Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNonconservative extension of Keplerian integrals and a new class of integrable system
70
0
0.0
(
0
)
Authors
Javier Roa
Ask ChatGPT about the research
No Arabic abstract
The invariance of the Lagrangian under time translations and rotations in Keplers problem yields the conservation laws related to the energy and angular momentum. Noethers theorem reveals that these same symmetries furnish generalized forms of the first integrals in a special nonconservative case, which approximates various physical models. The system is perturbed by a biparametric acceleration with components along the tangential and normal directions. A similarity transformation reduces the biparametric disturbance to a simpler uniparametric forcing along the velocity vector. The solvability conditions of this new problem are discussed, and closed-form solutions for the integrable cases are provided. Thanks to the conservation of a generalized energy, the orbits are classified as elliptic, parabolic, and hyperbolic. Keplerian orbits appear naturally as particular solutions to the problem. After characterizing the orbits independently, a unified form of the solution is built based on the Weierstrass elliptic functions. The new trajectories involve fundamental curves such as cardioids and logarithmic, sinusoidal, and Cotes spirals. These orbits can represent the motion of particles perturbed by solar radiation pressure, of spacecraft with continuous thrust propulsion, and some instances of Schwarzschild geodesics. Finally, the problem is connected with other known integrable systems in celestial mechanics.
rate research
Read More
Disks of bodies orbiting a much more massive central object are extremely common in astrophysics. When the orbits comprising such disks are eccentric, we show they are susceptible to a new dynamical instability. Gravitational forces between bodies in the disk drive exponential growth of their orbital inclinations and clustering in their angles of pericenter, expanding an initially thin disk into a conical shape by giving each orbit an identical tilt with respect to the disk plane. This new instability dynamically produces the unusual distribution of orbits observed for minor planets beyond Neptune, suggesting that the instability has shaped the outer Solar System. It also implies a large initial disk mass (1-10 Earth masses) of scattered bodies at hundreds of AU; we predict increasing numbers of detections of minor planets clustered in their angles of pericenter with high inclinations.
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain special cases of the main results presented here are also pointed out for the extended Gauss hypergeometric and confluent hypergeometric functions.
The recent Advanced LIGO detections of coalescing black hole binaries (BHBs) imply a large population of such systems emitting at milli-Hz frequencies, accessible to the Laser Interferometer Space Antenna (LISA). We show that these systems provide a new class of cosmological standard sirens. Direct LISA luminosity distance -$D_l$- measurements, combined with the inhomogeneous redshift -$z$- distribution of possible host galaxies provide an effective way to populate the $D_l-z$ diagram at $z<0.1$, thus allowing a precise local measurement of the Hubble expansion rate. To be effective, the method requires a sufficiently precise LISA distance determination and sky localization of a sizeable number of BHBs, which is best achieved for a 6-link detector configuration. We find that, for a BHB population consistent with current fiducial LIGO rates, the Hubble constant $H_0$ can be determined at the $sim$5% and $sim$2% level (68% confidence) assuming two and five million Km arm-length respectively.
In four dimensions, the most general metric admitting two Killing vectors and a rank-two Killing tensor can be parameterized by ten arbitrary functions of a single variable. We show that picking a special vierbien, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provide an straightforward connection between the most general integrable structure and the Carter family of spacetimes.
Context: Rotationally supported disks are critical in the star formation process. The questions of when do they form and what factors influence or hinder their formation have been studied but are largely unanswered. Observations of early stage YSOs are needed to probe disk formation. Aims: VLA1623 is a triple non-coeval protostellar system, with a weak magnetic field perpendicular to the outflow, whose Class 0 component, VLA1623A, shows a disk-like structure in continuum with signatures of rotation in line emission. We aim to determine whether this structure is in part or in whole a rotationally supported disk, i.e. a Keplerian disk, and what are its characteristics. Methods: ALMA Cycle 0 Early Science 1.3 mm continuum and C$^{18}$O (2-1) observations in the extended configuration are presented here and used to perform an analysis of the disk-like structure using PV diagrams and thin disk modelling with the addition of foreground absorption. Results: The PV diagrams of the C$^{18}$O line emission suggest the presence of a rotationally supported component with a radius of at least 50 AU. Kinematical modelling of the line emission shows that the disk out to 180 AU is actually rotationally supported, with the rotation being well described by Keplerian rotation out to at least 150 AU, and the central source mass to be $sim$0.2 M$_{sun}$ for an inclination of 55$^{circ}$. Pure infall and conserved angular momentum rotation models are excluded. Conclusions: VLA1623A, a very young Class 0 source, presents a disk with an outer radius $R_{rm out}$ = 180 AU with a Keplerian velocity structure out to at least 150 AU. The weak magnetic fields and recent fragmentation in this region of rho Ophiuchus may have played a lead role in the formation of the disk.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
