Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solar system dynamics in general relativity   Recent work in the literature has advocated using the Earth-Moon-planetoid
Lagrangian points as observables, in order to test general relativity and
effective field theories of gravity in the solar system. However, since the
three-body problem of classical celestial mechanics is just an approximation of
a much more complicated setting, where all celestial bodies in the solar system
are subject to their mutual gravitational interactions, while solar radiation
pressure and other sources of nongravitational perturbations also affect the
dynamics, it is conceptually desirable to improve the current understanding of
solar system dynamics in general relativity, as a first step towards a more
accurate theoretical study of orbital motion in the weak-gravity regime. For
this purpose, starting from the Einstein equations in the de Donder-Lanczos
gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic
motion of celestial bodies, showing in detail under which conditions the
effects of internal structure and finite extension get cancelled in general
relativity to first post-Newtonian order. The resulting nonlinear ordinary
differential equations for the motion of planets and satellites are solved for
the Earth's orbit about the Sun, written down in detail for the Sun-Earth-Moon
system, and investigated for the case of planar motion of a body immersed in
the gravitational field produced by the other bodies (e.g. planets with their
satellites). At this stage, we prove an exact property, according to which the
fourth-order time derivative of the original system leads to a linear system of
ordinary differential equations. This opens an interesting perspective on
forthcoming research on planetary motions in general relativity within the
solar system, although the resulting equations remain a challenge for numerical
and qualitative studies.

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The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org