arXiv subjects

L. Acedo

Publications and source records attributed to L. Acedo.

At least 19 recordsLinked to original sources

arXiv2017

A possible flyby anomaly for Juno at Jupiter

In the last decades there have been an increasing interest in improving the accuracy of spacecraft navigation and trajectory data. In the course of this plan some anomalies have been found that cannot, in principle, be explained in the context of the most accurate orbital models including all known effects from classical dynamics and general relativity. Of particular interest for its puzzling nature, and the lack of any accepted explanation for the moment, is the flyby anomaly discovered in some spacecraft flybys of the Earth over the course of twenty years. This anomaly manifest itself as the impossibility of matching the pre and post-encounter Doppler tracking and ranging data within a single orbit but, on the contrary, a difference of a few mm$/$s in the asymptotic velocities is required to perform the fitting. Nevertheless, no dedicated missions have been carried out to elucidate the origin of this phenomenon with the objective either of revising our understanding of gravity or to improve the accuracy of spacecraft Doppler tracking by revealing a conventional origin. With the occasion of the Juno mission arrival at Jupiter and the close flybys of this planet, that are currently been performed, we have developed an orbital model suited to the time window close to the perijove. This model shows that an anomalous acceleration of a few mm$/$s$^2$ is also present in this case. The chance for overlooked conventional or possible unconventional explanations is discussed.

astro-ph.EP↗

arXiv2017

Anomalous accelerations in spacecraft flybys of the Earth

The flyby anomaly is a persistent riddle in astrodynamics. Orbital analysis in several flybys of the Earth since the Galileo spacecraft flyby of the Earth in 1990 have shown that the asymptotic post-encounter velocity exhibits a difference with the initial velocity that cannot be attributed to conventional effects. To elucidate its origin, we have developed an orbital program for analyzing the trajectory of the spacecraft in the vicinity of the perigee, including both the Sun and the Moon's tidal perturbations and the geopotential zonal, tesseral and sectorial harmonics provided by the EGM96 model. The magnitude and direction of the anomalous acceleration acting upon the spacecraft can be estimated from the orbital determination program by comparing with the trajectories fitted to telemetry data as provided by the mission teams. This acceleration amounts to a fraction of a mm/s$^2$ and decays very fast with altitude. The possibility of some new physics of gravity in the altitude range for spacecraft flybys is discussed.

astro-ph.EP↗

arXiv2017

Modal series expansions for plane gravitational waves

Propagation of gravitational disturbances at the speed of light is one of the key predictions of the General Theory of Relativity. This result is now backed indirectly by the observations of the behaviour of the ephemeris of binary pulsar systems. These new results have in- creased the interest in the mathematical theory of gravitational waves in the last decades and several mathematical approaches have been developed for a better understanding of the solutions. In this paper we develop a modal series expansion technique in which solutions can be built for plane waves from a seed integrable function. The convergence of these series is proven by the Raabe- Duhamel criteria and we show that these solutions are characterized by a well-defined and finite curvature tensor and also a finite energy content.

gr-qc↗

arXiv2017

Kinematics effects of atmospheric friction in spacecraft flybys

Gravity assist manoeuvres are one of the most succesful techniques in astrodynamics. In these trajectories the spacecraft comes very close to the surface of the Earth, or other Solar system planets or moons, and, as a consequence, it experiences the effect of atmospheric friction by the outer layers of the Earth's atmosphere or ionosphere. In this paper we analyze a standard atmospheric model to estimate the density profile during the two Galileo flybys, the NEAR and the Juno flyby. We show that, even allowing for a margin of uncertainty in the spacecraft cross-section and the drag coefficient, the observed -8 mm/sec anomalous velocity decrease during the second Galileo flyby of December, 8th, 1992 cannot be attributed only to atmospheric friction. On the other hand, for perigees on the border between the termosphere and the exosphere the friction only accounts for a fraction of a millimeter per second in the final asymptotic velocity.

physics.space-ph↗

arXiv2017

The flyby anomaly: A multivariate analysis approach

The flyby anomaly is the unexpected variation of the asymptotic post-encounter velocity of a spacecraft with respect to the pre-encounter velocity as it performs a slingshot manoeuvre. This effect has been detected in, at least, six flybys of the Earth but it has not appeared in other recent flybys. In order to find a pattern in these, apparently contradictory, data several phenomenological formulas have been proposed but all have failed to predict a new result in agreement with the observations. In this paper we use a multivariate dimensional analysis approach to propose a fitting of the data in terms of the local parameters at perigee, as it would occur if this anomaly comes from an unknown fifth force with latitude dependence. Under this assumption, we estimate the range of this force around 300 km.

astro-ph.EP↗

arXiv2016

On the effect of ocean tides and tesseral harmonics on spacecraft flybys of the Earth

The so-called flyby anomaly has encouraged several authors to analyze in detail the minor perturbative contributions to the trajectory of spacecraft performing a flyby manoeuvre. This anomaly consist of an unexplained increase or decrease of the asymptotic velocity of the spacecraft after a flyby of the Earth in the range of a few mm per second. Some order of magnitude estimations have been performed in recent years to dismiss many possible conventional effects as the source of such an anomaly but no explanation has been found yet. In this paper we perform a study of the perturbation induced by ocean tides in a flybying spacecraft by considering the time dependence of the location of the high tide as the Moon follows its orbit. We show that this effect implies a change of the spacecraft velocity of a few micrometers per second. We also consider the coupling of tesseral harmonics inhomogeneities and the rotation of the Earth and its impact of the spacecraft outgoing velocity. Significant corrections to the observed asymptotic velocities are found in this case but neither their sign nor their magnitude coincide with the anomalies. So, we can also rule this out as a conventional explanation.

physics.space-ph↗

arXiv2016

On a correlation among azimuthal velocities and the flyby anomaly sign

Data of six flybys, those of Galileo I, Galileo II, NEAR, Cassini, Rosetta and Messenger were reported by Anderson et al \citep{Anderson}. Four of them: Galileo I, NEAR, Rosetta and Messenger gain Newtonian energy during the flyby transfer, while Galileo II and Cassini lose energy. This is, in both cases, a surprising anomaly since Newtonian forces derive from a potential and they are, therefore, conservative. We show here that the gravitational field of a rotating planet as derived from a new model introduces a non conservative force that gives a partial, but in our opinion satisfactory, explanation of these anomalies and suggests a correlation between the sign of the anomaly and the sign of the azimuthal velocity at perigee.

physics.space-ph↗

arXiv2015

Electromagnetic Waves in a Uniform Gravitational Field and Planck's Postulate

The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earth's surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The resulting gravitational time-dilation near these masses gives rise to a frequency change of any periodic process, including electromagnetic oscillations as the wave propagates across the gravitational field. This phenomenon can be tackled with classical electrodynamics assuming a curved spacetime background and Maxwell's equations in a generally covariant form. In the present paper, we show that in a classical field-theoretical context the gravitational redshift can be interpreted as the propagation of electromagnetic waves in a medium with corresponding conductivity $σ=g/(μ_0 c^3)$, where $g$ is the gravitational acceleration and $μ_0$ is the vacuum magnetic permeability. Moreover, the energy density of the wave remains proportional to its frequency in agreement with Planck's postulate.

gr-qc↗

arXiv2015

The flyby anomaly: A case for strong gravitomagnetism ?

In the last two decades an anomalous variation in the asymptotic velocity of spacecraft performing a flyby manoeuvre around Earth has been discovered through careful Doppler tracking and orbital analysis. No viable hypothesis for a conventional explanation of this effect has been proposed and its origin remains unexplained. In this paper we discuss a strong transversal component of the gravitomagnetic field as a possible source of the flyby anomaly. We show that the perturbations induced by such a field could fit the anomalies both in sign and order of magnitude. But, although the secular contributions to the Gravity Probe B experimental results and the Lense-Thirring effect in geodynamics satellites can be made null, the detailed orbital evolution is easily in conflict with such an enhanced gravitomagnetic effect.

gr-qc↗

arXiv2014

Anomalous Post-Newtonian terms and the secular increase of the Astronomical Unit

In the last decade a major debate has emerged on the astrophysics community concerning the anomalous behaviour of the astronomical unit, the fundamental scale of distances in the Solar system. Several independent studies have combined radar ranging and optical data from the last four decades to come to the conclusion that the astronomical unit is increasing by several meters per century. It is abundantly clear that General Relativity cannot account for this new effect, although an still undefined angular momentum transfer mechanism could provide the simpler and more conventional explanation. Here we investigate several anomalous post-newtonian terms containing only the product of the mass and angular momentum of the Sun as well as its Schwarzschild radius in order to determine if they could explain the secular increase of the astronomical unit and the recently reported increase of Lunar eccentricity. If these anomalies are confirmed, searching for a modification of General Relativity predicting these terms could have far-reaching consequences.

gr-qc↗

arXiv2012

The penetrable-sphere fluid in the high-temperature, high-density limit

We consider a fluid of $d$-dimensional spherical particles interacting via a pair potential $ϕ(r)$ which takes a finite value $ε$ if the two spheres are overlapped ($r<σ$) and 0 otherwise. This penetrable-sphere model has been proposed to describe the effective interaction of micelles in a solvent. We derive the structural and thermodynamic functions in the limit where the reduced temperature $k_BT/ε$ and density $ρσ^d$ tend to infinity, their ratio being kept finite. The fluid exhibits a spinodal instability at a certain maximum scaled density where the correlation length diverges and a crystalline phase appears, even in the one-dimensional model. By using a simple free-volume theory for the solid phase of the model, the fluid-solid phase transition is located.

cond-mat.stat-mech↗

arXiv2011

A WDM model for the evolution of galactic halos

It is a well-known fact that the gravitational effect of dark matter in galaxies is only noticeable when the orbital accelerations drop below $a_0 \simeq 2\times 10^{-8}$ cm s$^{-1}$ (Milgrom's Law). This peculiarity of the dynamic behaviour of galaxies was initially ascribed to a modification of Newtonian dynamics (MOND theory) and, consequently, it was used as an argument to criticize the dark matter hypothesis. In our model, warm dark matter is composed by collisionless Vlasov particles with a primordial typical velocity $\simeq 330$ km s$^{-1}$ and, consequently, they evaporated from galactic cores and reorganized in halos with a cusp at a finite distance from the galactic center (in contrast with Cold Dark Matter simulations which predict a cusp at the center of galaxies). This is confirmed by mean-field N-body simulations of the self-gravitating Vlasov dark matter particles in the potential well of the baryonic core. The rest mass of these particles, $μ$, is determined from a kinetic theory of the early universe with a cosmological constant. We find that $μ$ is in the range of a few keV. This result makes sterile neutrinos the best suited candidates for the main component of dark matter.

astro-ph.CO↗

arXiv2004

Average shape of fluctuations for subdiffusive walks

We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a table-like form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.

cond-mat.stat-mech↗

arXiv2004

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone.

cond-mat.stat-mech↗

arXiv2003

Some exact results for the trapping of subdiffusive particles in one dimension

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is made

cond-mat.stat-mech↗

arXiv2003

On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.

math.NA↗

arXiv2003

Order statistics of Rosenstock's trapping problem in disordered media

The distribution of times $t_{j,N}$ elapsed until the first $j$ independent random walkers from a set of $N \gg 1$, all starting from the same site, are trapped by a quenched configuration of traps randomly placed on a disordered lattice is investigated. In doing so, the cumulants of the distribution of the territory explored by $N$ independent random walkers $S_N(t)$ and the probability $Φ_N(t)$ that no particle of an initial set of $N$ is trapped by time $t$ are considered. Simulation results for the two-dimensional incipient percolation aggregate show that the ratio between the $n$th cumulant and the $n$th moment of $S_N(t)$ is, for large $N$, (i) very large in comparison with the same ratio in Euclidean media, and (ii) almost constant. The first property implies that, in contrast with Euclidean media, approximations of order higher than the standard zeroth-order Rosenstock approximation are required to provide a reasonable description of the trapping order statistics. Fortunately, the second property (which has a geometric origin) can be exploited to build these higher-order Rosenstock approximations. Simulation results for the two-dimensional incipient percolation aggregate confirm the predictions of our approach.

cond-mat.stat-mech↗

arXiv2003

Heat capacity of square-well fluids of variable width

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.

cond-mat.stat-mech↗