Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple scaling for the minimum instability time-scale of two widely
  spaced planets   Long-term instability in multi-planet exosystems is a crucial consideration
when confirming putative candidates, analyzing exoplanet populations,
constraining the age of exosystems, and identifying the sources of white dwarf
pollution. Two planets which are Hill stable are separated by a wide-enough
distance to ensure that they will never collide. However, Hill stable planetary
systems may eventually manifest Lagrange instability when the outer planet
escapes or the inner planet collides with the star. We show empirically that
for two nearly coplanar Hill stable planets with eccentricities less than about
0.3, instability can manifest itself only after a time corresponding to X
initial orbits of the inner planet, where log_{10}(X) is of the order of 5.2
mu^{-0.18} and mu is the planet-star mass ratio measured in (Jupiter mass/Solar
mass). This relation applies to any type of equal-mass secondaries, and
suggests that two low-eccentricity Hill stable terrestrial-mass or smaller-mass
planets should be Lagrange stable throughout the main sequence lifetime of any
white dwarf progenitor. However, Hill stable giant planets are not guaranteed
to be Lagrange stable, particularly within a few tens of percent beyond the
critical Hill separation. Our scaling represents a useful "rule of thumb" for
planetary population syntheses or individual systems for which performing
detailed long-term integrations is unfeasible.

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The categories of this paper are: math
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: bayes-an