32 research outputs found
Towards an interpretation of MOND as a modification of inertia
We explore the possibility that Milgrom's Modified Newtonian Dynamics (MOND)
is a manifestation of the modification of inertia at small accelerations.
Consistent with the Tully-Fisher relation, dynamics in the small acceleration
domain may originate from a quartic (cubic) velocity-dependence of energy
(momentum) whereas gravitational potentials remain linear with respect to mass.
The natural framework for this interpretation is Finsler geometry. The simplest
static isotropic Finsler metric of a gravitating mass that incorporates the
Tully-Fisher relation at small acceleration is associated with a spacetime
interval that is either a homogeneous quartic root of polynomials of local
displacements or a simple root of a rational fraction thereof. We determine the
low energy gravitational equation and find that Finsler spacetimes that produce
a Tully-Fisher relation require that the gravitational potential be modified.
For an isolated mass, Newton's potential is replaced by where is MOND's acceleration scale and is a yet
undetermined distance scale. Orbital energy is linear with respect to mass but
angular momentum is proportional to . Asymptotic light deflection
resulting from time curvature is similar to that of a singular isothermal
sphere implying that space curvature must be the main source of deflection in
static Finsler spacetimes possibly through the presence of the distance scale
that appears in the asymptotic form of the gravitational potential. The
quartic nature of the Finsler metric hints at the existence of an underlying
area-metric that describes the effective structure of spacetime.Comment: Revised version, 9 pages, 1 figure. Accepted for publication in
Monthly Notices of the Royal Astronomical Societ
Origin theories for the eccentricities of extrasolar planets
Half the known extrasolar planets have orbital eccentricities in excess of
0.3. Such large eccentricities are surprising as it is thought that planets
form in a protoplanetary disk on nearly circular orbits much like the current
states of the solar system planets. Possible explanations for the large
planetary eccentricities include the perturbations that accompany planet-planet
scattering, the tidal interaction between the gas disk and the planets, Kozai's
secular eccentricity cycles, the eccentricity excitation during planetary pair
migration in mean motion resonance, the perturbations by stellar encounters,
stellar-like relaxation that occurs if planets formed through gravitational
instability, and the relative acceleration by the stellar jet system of the
host star with respect to the companion. In this chapter, we comment on the
relevance and characteristics of the various eccentricity origin theories.Comment: 23 pages, 8 figures. Review lecture at the 2006 Aussois Winter School
"Open Problems in Celestial Mechanics". To appear in Lecture Notes in
Physics, Springe
On dynamical friction in a gaseous medium with a boundary
Dynamical friction arises from the interaction of a perturber and the
gravitational wake it excites in the ambient medium. We study the effects of
the presence of a boundary on dynamical friction by studying analytically the
interaction of perturber with uniform rectilinear motion in a uniform
homogeneous medium with a reflecting planar boundary. Wake reflection at a
medium's boundary may occur at the edges of truncated disks perturbed by
planetary or stellar companions as well as in numerical simulations of
planet-disk interaction with no-outflow boundary conditions. In this paper, we
show that the presence of the boundary modifies the behaviour of dynamical
friction significantly. We find that perturbers are invariably pushed away from
the boundary and reach a terminal subsonic velocity near Mach 0.37 regardless
of initial velocity. Dynamical friction may even be reversed for Mach numbers
less than 0.37 thereby accelerating instead of decelerating the perturber.
Perturbers moving parallel to the boundary feel additional friction orthogonal
to the direction of motion that is much stronger than the standard friction
along the direction of motion. These results indicate that the common use of
the standard Chandrasekhar formula as a short hand estimate of dynamical
friction may be inadequate as observed in various numerical simulations.Comment: Revised version, 28 pages, 10 figures, Accepted for publication in
Astrophysics & Space Scienc
Coorbital capture at arbitrary inclination
The process of capture in the coorbital region of a solar system planet is
studied. Absolute capture likelihood in the 1:1 resonance is determined by
randomly constructed statistical ensembles numbering of
massless asteroids that are set to migrate radially from the outer to the inner
boundaries of the coorbital region of a Jupiter-mass planet. Orbital states
include coorbital capture, ejection, collisions with the Sun and the planet and
free-crossing of the coorbital region. The relative efficiency of retrograde
capture with respect to prograde capture is confirmed as an intrinsic property
of the coorbital resonance. Half the asteroids cross the coorbital region
regardless of eccentricity and for any inclination less than . We
also find that the recently discovered retrograde coorbital of Jupiter,
asteroid 2015 BZ509, lies almost exactly at the capture efficiency peak
associated with its orbital parameters.Comment: 8 pages. 2 figures. Submitted to Journal of Computational and Applied
Mathematic
The disturbing function for polar Centaurs and transneptunian objects
The classical disturbing function of the three-body problem is based on an
expansion of the gravitational interaction in the vicinity of nearly coplanar
orbits. Consequently, it is not suitable for the identification and study of
resonances of the Centaurs and transneptunian objects on nearly polar orbits
with the solar system planets. Here, we provide a series expansion algorithm of
the gravitational interaction in the vicinity of polar orbits and produce
explicitly the disturbing function to fourth order in eccentricity and
inclination cosine. The properties of the polar series differ significantly
from those of the classical disturbing function: the polar series can model any
resonance as the expansion order is not related to the resonance order. The
powers of eccentricity and inclination of the force amplitude of a :
resonance do not depend on the value of the resonance order but only on
its parity. Thus all even resonance order eccentricity amplitudes are and odd ones to lowest order in eccentricity . With the new
findings on the structure of the polar disturbing function and the possible
resonant critical arguments, we illustrate the dynamics of the polar resonances
1:3, 3:1, 2:9 and 7:9 where transneptunian object 471325 could currently be
locked.Comment: 18 pages, 9 figures, 7 tables. Accepted for publication in Monthly
Notices of the Royal Astronomical Societ
Orbit injection of planet-crossing asteroids
Solar system Centaurs originate in transneptunian space from where planet
orbit crossing events inject their orbits inside the giant planets' domain.
Here, we examine this injection process in the three-body problem by studying
the orbital evolution of transneptunian asteroids located at Neptune's
collision singularity as a function of the Tisserand invariant, T. Two
injection modes are found, one for T>0.1, or equivalently prograde inclinations
far from the planet, where unstable motion dominates injection, and another for
T<= 0.1, or equivalently polar and retrograde inclinations far from the planet,
where stable motion dominates injection. The injection modes are independent of
the initial semi-major axis and the dynamical time at the collision
singularity. The simulations uncovered a region in the polar corridor where the
dynamical time exceeds the solar system's age suggesting the possibility of
long-lived primordial polar transneptunian reservoirs that supply Centaurs to
the giant planets' domain.Comment: 13 pages, 12 figures. Accepted for publication in Monthly Notices of
the Royal Astronomical Societ
The excitation of planetary orbits by stellar jet variability and polarity reversal
Planets form in active protoplanetary disks that sustain stellar jets.
Momentum loss from the jet system may excite the planets' orbital eccentricity
and inclination (Namouni 2005, AJ 130, 280). Evaluating quantitatively the
effects of such excitation requires a realistic modeling of the momentum loss
profiles associated with stellar jets. In this work, we model linear momentum
loss as a time-variable stochastic process that results in a zero mean stellar
acceleration. Momentum loss may involve periodic or random polarity reversals.
We characterize orbital excitation as a function of the variability timescale
and identify a novel excitation resonance between a planet's orbital period and
the jet's variability timescale where the former equals twice the latter. For
constant variability timescales, resonance is efficient for both periodic and
random polarity reversals, the latter being stronger than the former. For a
time variable variability timescale, resonance crossing is a more efficient
excitation mechanism when polarity reversals are periodic. Each polarity
reversal type has distinct features that may help constrain the magnetic
history of the star through the observation of its planetary companions. For
instance, outward planet migration to large distances from parent stars is one
of the natural outcomes of periodic polarity reversal excitation if resonance
crossing is sufficiently slow. Applying the excitation mechanism to the solar
system, we find that the planet-jet variability resonance with periodic
polarity reversal momentum loss is a possible origin for the hitherto
unexplained inclination of Jupiter's orbit by 6 deg. with respect to the Sun's
equator.Comment: 16 pages, 10 figures. published in Astrophysics & Space Scienc
A numerical investigation of coorbital stability and libration in three dimensions
Motivated by the dynamics of resonance capture, we study numerically the
coorbital resonance for inclination180 >=I>=0 in the circular restricted
three-body problem. We examine the similarities and differences between planar
and three dimensional coorbital resonance capture and seek their origin in the
stability of coorbital motion at arbitrary inclination. After we present
stability maps of the planar prograde and retrograde coorbital resonances, we
characterize the new coorbital modes in three dimensions. We see that
retrograde mode I (R1) and mode II (R2) persist as we change the relative
inclination, while retrograde mode III (R3) seems to exist only in the planar
problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue
to an horseshoe-orbit. The Kozai-Lidov resonance is active for retrograde
orbits as well as prograde orbits and plays a key role in coorbital resonance
capture. Stable coorbital modes exist at all inclinations, including retrograde
and polar obits. This result confirms the robustness the coorbital resonance at
large inclination and encourages the search for retrograde coorbital companions
of the solar system's planets.Comment: accepted for publication in Celestial Mechanics and Dynamical
Astronom