23 research outputs found
Long-term perturbations due to a disturbing body in elliptic inclined orbit
In the current study, a double-averaged analytical model including the action
of the perturbing body's inclination is developed to study third-body
perturbations. The disturbing function is expanded in the form of Legendre
polynomials truncated up to the second-order term, and then is averaged over
the periods of the spacecraft and the perturbing body. The efficiency of the
double-averaged algorithm is verified with the full elliptic restricted
three-body model. Comparisons with the previous study for a lunar satellite
perturbed by Earth are presented to measure the effect of the perturbing body's
inclination, and illustrate that the lunar obliquity with the value 6.68\degree
is important for the mean motion of a lunar satellite. The application to the
Mars-Sun system is shown to prove the validity of the double-averaged model. It
can be seen that the algorithm is effective to predict the long-term behavior
of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged
model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure
Motion of dust in mean-motion resonances with planets
Effect of stellar electromagnetic radiation on motion of spherical dust
particle in mean-motion orbital resonances with a planet is investigated.
Planar circular restricted three-body problem with the Poynting-Robertson (P-R)
effect yields monotonous secular evolution of eccentricity when the particle is
trapped in the resonance. Elliptically restricted three-body problem with the
P-R effect enables nonmonotonous secular evolution of eccentricity and the
evolution of eccentricity is qualitatively consistent with the published
results for the complicated case of interaction of electromagnetic radiation
with nonspherical dust grain. Thus, it is sufficient to allow either nonzero
eccentricity of the planet or nonsphericity of the grain and the orbital
evolutions in the resonances are qualitatively equal for the two cases. This
holds both for exterior and interior mean-motion orbital resonances. Evolutions
of longitude of pericenter in the planar circular and elliptical restricted
three-body problems are shown. Our numerical integrations suggest that any
analytic expression for secular time derivative of the particle's longitude of
pericenter does not exist, if a dependence on semi-major axis, eccentricity and
longitude of pericenter is considered (the P-R effect and mean-motion resonance
with the planet in circular orbit is taken into account).
Change of optical properties of the spherical grain with the heliocentric
distance is also considered. The change of the optical properties: i) does not
have any significant influence on secular evolution of eccentricity, ii) causes
that the shift of pericenter is mainly in the same direction/orientation as the
particle motion around the Sun. The statements hold both for circular and
noncircular planetary orbits.Comment: 22 pages, 12 figure
A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876
Investigations of two resonant planets orbiting a star or two resonant
satellites orbiting a planet often rely on a few resonant and secular terms in
order to obtain a representative quantitative description of the system's
dynamical evolution. We present a semianalytic model which traces the orbital
evolution of any two resonant bodies in a first- through fourth-order
eccentricity or inclination-based resonance dominated by the resonant and
secular arguments of the user's choosing. By considering the variation of
libration width with different orbital parameters, we identify regions of phase
space which give rise to different resonant ''depths,'' and propose methods to
model libration profiles. We apply the model to the GJ 876 extrasolar planetary
system, quantify the relative importance of the relevant resonant and secular
contributions, and thereby assess the goodness of the common approximation of
representing the system by just the presumably dominant terms. We highlight the
danger in using ''order'' as the metric for accuracy in the orbital solution by
revealing the unnatural libration centers produced by the second-order, but not
first-order, solution, and by demonstrating that the true orbital solution lies
somewhere ''in-between'' the third- and fourth-order solutions. We also present
formulas used to incorporate perturbations from central-body oblateness and
precession, and a protoplanetary or protosatellite thin disk with gaps, into a
resonant system. We quantify these contributions to the GJ 876 system, and
thereby highlight the conditions which must exist for multi-planet exosystems
to be significantly influenced by such factors. We find that massive enough
disks may convert resonant libration into circulation; such disk-induced
signatures may provide constraints for future studies of exoplanet systems.Comment: 39 pages of body text, 21 figures, 5 tables, 1 appendix, accepted for
publication in Celestial Mechanics and Dynamical Astronom
Computation of the potential of a simple inhomogeneous equipotential layer with a given density on a given surface
Chaotic diffusion caused by close encounters with several massive asteroids
Context. Close encounters with (1) Ceres and (4) Vesta, the two most massive bodies in the main belt, are known to be a mechanism of dynamical mobility able to significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Recently, it has been shown that drift rates caused by close encounters with massive asteroids may change significantly on timescales of 30 Myr when different models (i.e., different numbers of massive asteroids) are considered.
Aims. So far, not much attention has been given to the case of diffusion caused by the other most massive bodies in the main belt: (2) Pallas, (10) Hygiea, and (31) Euphrosyne, the third, fourth, and one of the most massive highly inclined asteroids in the main belt, respectively. Since (2) Pallas is a highly inclined object, relative velocities at encounter with other asteroids tend to be high and changes in proper elements are therefore relatively small. It was thus believed that the scattering effect caused by highly inclined objects in general should be small. Can diffusion by close encounters with these asteroids be a significant mechanism of long-term dynamical mobility?
Methods. By performing simulations with symplectic integrators, we studied the problem of scattering caused by close encounters with (2) Pallas, (10) Hygiea, and (31) Euphrosyne when only the massive asteroids (and the eight planets) are considered, and the other massive main belt asteroids and non-gravitational forces are also accounted for.
Results. By finding relatively small values of drift rates for (2) Pallas, we confirm that orbital scattering by this highly inclined object is indeed a minor effect. Unexpectedly, however, we obtained values of drift rates for changes in proper semi-major axis a caused by (10) Hygiea and (31) Euphrosyne larger than what was previously found for scattering by (4) Vesta. These high rates may have repercussions on the orbital evolution and age estimate of their respective families