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Regular quaternion differential equations of the perturbed orbital motion of a cosmic body (in particular, a spacecraft, an asteroid) in the Earth’s gravitational field are considered, which take into account zonal, tesseral and sectorial harmonics of the field. These equations, unlike classical equations, are regular (do not contain special points such as singularity (division by zero)) for perturbed orbital motion in the central gravitational field of the Earth. In these equations, the main variables are four-dimensional Kustaanheim–Stiefel variables (KS-variables) or four-dimensional variables proposed by the author of the article, in which the equations of orbital motion have a simpler and symmetric structure compared to equations in KS-variables. Additional variables in the equations are orbital energy and time. The new independent variable is related to time by a differential relation containing the distance from the cosmic body to the Earth’s center of mass (the Sundman differential time transformation is used). Regular equations of perturbed orbital motion in quaternion osculating (slowly changing) variables are proposed. The equations are convenient for using methods of nonlinear mechanics and high-precision numerical calculations, in particular, for forecasting and correcting the orbital motion of spacecraft. In the case of orbital motion in the Earth’s gravitational field, the description of which takes into account the central and zonal harmonics of the field, the first integrals of the equations of orbital motion of the eighth order are given, changes of variables and transformations of these equations are considered, which made it possible to obtain closed systems of differential equations of the sixth order for the study of orbital motion, as well as systems of differential equations of the fourth and third orders, including a system of differential equations of the third order with respect to the distance from the cosmic body to the center of mass of the Earth and the sine of geocentric latitude, as well as a system of two integro-differential equations of the first order with respect to these two variables.

A magnetic micro stirrer bar (MMSB) is used in the mixing operation of microfluidic devices. We have established a low-cost and easy method to make MMSBs using magnetic (neodymium magnets, magnet sheets) or non-magnetic powders (SUS304) as materials. We demonstrated three kinds of MMSB have respective advantages. To confirm the practical use of this MMSB, a cell suspension of the motile unicellular green alga Chlamydomonas reinhardtii was stirred in microwells. As a result, the number of rotating cells increased with only one of the two flagella mechanically removed by the shear force of the rotating bar, which facilitates the kinetic analysis of the flagellar motion of the cell. The rotational motion of the monoflagellate cell was modeled as translational (orbital) + spinning motion of a sphere in a viscous fluid and the driving force per flagellum was confirmed to be consistent with previous literature. Since the present method does not use genetic manipulations or chemicals to remove a flagellum, it is possible to obtain cells in a more naturally viable state quickly and easily than before. However, since the components eluted from the powder material harm the health of cells, it was suggested that MMSB coated with resin for long-term use would be suitable for more diverse applications.

Direct imaging of exoplanetary systems is a powerful technique that can reveal Jupiter-like planets in wide orbits, can enable detailed characterization of planetary atmospheres, and is a key step toward imaging Earth-like planets. Imaging detections are challenging because of the combined effect of small angular separation and large luminosity contrast between a planet and its host star. High-contrast observations with the Keck and Gemini telescopes have revealed three planets orbiting the star HR 8799, with projected separations of 24, 38, and 68 astronomical units. Multi-epoch data show counter clockwise orbital motion for all three imaged planets. The low luminosity of the companions and the estimated age of the system imply planetary masses between 5 and 13 times that of Jupiter. This system resembles a scaled-up version of the outer portion of our solar system.

The advancement of on-orbit servicing and space debris removal missions has established high-precision visual perception for non-cooperative spacecraft as a key research focus. However, the availability of high-quality, diverse spacecraft image datasets is severely limited due to extreme on-orbit imaging conditions, data confidentiality, and morphological diversity of targets, significantly constraining the advancement of data-driven algorithms in this domain. To address this challenge, we propose a relative orbital motion-guided framework for generating multimodal visual data of spacecraft. The proposed method integrates an orbital dynamics model into the synthetic data generation pipeline to simulate typical relative motion patterns between the camera and the target in a realistic orbital environment, thereby generating image sequences characterized by continuous spatiotemporal evolution. Targeting four representative spacecraft—Tiangong, Spacedragon, ICESat, and Cassini—this work simultaneously generates a dataset comprising 8000 samples, each containing four strictly aligned modalities: RGB images, instance segmentation masks, depth maps, and surface normal maps, along with precise 6-degree-of-freedom (6-DoF) pose ground truth. Furthermore, an end-to-end physical image degradation model is developed to accurately simulate the complete imaging chain—from optical diffraction and aberrations to sensor sampling and noise—thereby effectively narrowing the domain gap between synthetic and real data. By addressing three key aspects—physical motion modeling, synchronous multimodal ground truth, and imaging degradation simulation—this work provides a crucial data foundation for training, testing, and validating data-driven on-orbit perception algorithms.

We present a theoretic analysis on (azimuthal) spin momentum-dependent orbital motion experienced by particles in a circularly-polarized annular focused field. Unlike vortex phase-relevant (azimuthal) orbital momentum flow whose direction is specified by the sign of topological charge, the direction of (azimuthal) spin momentum flow is determined by the product of the field's polarization ellipticity and radial derivative of field intensity. For an annular focused field with a definite polarization ellipticity, the intensity's radial derivative has opposite signs on two sides of the central ring (intensity maximum), causing the spin momentum flow to reverse its direction when crossing the central ring. When placed in such a spin momentum flow, a probe particle is expected to response to this flow configuration by changing the direction of orbital motion as it traversing from one side to the other. The reversal of the particle's orbital motion is a clear sign that spin momentum flow can affect particles' orbital motion alone even without orbital momentum flow. More interestingly, for dielectric particles the spin momentum-dependent orbital motion tends to be 'negative', i.e., in the opposite direction of the spin momentum flow. This arises mainly because of spin-orbit interaction during the scattering process. For the purpose of experimental observation, we suggest the introduction of an auxiliary radially-polarized illumination to adjust the particle's radial equilibrium position, for the radial gradient force of the circularly-polarized annular focused field tends to constrain the particle at the ring of intensity maximum.

The image-charge detection provides a new direct method for the detection of the Rydberg transition of electrons trapped on the surface of liquid helium. The interest in this method is motivated by the possibility to accomplish the spin state readout for a single trapped electron, thus opening a new pathway towards using electron spins on liquid helium for quantum computing. Here, we report on the image-charge detection of the Rydberg transition in a many-electron system confined in an array of 20 μ m wide and 4 μ m deep channels filled with superfluid helium. Such detection is made possible because of a significant enhancement of the image-charge signal due to close proximity of trapped electrons to the electrodes embedded in the microchannel structure. The transition frequency of electrons in the range of 400–500 GHz is highly controllable by the dc bias voltages applied to the device and is in a good agreement with our calculations. This work demonstrates that microchannel structures provide a suitable platform for electron manipulation and their quantum state detection, with a feasibility of scaling the detection method to a single electron.

Sun-Earth co-orbital motions have an important value in deep space explorations due to their unique orbital characteristics and spatial configurations. In this paper, we investigate the influence of the solar radiation pressure (SRP) on the Sun-Earth co-orbital motion. Firstly, we derive several analytical formulas of the effect of the SRP on orbital elements. Then, based on the analytical results, the orbital variables of perturbed distant retrograde orbits (DROs) and perturbed tadpole (TP) orbits around triangular libration points are studied, and the validity of those conclusions is demonstrated by numerical integration. Finally, we derive an approximate expression to analyze the drift trend of triangular libration points under the SRP and explain the drift phenomena of libration centers of perturbed co-orbital motions. The conclusions obtained in this paper could be used to design control laws of the perturbed Sun-Earth co-orbital motion in the future.

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill’s sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill’s sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

We study the motion of an asteroid being in retrograde 1/1 resonance with Jupiter (co-orbital motion). We consider the planar case (i=180°) and Jupiter is on a circular or elliptic orbit (e′ = 0.048). In the cirular model we compute families of symmetric periodic orbits and their stability type. In the elliptic model we have isolated periodic orbits which affect the orbital modes of motion as it is shown by the FLI dynamical maps.