81 research outputs found
Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach
We derive an expression for the mutual gravitational force and torque of two
bodies having arbitrary shapes and mass distributions, as an expansion in power
series of their products of inertia and of the relative coordinates of their
centres of mass. The absolute convergence of all the power series developed is
rigorously demonstrated. The absence of transcendental functions makes this
formalism suitable for fast numerical applications. The products of inertia
used here are directly related to the spherical harmonics coefficients, and we
provide a detailed analysis of this relationship.Comment: 13 pages, accepted by Celestial Mechanics and Dynamical Astronom
Eccentricity Evolution for Planets in Gaseous Disks
We investigate the hypothesis that interactions between a giant planet and
the disk from which it forms promote eccentricity growth. These interactions
are concentrated at discrete Lindblad and corotation resonances. Interactions
at principal Lindblad resonances cause the planet's orbit to migrate and open a
gap in the disk if the planet is sufficiently massive. Those at first order
Lindblad and corotation resonances change the planet's orbital eccentricity.
Eccentricity is excited by interactions at external Lindblad resonances which
are located on the opposite side of corotation from the planet, and damped by
co-orbital Lindblad resonances which overlap the planet's orbit. If the planet
clears a gap in the disk, the rate of eccentricity damping by co-orbital
Lindblad resonances is reduced. Density gradients associated with the gap
activate eccentricity damping by corotation resonances at a rate which
initially marginally exceeds that of eccentricity excitation by external
Lindblad resonances. But the corotation torque drives a mass flux which reduces
the density gradient near the resonance. Sufficient partial saturation of
corotation resonances can tip the balance in favor of eccentricity excitation.
A minimal initial eccentricity of a few percent is required to overcome viscous
diffusion which acts to unsaturate corotation resonances by reestablishing the
large scale density gradient. Thus eccentricity growth is a finite amplitude
instability. Formally, interactions at the apsidal resonance, which is a
special kind of co-orbital Lindblad resonance, appears to damp eccentricity
faster than external Lindblad resonances can excite it. However, apsidal waves
have such long wavelengths that they do not propagate in protoplanetary disks.
This reduces eccentricity damping by the apsidal resonance to a modest level.Comment: Submitted to Ap
Spectral study of Venus global topography and geoid from Magellan and PVO data
An analysis of newly available global harmonic models for topography and geoid on Venus was conducted. It was found that the power spectral density for Venus topography has a power law dependence on wave-number characteristic of Brown Noise, similar to what is found for the Earth. However, the Venus topography spectrum presents a rollover at lower degree (l = 3) than is observed for the Earth spectrum and has smaller amplitudes than that of the Earth's. The Venus geoid also obeys a power law relationship, at least for small values of l, but with a smaller slope and more power (for l greater than 3) than the Earth geoid
Mars and frame-dragging: study for a dedicated mission
In this paper we preliminarily explore the possibility of designing a
dedicated satellite-based mission to measure the general relativistic
gravitomagnetic Lense-Thirring effect in the gravitational field of Mars. The
focus is on the systematic error induced by the multipolar expansion of the
areopotential and on possible strategies to reduce it. It turns out that the
major sources of bias are the Mars'equatorial radius R and the even zonal
harmonics J_L, L = 2,4,6... of the areopotential. An optimal solution, in
principle, consists of using two probes at high-altitudes (a\approx 9500-9600
km) and different inclinations, and suitably combining their nodes in order to
entirely cancel out the bias due to \delta R. The remaining uncancelled
mismodelled terms due to \delta J_L, L = 2,4,6,... would induce a bias \lesssim
1%, according to the present-day MGS95J gravity model, over a wide range of
admissible values of the inclinations. The Lense-Thirring out-of-plane shifts
of the two probes would amount to about 10 cm yr^-1.Comment: LaTex2e, 16 pages, 5 figures, no tables. To appear in General
Relativity and Gravitatio
The gravitational instability of a stream of co-orbital particles
We describe the dynamics of a stream of equally spaced macroscopic particles
in orbit around a central body (e.g. a planet or star). A co-orbital
configuration of small bodies may be subject to gravitational instability,
which takes the system to a spreading, disordered and collisional state. We
detail the linear instability's mathematical and physical features using the
shearing sheet model and subsequently track its nonlinear evolution with local
N-body simulations. This model provides a convenient tool with which to
understand the gravitational and collisional dynamics of narrow belts, such as
Saturn's F-ring and the streams of material wrenched from tidally disrupted
bodies. In particular, we study the tendency of these systems to form
long-lived particle aggregates. Finally, we uncover an unexpected connection
between the linear dynamics of the gravitational instability and the
magnetorotational instability.Comment: 11 pages, 7 figures, 1 table. MNRAS, accepte
Theory of the Mercury's spin-orbit motion and analysis of its main librations
The upcoming space missions, MESSENGER and BepiColombo with onboard
instrumentation capable of measuring the rotational parameters stimulate the
objective to reach an accurate theory of the rotational motion of Mercury. For
obtaining the real motion of Mercury, we have used our relativistic BJV model
of solar system integration including the coupled spin-orbit motion of the
Moon. We have extended this model by generalizing the spin-orbit couplings to
the terrestrial planets, notably Mercury. The updated model is called SONYR
(acronym of Spin-Orbit N-BodY Relativistic model). The SONYR model giving an
accurate solution of the spin-orbit motion of Mercury permits to analyze the
different families of the Hermean rotational librations. The spin-orbit motion
of Mercury is characterized by two proper frequencies (namely 15.847 and 1066
years) and its 3:2 resonance presents a second synchronism which can be
understood as a spin-orbit secular resonance (278 898 years). By using the
SONYR model, we find a new determination of the mean obliquity, namely 1.6
arcminutes. Besides, we identify in the Hermean librations the impact of the
uncertainty of the greatest principal moment of inertia (\cmr2) on the
obliquity and on the libration in longitude (2.3 mas and 0.45 as respectively
for an increase of 1% on the \cmr2 value). These determinations prove to be
suitable for providing constraints on the internal structure of Mercury.Comment: 15 pages, 14 figures, 3 tables, accepted version to A&A (4 sept 2003
On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied
in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can
be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction.
On the light-cone, the vacuum structure of this theory is encoded in the
dynamical zero mode of a gluon and a constrained mode of the scalar field. The
latter satisfies a linear constraint, suggesting no nontrivial vacua in the
present paradigm for symmetry breaking on the light-cone. I develop a
diagrammatic method to solve the constraint equation. In the adiabatic
approximation I compute the quantum mechanical potential governing the
dynamical gauge mode. Due to a condensation of the lowest omentum modes of the
dynamical gluons, a centrifugal barrier is generated in the adiabatic
potential. In the present theory however, the barrier height appears too small
to make any impact in this odel. Although the theory is superrenormalisable on
naive powercounting grounds, the removal of ultraviolet divergences is
nontrivial when the constrained mode is taken into account. The open aspects of
this problem are discussed in detail.Comment: LaTeX file, 26 pages. 14 postscript figure
Advancing Tests of Relativistic Gravity via Laser Ranging to Phobos
Phobos Laser Ranging (PLR) is a concept for a space mission designed to
advance tests of relativistic gravity in the solar system. PLR's primary
objective is to measure the curvature of space around the Sun, represented by
the Eddington parameter , with an accuracy of two parts in ,
thereby improving today's best result by two orders of magnitude. Other mission
goals include measurements of the time-rate-of-change of the gravitational
constant, and of the gravitational inverse square law at 1.5 AU
distances--with up to two orders-of-magnitude improvement for each. The science
parameters will be estimated using laser ranging measurements of the distance
between an Earth station and an active laser transponder on Phobos capable of
reaching mm-level range resolution. A transponder on Phobos sending 0.25 mJ, 10
ps pulses at 1 kHz, and receiving asynchronous 1 kHz pulses from earth via a 12
cm aperture will permit links that even at maximum range will exceed a photon
per second. A total measurement precision of 50 ps demands a few hundred
photons to average to 1 mm (3.3 ps) range precision. Existing satellite laser
ranging (SLR) facilities--with appropriate augmentation--may be able to
participate in PLR. Since Phobos' orbital period is about 8 hours, each
observatory is guaranteed visibility of the Phobos instrument every Earth day.
Given the current technology readiness level, PLR could be started in 2011 for
launch in 2016 for 3 years of science operations. We discuss the PLR's science
objectives, instrument, and mission design. We also present the details of
science simulations performed to support the mission's primary objectives.Comment: 25 pages, 10 figures, 9 table
Mutual Potential of Homogeneous Polyhedra
The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O (6 n ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42570/1/10569_2004_Article_4621.pd
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