Relativistic Effects for a Hydrogen Rydberg Atom in a High-Frequency Laser Field: Analytical Results

Previously published analytical results for the effects of a high-frequency laser field on hydrogen Rydberg atoms demonstrated that the unperturbed elliptical orbit of the Rydberg electron, generally is engaged simultaneously in the precession of the orbital plane about the direction of the laser field and in the precession within the orbital plane. These results were obtained while disregarding relativistic effects. In the present paper, we analyze the relativistic effect for hydrogenic Rydberg atoms or ions in a high-frequency linearly- or circularly-polarized laser field, the effect being an additional precession of the electron orbit in its own plane. For the linearly-polarized laser field, the general case, where the electron orbit is not perpendicular to the direction of the laser field, we showed that the precession of the electron orbit within its plane can vanish at some critical polar angle θc of the orbital plane. We calculated analytically the dependence of the critical angle on the angular momentum of the electron and on the parameters of the laser field. Finally, for the particular situation, where the electron orbit is perpendicular to the direction of the laser field, we demonstrated that the relativistic precession and the precession due to the laser field occur in the opposite directions. As a result, the combined effect of these two kinds of the precession is smaller than the absolute value of each of them. We showed that by varying the ratio of the laser field strength F to the square of the laser field frequency ω, one can control the precession frequency of the electron orbit and even make the precession vanish, so that the elliptical orbit of the electron would become stationary. This is a counterintuitive result.

A Review of Routing Algorithms Based on Multi-Layer Satellite Networks

Compared with single layer satellite network, satellite distribution of multi-layer satellite networks in the double layer or multilayer orbital plane, combines all the advantages of engaging subjects of the satellite, therefore contains its low vulnerability, good robustness, high stability, high spectrum efficiency and system throughput, channel characteristics such as large capacity, in the satellite network is a very promising direction. Multilayer satellite network also has some inevitable disadvantages, that is, the number of nodes and the number of links is large, so it has the characteristics of frequent changes in network topology, which requires higher routing algorithm. There are many researches on routing algorithms based on multi-layer satellite networks at home and abroad. This paper introduces the general situation of multi-layer satellite network, classifies the existing routing algorithms of multi-layer satellite network according to different standards, analyzes several typical routing algorithms in detail, points out the advantages and disadvantages, and summarizes the future development trend.

Numerical modeling of a proton spin-flipping system in the spin transparency mode at an integer spin resonance in JINR's Nuclotron

In this paper we propose a lattice insertion for the Nuclotron ring called a “spin navigator” that can adjust any direction of the proton polarization in the orbital plane using weak solenoids. The polarization control is realized in the spin transparency mode at the energy of 108 MeV, which corresponds to the integer spin resonance γ G = 2. The requirements on the navigator solenoid fields are specified considering the criteria for stability of the spin motion during any manipulation of the polarization direction in an experiment. The paper presents the results of numerical modeling of the proton spin dynamics in the Nuclotron ring operated in the spin transparency mode. The verified spin navigator is aimed at an experimental study of a spin-flipping system using the Nuclotron ring. The results are relevant to the NICA (JINR), EIC (BNL) and COSY (FZJ) facilities where the spin transparency mode can be applied for polarization control.

The Clustering of Orbital Poles Induced by the LMC: Hints for the Origin of Planes of Satellites

A significant fraction of Milky Way (MW) satellites exhibit phase-space properties consistent with a coherent orbital plane. Using tailored N-body simulations of a spherical MW halo that recently captured a massive (1.8 × 1011 M ⊙) LMC-like satellite, we identify the physical mechanisms that may enhance the clustering of orbital poles of objects orbiting the MW. The LMC deviates the orbital poles of MW dark matter particles from the present-day random distribution. Instead, the orbital poles of particles beyond R ≈ 50 kpc cluster near the present-day orbital pole of the LMC along a sinusoidal pattern across the sky. The density of orbital poles is enhanced near the LMC by a factor δ ρ max = 30% (50%) with respect to underdense regions and δ ρ iso = 15% (30%) relative to the isolated MW simulation (no LMC) between 50 and 150 kpc (150–300 kpc). The clustering appears after the LMC’s pericenter (≈50 Myr ago, 49 kpc) and lasts for at least 1 Gyr. Clustering occurs because of three effects: (1) the LMC shifts the velocity and position of the central density of the MW’s halo and disk; (2) the dark matter dynamical friction wake and collective response induced by the LMC change the kinematics of particles; (3) observations of particles selected within spatial planes suffer from a bias, such that measuring orbital poles in a great circle in the sky enhances the probability of their orbital poles being clustered. This scenario should be ubiquitous in hosts that recently captured a massive satellite (at least ≈1:10 mass ratio), causing the clustering of orbital poles of halo tracers.

Evolution of the rotational motion of a viscoelastic planet with a core on an elliptical orbit

The work is devoted to the study of the evolution of the rotational motion of a planet in the central Newtonian field of forces. The planet is modeled by a body consisting of a solid core and a viscoelastic shell rigidly attached to it. A limited formulation of the problem is considered, when the center of mass of the planet moves along a given Keplerian elliptical orbit. The equations of motion are derived in the form of a system of Routh equations using the canonical Andoyer variables, which are “action-angle” variables in the unperturbed problem and have the form of integro-differential equations with partial derivatives. The technique developed by V.G. Vilke is used for mechanical systems with an infinite number of degrees of freedom. A system of ordinary differential equations is obtained by the method of separation of motions. The system describes the rotational motion of the planet taking into account the perturbations caused by elasticity and dissipation. An evolutionary system of equations for the “action” variables and slow angular variables is obtained by the averaging method. A phase portrait is constructed that describes the mutual change in the modulus of the angular momentum vector G of the rotational motion and the cosine of the angle between this vector and the normal to the orbital plane of the planet’s center of mass. A stationary solution of the evolutionary system of equations is found, which is asymptotically stable. It is shown that in stationary motion, the angular momentum vector G is orthogonal to the orbital plane, and the limiting value of the modulus of this vector depends on the eccentricity of the elliptical orbit. The constructed mathematical model can be used to study the tidal evolution of the rotational motion of planets and satellites. The results obtained in this work are consistent with the results of previous studies in this area.

ON THE EFFECTS OF SOLAR RADIATION PRESSURE ON THE DEVIATION OF ASTEROIDS

In this work, we study the effects of solar radiation pressure (SRP) on the problem of changing the orbit of an asteroid to support planetary defense, scientific research, or exploitation of materials. This alternative considers a tethered reflective balloon (or a set of reflective balloons) attached to the asteroid, with a high area-to-mass ratio, to use the SRP to deflect a potentially hazardous asteroid (PHA) or to approximate the target asteroid to Earth. The tether is assumed to be inextensible and massless, and the motion is described only in the orbital plane of the asteroid around the Sun. The model is then used to study the effects that the tether length, the reflectivity coefficient, and the area-to-mass ratio have on the deviation of the trajectory of the asteroid.

Conceptual design studies of an electrically propelled upper stage for deployment of a multi-plane orbital constellation of small spacecraft

The paper presents results of conceptual design studies to determine configuration of an electrically propelled upper stage (EPUS) – a space transportation stage (a space tug) with main engines based on electric propulsion powered by solar arrays. It addresses the problem of deploying a multi-plane orbital constellation of small spacecraft (SSC) using an electrically propelled upper stage. It proposes to change the SSC operational orbital planes based on the effect of the difference in precession rates between the parking and the working orbits owing to the effect of eccentricity in the Earth gravitational field. Requirements have been defined for the EPUS electrical propulsion system that take into account the need to operate it to offset the aerodynamic drag while waiting in the parking orbit for the SSC operational orbital plane to turn. It demonstrates the feasibility of employing four EPUS that use Stationary Plasma Thruster-type electric propulsion as their main engines and gallium arsenide solar arrays for deployment in a 600 km orbit in four planes an orbital constellation of 24 small spacecraft with a mass of ~250 kg each using one launch of a medium capacity launch vehicle of Soyuz-2.1b type. Key words: Electrically propelled upper stage, electric propulsion, small spacecraft, orbital constellation.

Conceptual design studies of an electrically propelled upper stage for deployment of a multi-plane orbital constellation of small spacecraft

The paper presents results of conceptual design studies to determine configuration of an electrically propelled upper (a space tug) with main engines arrays. It addresses the problem stage (EPUS) — a space transportation stage based on electric propulsion powered by solar of deploying a multi-plane orbital constellation of to in of small spacecraft (SSC) using an electrically propelled upper stage. It proposes change the SSC operational orbital planes based on the effect of precession rates between the parking and the working orbits eccentricity in the Earth gravitational field. Requirements owing have the difference to the effect been defined for the EPUS electrical propulsion system that take into account the need to operate it to offset the aerodynamic drag while waiting in the parking orbit for the SSC operational orbital plane to turn. It demonstrates the feasibility of employing four EPUS that use Stationary Plasma Thruster-type electric propulsion as their main engines and gallium arsenide solar arrays for deployment in a 600 km orbit in four planes an orbital constellation of 24 small spacecraft with a mass of ~250 kg each using one launch of a medium capacity launch vehicle of Soyuz-2.1b type.

Evolutionary Optimization of Multirendezvous Impulsive Trajectories

This paper investigates the use of evolutionary algorithms for the optimization of time-constrained impulsive multirendezvous missions. The aim is to find the minimum- Δ V trajectory that allows a chaser spacecraft to perform, in a prescribed mission time, a complete tour of a set of targets, such as space debris or artificial satellites, which move on the same orbital plane at slightly different altitudes. For this purpose, a two-level design approach is pursued. First, an outer-level combinatorial problem is defined, dealing with the simultaneous optimization of the sequence of targets and the rendezvous epochs. The suggested approach is first tested by assuming that all transfer legs last exactly the same amount of time; then, the time domain is discretized over a finer grid, allowing a more appropriate sizing of the time window allocated for each leg. The outer-level problem is solved by an in-house genetic algorithm, which features an effective permutation-preserving solution encoding. A simple, but fairly accurate, heuristic, based on a suboptimal four-impulse analytic solution of the single-target rendezvous problem, is used when solving the combinatorial problem for a fast guess at the transfer cost, given the departure and arrival epochs. The outer-level problem solution is used to define an inner-level NLP problem, concerning the optimization of each body-to-body transfer leg. In this phase, the encounter times are further refined. The inner-level problem is tackled through an in-house multipopulation self-adaptive differential evolution algorithm. Numerical results for case studies including up to 20 targets with different time grids are presented.