Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The disturbing function for polar Centaurs and transneptunian objects   The classical disturbing function of the three-body problem is based on an
expansion of the gravitational interaction in the vicinity of nearly coplanar
orbits. Consequently, it is not suitable for the identification and study of
resonances of the Centaurs and transneptunian objects on nearly polar orbits
with the solar system planets. Here, we provide a series expansion algorithm of
the gravitational interaction in the vicinity of polar orbits and produce
explicitly the disturbing function to fourth order in eccentricity and
inclination cosine. The properties of the polar series differ significantly
from those of the classical disturbing function: the polar series can model any
resonance as the expansion order is not related to the resonance order. The
powers of eccentricity and inclination of the force amplitude of a $p$:$q$
resonance do not depend on the value of the resonance order $|p-q|$ but only on
its parity. Thus all even resonance order eccentricity amplitudes are $\propto
e^2$ and odd ones $\propto e$ to lowest order in eccentricity $e$. With the new
findings on the structure of the polar disturbing function and the possible
resonant critical arguments, we illustrate the dynamics of the polar resonances
1:3, 3:1, 2:9 and 7:9 where transneptunian object 471325 could currently be
locked.

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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-th