J/A+A/605/A23 Restricted planar three-body problem (Pichierri+, 2017)
Extreme secular excitation of eccentricity inside mean motion resonance:
Small bodies driven into star-grazing orbits by planetary perturbations.
Pichierri G., Morbidelli A., Lai D.
<Astron. Astrophys. 605, A23 (2017)>
=2017A&A...605A..23P 2017A&A...605A..23P (SIMBAD/NED BibCode)
ADC_Keywords: Models ; Minor planets
Keywords: celestial mechanics -
planets and satellites: dynamical evolution and stability -
minor planets, asteroids: general - white dwarfs -
methods: analytical
Abstract:
It is well known that asteroids and comets fall into the Sun. Metal
pollution of white dwarfs and transient spectroscopic signatures of
young stars like beta-Pic provide growing evidence that extra solar
planetesimals can attain extreme orbital eccentricities and fall onto
their parent stars.
We aim to develop a general, practically implementable,
semi-analytical theory of secular eccentricity excitation of small
bodies (planetesimals) in mean motion resonances with an eccentric
planet valid for arbitrary values of the eccentricities and including
the short-range force due to General Relativity. Our semi-analytic
model for the restricted planar three-body problem does not make use
of any series expansion and therefore is valid for any values of
eccentricities and semi-major axes ratios. The model is based on the
application of the adiabatic principle, which is valid when the
precession period of the longitude of pericenter of the planetesimal
is much longer than the libration period in the mean motion resonance.
This holds down to vanishingly small eccentricities in resonances of
order larger than 1. We provide a Mathematica notebook with the
implementation of the model allowing direct use to the interested
reader.
We confirm that the 4:1 mean motion resonance with a moderately
eccentric (e'≲0.1) planet is the most powerful one to lift the
eccentricity of planetesimals from nearly circular orbits to
star-grazing ones. However, if the planet is too eccentric, we find
that this resonances becomes unable to pump the planetesimal's
eccentricity to very high value. The inclusion of the General
Relativity effect imposes a condition on the mass of the planet to
drive the planetsimals into star-grazing orbits. For a planetesimal at
∼1AU around a solar-mass star (or white dwarf), we find a threshold
planetary mass of about 17 Earth masses. We finally derive an
analytical formula for this critical mass.
Planetesimals can easily fall onto the central star even in the
presence of a single moderately eccentric planet, but only from the
vicinity of the 4:1 mean motion resonance. For sufficiently high
planetary masses the General Relativity effect does not prevent the
achievement of star-grazing orbits.
Description:
In this paper, we will focus mainly on resonances of order higher than
1, because they are much more efficient in pushing the eccentricity e
from ∼0 to ∼1. In this case, for e<e' our approach is valid down to
very small values of the eccentricity.
We make available a Mathematica notebook which implements the
calculations outlined in the paper, to allow the interested reader to
examine the effect of secular dynamics inside mean motion resonances
for other applications.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
SecResInMMR.nb 82 42469 Mathematica notebook (vnd.wolfram.nb application)
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Acknowledgements:
Gabriele Pichierri, Gabriele.Pichierri(at)oca.eu
(End) Patricia Vannier [CDS] 12-Jun-2017