274,558 research outputs found
Solar sail orbits at artificial Sun-Earth libration points
In this Note a new family of solar sail orbits will be investigated in the sun-Earth circular restricted three-body problem. It will be shown that periodic orbits can be developed that are displaced above or below the plane of the restricted three-body system. Whereas traditional halo orbits are centered on the classical libration points, these new orbits are associated with artificial libration points. The orbits are retrograde, circular orbits with a period half that of the orbit period of the two primary masses of the problem. Numerical analysis of stability and controllability of the orbits shows that the orbits are unstable but completely controllable with both lightness number (sail areal density) and sail attitude
Resonant periodic orbits in the exoplanetary systems
The planetary dynamics of , , , and mean motion
resonances is studied by using the model of the general three body problem in a
rotating frame and by determining families of periodic orbits for each
resonance. Both planar and spatial cases are examined. In the spatial problem,
families of periodic orbits are obtained after analytical continuation of
vertical critical orbits. The linear stability of orbits is also examined.
Concerning initial conditions nearby stable periodic orbits, we obtain
long-term planetary stability, while unstable orbits are associated with
chaotic evolution that destabilizes the planetary system. Stable periodic
orbits are of particular importance in planetary dynamics, since they can host
real planetary systems. We found stable orbits up to of mutual
planetary inclination, but in most families, the stability does not exceed
-, depending on the planetary mass ratio. Most of these
orbits are very eccentric. Stable inclined circular orbits or orbits of low
eccentricity were found in the and resonance, respectively.Comment: Accepted for publication in Astrophysics and Space Science. Link to
the published article on Springer's website was inserte
A unified framework for the orbital structure of bars and triaxial ellipsoids
We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (~4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (~7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediate axis owing to the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (~2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform some x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies
Orbits in the H2O molecule
We study the forms of the orbits in a symmetric configuration of a realistic
model of the H2O molecule with particular emphasis on the periodic orbits. We
use an appropriate Poincar\'e surface of section (PSS) and study the
distribution of the orbits on this PSS for various energies. We find both
ordered and chaotic orbits. The proportion of ordered orbits is almost 100% for
small energies, but decreases abruptly beyond a critical energy. When the
energy exceeds the escape energy there are still non-escaping orbits around
stable periodic orbits. We study in detail the forms of the various periodic
orbits, and their connections, by providing appropriate stability and
bifurcation diagrams.Comment: 21 pages, 14 figures, accepted for publication in CHAO
Ballistic Orbits and Front Speed Enhancement for ABC Flows
We study the two main types of trajectories of the ABC flow in the
near-integrable regime: spiral orbits and edge orbits. The former are helical
orbits which are perturbations of similar orbits that exist in the integrable
regime, while the latter exist only in the non-integrable regime. We prove
existence of ballistic (i.e., linearly growing) spiral orbits by using the
contraction mapping principle in the Hamiltonian formulation, and we also find
and analyze ballistic edge orbits. We discuss the relationship of existence of
these orbits with questions concerning front propagation in the presence of
flows, in particular, the question of linear (i.e., maximal possible) front
speed enhancement rate for ABC flows.Comment: 39 pages, 26 figure
Natural and sail-displaced doubly-symmetric Lagrange point orbits for polar coverage
This paper proposes the use of doubly-symmetric, eight-shaped orbits in the circular restricted three-body problem for continuous coverage of the high-latitude regions of the Earth. These orbits, for a range of amplitudes, spend a large fraction of their period above either pole of the Earth. It is shown that they complement Sun-synchronous polar and highly eccentric Molniya orbits, and present a possible alternative to low thrust pole-sitter orbits. Both natural and solar-sail displaced orbits are considered. Continuation methods are described and used to generate families of these orbits. Starting from ballistic orbits, other families are created either by increasing the sail lightness number, varying the period or changing the sail attitude. Some representative orbits are then chosen to demonstrate the visibility of high-latitude regions throughout the year. A stability analysis is also performed, revealing that the orbits are unstable: it is found that for particular orbits, a solar sail can reduce their instability. A preliminary design of a linear quadratic regulator is presented as a solution to stabilize the system by using the solar sail only. Finally, invariant manifolds are exploited to identify orbits that present the opportunity of a ballistic transfer directly from low Earth orbit
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