The three-body problem and the Hannay angle

Details The three-body problem and the Hannay angle The three-body problem and the Hannay angle

2003-12-19

arxiv.org/abs/astro-ph/0312551v3

Nonlinearity 18 (2005) 45

Astronomy and Astrophysics

Astrophysics

11 pages. Accepted by Nonlinearity

Scientific paper

10.1088/0951-7715/18/1/003

The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In the present work, three main results are obtained. Firstly, a formal connection between perturbation theory and the Hamiltonian adiabatic approach shows that both lead to the Hannay angle; it is thus emphasised that this effect is already contained in classical celestial mechanics, although not yet defined nor evaluated separately. Secondly, a more general expression of the Hannay angle, valid for an action-dependent potential is given; such a generalised expression takes into account that the restricted three-body problem is a time-dependent, two degrees of freedom problem even when restricted to the circular motion of the test body. Consequently, (some of) the eccentricity terms cannot be neglected {\it a priori}. Thirdly, we present a new numerical estimate for the Earth adiabatically driven by Jupiter. We also point out errors in a previous derivation of the Hannay angle for the circular restricted three-body problem, with an action-independent potential.

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