Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The inclination of the planetary system relative to the solar equator
  may be explained by the presence of Planet 9   We evaluate the effects of a distant planet, commonly known as planet 9, on
the dynamics of the giant planets of the Solar System. We find that, given the
large distance of planet 9, the dynamics of the inner giant planets can be
decomposed into a classic Lagrange-Laplace dynamics relative to their own
invariant plane (the plane orthogonal to their total angular momentum vector)
and a slow precession of said plane relative to the total angular momentum
vector of the Solar System, including planet 9. Under some specific
configurations for planet 9, this precession can explain the current tilt of
approximately 6 degrees between the invariant plane of the giant planets and
the solar equator. An analytical model is developed to map the evolution of the
inclination of the inner giant planets' invariant plane as a function of the
planet 9's mass, inclination, eccentricity and semimajor axis, and some
numerical simulations of the equations of motion of the giant planets and
planet 9 are performed to validate our analytical approach. The longitude of
the ascending node of planet 9 is found to be linked to the longitude of the
ascending node of the giant planets' invariant plane, which also constrain the
longitude of the node of planet 9 on the ecliptic. Some of the planet 9
configurations that allow explaining the current solar tilt are compatible with
those proposed to explain the orbital confinement of the most distant Kuiper
belt objects. Thus, this work on the one hand gives an elegant explanation for
the current tilt between the invariant plane of the inner giant planets and the
solar equator and, on the other hand, adds new constraints to the orbital
elements of planet 9.

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The categories of this paper are: quant-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat