrium' points we show the structure of these regions derived
from results of extensive numerical integrations for Jupiter and
Neptune.
Key words:
stability analysis, three body problem, planetary systems
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