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.

On the Dominant Lunisolar Perturbations for Long-Term Eccentricity Variation: The Case of Molniya Satellite Orbits

The aim of this work is to investigate the main dominant terms of lunisolar perturbations that affect the orbital eccentricity of a Molniya satellite in the long term. From a practical point of view, these variations are important in the context of space situational awareness—for instance, to model the long-term evolution of artificial debris in a highly elliptical orbit or to design a reentry end-of-life strategy for a satellite in a highly elliptical orbit. The study assumes a doubly averaged model including the Earth’s oblateness effect and the lunisolar perturbations up to the third-order expansion. The work presents three important novelties with respect to the literature. First, the perturbing terms are ranked according to their amplitudes and periods. Second, the perturbing bodies are not assumed to move on circular orbits. Third, the lunisolar effect on the precession of the argument of pericenter is analyzed and discussed. As an example of theoretical a application, we depict the phase space description associated with each dominant term, taken as isolated, and we show which terms can apply to the relevant dynamics in the same region.

An Improved Equivalent Squint Range Model and Imaging Approach for Sliding Spotlight SAR Based on Highly Elliptical Orbit

As an emerging orbital system with flexibility and brand application prospects, the highly elliptical orbit synthetic aperture radar (HEO SAR) can achieve both a low orbit detailed survey and continuous earth surface observation in high orbit, which could be applied to marine reconnaissance and surveillance. However, due to its large eccentricity, two challenges have been faced in the signal processing of HEO SAR at present. The first challenge is that the traditional equivalent squint range model (ESRM) fails to accurately describe the entire range for the whole orbit period including the perigee, the apogee, and the squint subduction section. The second one is to exploit an efficient HEO SAR imaging algorithm in the squinted case which solves the problem that traditional imaging algorithm fails to achieve the focused imaging processing of HEO SAR during the entire orbit period. In this paper, a novel imaging algorithm for HEO SAR is presented. Firstly, the signal model based on the geometric configuration of the large elliptical orbit is established and the Doppler parameter characteristics of SAR are analyzed. Secondly, due to the particularity of Doppler parameters variation in the whole period of HEO, the equivalent velocity and equivalent squint angle used in MESRM can no longer be applied, a refined fourth-order equivalent squint range model(R4-ESRM) that is suitable for HEO SAR is developed by introducing fourth-order Doppler parameter into Modified ESRM (MESRM), which accurately reconstructs the range history of HEO SAR. Finally, a novel imaging algorithm combining azimuth resampling and time-frequency domain hybrid correlation based on R4-ESRM is derived. Simulation is performed to demonstrate the feasibility and validity of the presented algorithm and range model, showing that it achieves the precise phase compensation and well focusing.

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.

Specifics of designing trajectories of perspective spacecraft for Venus exploration

The paper describes the mission profile of the perspective Venus exploration project spacecraft with launches planned for 2027−2031. The main aspects of selecting the optimal launch dates are considered. The sequences of an orbiter injection to a highly elliptical orbit and a lander delivery to the surface of Venus are described. The rationale for the operating orbit as well as for the injection sequence that will enable Venus-to-Earth data transfer are provided. The lifespan of the lander, including its parachute descent, is limited by the high temperature of the lower atmosphere close to the surface (up to 460 degrees Celsius) and is expected to be no more than three hours. Therefore, a key feature of the mission profile development is designing the sequence of the orbital vehicle maneuvers, which ensures robust communication with the lander during this time within a range of 40 thousand kilometers.

Probabilistic Reasoning and Inconsistency Identification in Graph-based Models

In 1998, the National Aeronautics and Space Administration (NASA) launched the Mars Climate Orbiter (MCO) as part of the Mars Surveyor ’98 program. Upon arrival at Mars, MCO was to enter an elliptical orbit around the planet. On the day of orbit insertion, ground control was able to track the spacecraft visually up to the point when it vanished behind the planet. Unfortunately, the spacecraft never reappeared on the other side. It was later discovered that the probe came too close to the planet, and crashed into the Martian surface. The cause? A previously undiscovered mismatch in the use of unit systems for performing certain calculations in parts of the ground station software [43].