15,041 research outputs found
Pseudo-High-Order Symplectic Integrators
Symplectic N-body integrators are widely used to study problems in celestial
mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2
and 6 substeps per timestep, respectively. The number of substeps increases
rapidly with order in timestep, rendering higher-order methods impractical.
However, symplectic integrators are often applied to systems in which
perturbations between bodies are a small factor of the force due to a dominant
central mass. In this case, it is possible to create optimized symplectic
algorithms that require fewer substeps per timestep. This is achieved by only
considering error terms of order epsilon, and neglecting those of order
epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6
substeps per step which effectively behave as 4th and 6th-order integrators
when epsilon is small. These algorithms are more efficient than the usual 2nd
and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical
Journa
Survival of Terrestrial Planets in the Presence of Giant Planet Migration
The presence of ``Hot Jupiters'', Jovian mass planets with very short orbital
periods orbiting nearby main sequence stars, has been proposed to be primarily
due to the orbital migration of planets formed in orbits initially much further
from the parent star. The migration of giant planets would have profound
effects on the evolution of inner terrestrial planets in these systems, and
previous analyses have assumed that no terrestrial planets survive after
migration has occurred. We present numerical simulations showing that a
significant fraction of terrestrial planets could survive the migration
process, eventually returning to circular orbits relatively close to their
original positions. A fraction of the final orbits are in the Habitable Zone,
suggesting that planetary systems with close-in giant planets are viable
targets for searches for Earth-like habitable planets around other stars.Comment: 5 pages, 3 figures, emulateapj. ApJL in press, referee comments
changes and edited for lengt
A decreased probability of habitable planet formation around low-mass stars
Smaller terrestrial planets (< 0.3 Earth masses) are less likely to retain
the substantial atmospheres and ongoing tectonic activity probably required to
support life. A key element in determining if sufficiently massive "sustainably
habitable" planets can form is the availability of solid planet-forming
material. We use dynamical simulations of terrestrial planet formation from
planetary embryos and simple scaling arguments to explore the implications of
correlations between terrestrial planet mass, disk mass, and the mass of the
parent star. We assume that the protoplanetary disk mass scales with stellar
mass as Mdisk ~ f Mstar^h, where f measures the relative disk mass, and 1/2 < h
< 2, so that disk mass decreases with decreasing stellar mass. We consider
systems without Jovian planets, based on current models and observations for M
stars. We assume the mass of a planet formed in some annulus of a disk with
given parameters is proportional to the disk mass in that annulus, and show
with a suite of simulations of late-stage accretion that the adopted
prescription is surprisingly accurate. Our results suggest that the fraction of
systems with sufficient disk mass to form > 0.3 Earth mass habitable planets
decreases for low-mass stars for every realistic combination of parameters.
This "habitable fraction" is small for stellar masses below a mass in the
interval 0.5 to 0.8 Solar masses, depending on disk parameters, an interval
that excludes most M stars. Radial mixing and therefore water delivery are
inefficient in lower-mass disks commonly found around low-mass stars, such that
terrestrial planets in the habitable zones of most low-mass stars are likely to
be small and dry.Comment: Accepted to ApJ. 11 pages, 6 figure
A methodology for selective removal of orbital debris
Earth-orbiting objects, large enough to be tracked, were surveyed for possible systematic debris removal. Based upon the statistical collision studies of others, it was determined that objects in orbits approximately 1000 km above the Earth's surface are at greatest collisional risk. Russian C-1B boosters were identified as the most important target of opportunity for debris removal. Currently, more than 100 in tact boosters are orbiting the Earth with apogees between 950 km and 1050 km. Using data provided by Energia USA, specific information on the C-1B booster, in terms of rendezvous and capture strategies, was discussed
A Dynamical Analysis of the 47 UMa Planetary System
The mass and period ratios of the two planets orbiting 47 UMa suggest a
possible kinship to the Jupiter-Saturn pair in our solar system. We explore the
current dynamical state of the 47 UMa system with numerical integrations, and
compare the results with analytic secular theory. We find that the planets in
the system are likely participating in a secular resonance in which the
difference in the longitudes of pericenter librates around zero. Alternately,
it is possible that the system is participating in the 7:3 mean motion
resonance. We show that stability considerations restrict the mutual
inclination between the two planets to 40 degrees or less, and that this result
is relatively insensitive to the total mass of the two planets. We present
hydrodynamical simulations which measure the torques exerted on the planets by
a hypothesized external protoplanetary disk. We show that planetary migration
in response to torques from the disk may have led to capture of the system into
a 7:3 mean-motion resonance, although it is unclear how the eccentricities of
the planets would have been damped after capture occured. We show that
Earth-mass planets can survive for long periods in some regions of the
habitable zone of the nominal co-planar system. A set of planetary accretion
calculations, however, shows that it is unlikely that large terrestrial planets
can form in the 47 UMa habitable zone.Comment: Accepted by the Astrophysical Journal (Original submission November
2001
The (In)Stability of Planetary Systems
We present results of numerical simulations which examine the dynamical
stability of known planetary systems, a star with two or more planets. First we
vary the initial conditions of each system based on observational data. We then
determine regions of phase space which produce stable planetary configurations.
For each system we perform 1000 ~1 million year integrations. We examine
upsilon And, HD83443, GJ876, HD82943, 47UMa, HD168443, and the solar system
(SS). We find that the resonant systems, 2 planets in a first order mean motion
resonance, (HD82943 and GJ876) have very narrow zones of stability. The
interacting systems, not in first order resonance, but able to perturb each
other (upsilon And, 47UMa, and SS) have broad regions of stability. The
separated systems, 2 planets beyond 10:1 resonance, (we only examine HD83443
and HD168443) are fully stable. Furthermore we find that the best fits to the
interacting and resonant systems place them very close to unstable regions. The
boundary in phase space between stability and instability depends strongly on
the eccentricities, and (if applicable) the proximity of the system to perfect
resonance. In addition to million year integrations, we also examined stability
on ~100 million year timescales. For each system we ran ~10 long term
simulations, and find that the Keplerian fits to these systems all contain
configurations which may be regular on this timescale.Comment: 37 pages, 49 figures, 13 tables, submitted to Ap
Crystallization of the oligopeptide-binding protein AppA from Bacillus subtilis
AppA is the membrane-anchored extracellular receptor component of an ABC transporter responsible for the uptake of oligopeptides into Bacillus subtilis. AppA has been overexpressed as a cleavable maltose-binding protein fusion in Escherichia coli. Following removal of the fusion portion, AppA has been crystallized from morpholino-ethanesulfonic acid-buffered solutions at pH 6.5 containing polyethylene glycol and zinc acetate. A complete X-ray diffraction data set extending to 2.3 Angstrom spacing has been collected
Planet Formation with Migration
In the core-accretion model, gas-giant planets form solid cores which then
accrete gaseous envelopes. Tidal interactions with disk gas cause a core to
undergo inward type-I migration in 10^4 to 10^5 years. Cores must form faster
than this to survive. Giant planets clear a gap in the disk and undergo inward
type-II migration in <10^6 years if observed disk accretion rates apply to the
disk as a whole. Type-II migration times exceed typical disk lifetimes if
viscous accretion occurs mainly in the surface layers of disks. Low turbulent
viscosities near the midplane may allow planetesimals to form by coagulation of
dust grains. The radius r of such planetesimals is unknown. If r<0.5 km, the
core formation time is shorter than the type-I migration timescale and cores
will survive. Migration is substantial in most cases, leading to a wide range
of planetary orbits, consistent with the observed variety of extrasolar
systems. When r is of order 100m and midplane alpha is of order 3 times 10^-5,
giant planets similar to those in the Solar System can form.Comment: 12 pages including 4 figure
Symmetry Scheme for Amino Acid Codons
Group theoretical concepts are invoked in a specific model to explain how
only twenty amino acids occur in nature out of a possible sixty four. The
methods we use enable us to justify the occurrence of the recently discovered
twenty first amino acid selenocysteine, and also enables us to predict the
possible existence of two more, as yet undiscovered amino acids.Comment: 18 pages which include 4 figures & 3 table
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