888 research outputs found
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus
system by considering a planar secular model, that can be regarded as a major
refinement of the approach first introduced by Lagrange. Indeed, concerning the
planetary orbital revolutions, we improve the classical circular approximation
by replacing it with a solution that is invariant up to order two in the
masses; therefore, we investigate the stability of the secular system for
rather small values of the eccentricities. First, we explicitly construct a
Kolmogorov normal form, so as to find an invariant KAM torus which approximates
very well the secular orbits. Finally, we adapt the approach that is at basis
of the analytic part of the Nekhoroshev's theorem, so as to show that there is
a neighborhood of that torus for which the estimated stability time is larger
than the lifetime of the Solar System. The size of such a neighborhood,
compared with the uncertainties of the astronomical observations, is about ten
times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1010.260
The HARPS search for southern extra-solar planets XIX. Characterization and dynamics of the GJ876 planetary system
Precise radial-velocity measurements for data acquired with the HARPS
spectrograph infer that three planets orbit the M4 dwarf star GJ876. In
particular, we confirm the existence of planet "d", which orbits every 1.93785
days. We find that its orbit may have significant eccentricity (e=0.14), and
deduce a more accurate estimate of its minimum mass of 6.3 Earth masses.
Dynamical modeling of the HARPS measurements combined with literature
velocities from the Keck Observatory strongly constrain the orbital
inclinations of the "b" and "c" planets. We find that i_b = 48.9 degrees and
i_c = 48.1 degrees, which infers the true planet masses of M_b = 2.64 Jupiter
masses and M_c = 0.83 Jupiter masses, respectively. Radial velocities alone, in
this favorable case, can therefore fully determine the orbital architecture of
a multi-planet system, without the input from astrometry or transits.
The orbits of the two giant planets are nearly coplanar, and their 2:1 mean
motion resonance ensures stability over at least 5 Gyr. The libration amplitude
is smaller than 2 degrees, suggesting that it was damped by some dissipative
process during planet formation. The system has space for a stable fourth
planet in a 4:1 mean motion resonance with planet "b", with a period around 15
days. The radial velocity measurements constrain the mass of this possible
additional planet to be at most that of the Earth.Comment: 10 pages, 10 figures, accepted for publication in Astronomy &
Astrophysic
New constraints on the location of P9 obtained with the INPOP19a planetary ephemeris
Context. We used the new released INPOP19a planetary ephemerides benefiting from Jupiter-updated positions by the Juno mission and reanalyzed Cassini observations. Aims. We test possible locations of the unknown planet P9. To do this, we used the perturbations it produces on the orbits of the outer planets, more specifically, on the orbit of Saturn. Methods. Two statistical criteria were used to identify possible acceptable locations of P9 according to (i) the difference in planetary positions when P9 is included compared with the propagated covariance matrix, and (ii) the χ2 likelihood of postfit residuals for ephemerides when P9 is included. Results. No significant improvement of the residuals was found for any of the simulated locations, but we provide zones that induce a significant degradation of the ephemerides. Conclusions. Based on the INPOP19a planetary ephemerides, we demonstrate that if P9 exists, it cannot be closer than 500 AU with a 5 M⊕ and no closer than 650 AU with a 10 M⊕ . We also show that there is no clear zone that would indicate the positive existence of planet P9, but there are zones for which the existence of P9 is compatible with the 3σ accuracy of the INPOP planetary ephemerides
Analysis of Cassini radio tracking data for the construction of INPOP19a: a new estimate of the Kuiper belt mass
Context. Recent discoveries of new trans-Neptunian objects have greatly increased the attention by the scientific community to this relatively unknown region of the solar system. The current level of precision achieved in the description of planet orbits has transformed modern ephemerides in the most updated tools for studying the gravitational interactions between solar system bodies. In this context, the orbit of Saturn plays a primary role, especially thanks to Cassini tracking data collected during its 13-year mission around the ringed planet. Planetary ephemerides are currently mainly built using radio data, in particular with normal points derived from range and Doppler observables exchanged between ground stations and interplanetary probes. Aims. We present an analysis of Cassini navigation data aimed at producing new normal points based on the most updated knowledge of the Saturnian system developed throughout the whole mission. We provide additional points from radio science dedicated passes of Grand Finale orbits and Titan flybys. An updated version of the INPOP planetary ephemerides based upon these normal points is presented, along with a new estimate of the mass of trans-Neptunian object rings located in the 2:1 and 3:2 mean motion resonances with Neptune. Methods. We describe in detail the orbit determination process performed to construct the normal points and their associated uncertainties and how we process those points to produce a new planetary ephemeris. Results. From the analysis, we obtained 623 new normal points for Saturn with metre-level accuracy. The ephemeris INPOP19a, including this new dataset, provides an estimated mass for the trans-Neptunian object rings of (0.061 ± 0.001)M⊕
Evolution of INPOP planetary ephemerides and Bepi-Colombo simulations
We give here a detailed description of the latest INPOP planetary ephemerides
INPOP20a. We test the sensitivity of the Sun oblateness determination obtained
with INPOP to different models for the Sun core rotation. We also present new
evaluations of possible GRT violations with the PPN parameters ,
and . With a new method for selecting acceptable alternative
ephemerides we provide conservative limits of about and
for and respectively using the
present day planetary data samples. We also present simulations of Bepi-Colombo
range tracking data and their impact on planetary ephemeris construction. We
show that the use of future BC range observations should improve these
estimates, in particular . Finally, interesting perspectives for the
detection of the Sun core rotation seem to be reachable thanks to the BC
mission and its accurate range measurements in the GRT frame.Comment: Proceedings of the IAU Symposium 364 "Multi-scale dynamics of space
objects
Where are the Uranus Trojans?
The area of stable motion for fictitious Trojan asteroids around Uranus'
equilateral equilibrium points is investigated with respect to the inclination
of the asteroid's orbit to determine the size of the regions and their shape.
For this task we used the results of extensive numerical integrations of orbits
for a grid of initial conditions around the points L4 and L5, and analyzed the
stability of the individual orbits. Our basic dynamical model was the Outer
Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations
of motion of fictitious Trojans in the vicinity of the stable equilibrium
points for selected orbits up to the age of the Solar system of 5 billion
years. One experiment has been undertaken for cuts through the Lagrange points
for fixed values of the inclinations, while the semimajor axes were varied. The
extension of the stable region with respect to the initial semimajor axis lies
between 19.05 < a < 19.3 AU but depends on the initial inclination. In another
run the inclination of the asteroids' orbit was varied in the range 0 < i < 60
and the semimajor axes were fixed. It turned out that only four 'windows' of
stable orbits survive: these are the orbits for the initial inclinations 0 < i
< 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at
least some Trojans around the Uranus Lagrange points for the stability window
at small and also high inclinations.Comment: 15 pages, 12 figures, submitted to CMD
Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis
We study the behaviour of the Standard map critical function in a
neighbourhood of a fixed resonance, that is the scaling law at the fixed
resonance. We prove that for the fundamental resonance the scaling law is
linear. We show numerical evidence that for the other resonances , , and and relatively prime, the scaling law follows a
power--law with exponent .Comment: AMS-LaTeX2e, 29 pages with 8 figures, submitted to Nonlinearit
Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn
The Cassini spacecraft collects high resolution images of the saturnian
satellites and reveals the surface of these new worlds. The shape and rotation
of the satellites can be determined from the Cassini Imaging Science Subsystem
data, employing limb coordinates and stereogrammetric control points. This is
the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new
rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).
Especially, Epimetheus is characterized by its horseshoe shape orbit and the
presence of the swap is essential to introduce explicitly into rotational
models. During its journey in the saturnian system, Cassini spacecraft
accumulates the observational data of the other satellites and it will be
possible to determine the rotational parameters of several of them. To prepare
these future observations, we built rotational models of the coorbital (also
called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition
to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and
L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital
of Dione. The goal of this study is to understand how the departure from the
Keplerian motion induced by the perturbations of the coorbital body, influences
the rotation of these satellites. To this aim, we introduce explicitly the
perturbation in the rotational equations by using the formalism developed by
Erdi (1977) to represent the coorbital motions, and so we describe the
rotational motion of the coorbitals, Janus and Epimetheus included, in compact
form
Aspects of the planetary Birkhoff normal form
The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L.
Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for
the planetary many--body problem opened new insights and hopes for the
comprehension of the dynamics of this problem. Remarkably, it allowed to give a
{\sl direct} proof of the celebrated Arnold's Theorem [V. I. Arnold. Uspehi
Math. Nauk. 1963] on the stability of planetary motions. In this paper, using a
"ad hoc" set of symplectic variables, we develop an asymptotic formula for this
normal form that may turn to be useful in applications. As an example, we
provide two very simple applications to the three-body problem: we prove a
conjecture by [V. I. Arnold. cit] on the "Kolmogorov set"of this problem and,
using Nehoro{\v{s}}ev Theory [Nehoro{\v{s}}ev. Uspehi Math. Nauk. 1977], we
prove, in the planar case, stability of all planetary actions over
exponentially-long times, provided mean--motion resonances are excluded. We
also briefly discuss perspectives and problems for full generalization of the
results in the paper.Comment: 44 pages. Keywords: Averaging Theory, Birkhoff normal form,
Nehoro{\v{s}}ev Theory, Planetary many--body problem, Arnold's Theorem on the
stability of planetary motions, Properly--degenerate kam Theory, steepness.
Revised version, including Reviewer's comments. Typos correcte
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