`Similar' coordinate systems and the Roche geometry. Application

Details `Similar' coordinate systems and the Roche geometry. Application `Similar' coordinate systems and the Roche geometry. Application

2011-10-21

arxiv.org/abs/1110.4764v1

Astrophysics and Space Science, volume 335, number 2, p.475-483, 2011

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

9 pages (preprint format), 9 figures, published in Astrophysics and Space Science

Scientific paper

10.1007/s10509-011-0747-1

A new equivalence relation, named relation of 'similarity' is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named 'similar' trajectories) are obtained; they have the theoretical role to give us new details in the restricted three-body problem. The 'similar' coordinate systems allow us in addition to obtain a unitary and an elegant demonstration of some analytical relations in the Roche geometry. As an example, some analytical relations published in Astrophysical Journal by Seidov in 2004 are demonstrated.

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