Optical Observations Research Articles

Constraining gravitational wave velocities using gravitational and electromagnetic wave observations of white dwarf binaries

ABSTRACT Although the general theory of relativity (GR) predicts that gravitational waves (GWs) have exactly the same propagation velocity as electromagnetic (EM) waves, many theories of gravity beyond GR expect otherwise. Accurate measurement of the difference in their propagation speed, or a tight constraint on it, could be crucial to validate or put limits on theories beyond GR. The proposed future space-borne GW detectors are poised to detect a substantial number of Galactic white dwarf binaries (GWDBs), which emit the GW as semimonochromatic signals. Concurrently, these GWDBs can also be identified as optical variable sources. Here we proposed that allocating a GWDB’s optical light curve and contemporaneous GW signal can be used to trace the difference between the velocity of GW and EM waves. Simulating GW and EM wave data from 14 verification binaries (VBs), our method constrains propagation-originated phase differences, limiting the discrepancy between the speed of light (c) and GW ($c_{GW}$). Through the utilization of LISA’s design sensitivity and the current precision in optical observation on GWDB, our study reveals that a four-year observation of the 14 recognized VBs results in a joint constraint that confines $\Delta c/c$ ($\Delta c = c_{\mathrm{GW}} - c$) to the range of $-2.1\times 10^{-12}$ and $4.8\times 10^{-12}$. Additionally, by incorporating this constraint on $c_{\mathrm{GW}}$, we are able to establish boundaries for the mass of the graviton, limiting it to $m_{\mathrm{g}}\le 3\times 10^{-23}\, e\mathrm{V}\,c^{-2}$, and for the parameter associated with local Lorentz violation, $\bar{s}_{00}$, constrained within the range of $-3.4\times 10^{-11}\le \bar{s}_{00}\le 1.5\times 10^{-11}$.

Monitoring discharge from deep-sea mining ships via optical satellite observations

Monitoring discharge from deep-sea mining ships via optical satellite observations

Improving correlation based super-resolution microscopy images through image fusion by self-supervised deep learning

Super-resolution imaging is a powerful tool in modern biological research, allowing for the optical observation of subcellular structures with great detail. In this paper, we present a deep learning approach for image fusion of intensity and super-resolution optical fluctuation imaging (SOFI) microscopy images. We construct a network that can successfully combine the advantages of these two imaging methods, producing a fused image with a resolution comparable to that of SOFI and an SNR comparable to that of the intensity image. We also demonstrate the effectiveness of our approach experimentally, specifically on cell samples where microtubules were stained with ATTO647N and imaged using a confocal microscope with a single photon fiber bundle camera, allowing for the simultaneous acquisition of an image scanning microscopy (ISM) image and a SOFISM (ISM and SOFI) image. Our network is designed as a self-supervised network and shows the ability to train on a single pair of images and to generalize to other image pairs without the need for additional training. Our approach offers a flexible and efficient way to combine the strengths of correlation based imaging techniques along with traditional intensity based microscopy, and can be readily applied to other fluctuation based imaging modalities.

New Series of Hydrogen-Bonded Liquid Crystal with High Birefringence and Conductivity.

Liquid crystals with high dielectric anisotropy, low operational thresholds, and significant birefringence (Δn) represent a key focus in soft matter research. This work introduces a novel series of hydrogen-bonded liquid crystals (HBLCs) derived from 4-n-alkoxybenzoic, 4-alkoxy-3-fluorobenzoic derivatives (nOBAF), 4-alkoxy-2,3-fluorobenzoic derivatives (nOBAFF), and 2-fluoro-4-nitrobenzoic acid. The HBLCs were characterized using Fourier transform infrared spectroscopy, and their thermal behavior was evaluated via differential scanning calorimetry. Optical observations were conducted using polarized optical microscopy. The results indicate that mixtures containing benzoic acid with a bilateral fluorine substituent exhibit both SmA and SmC phases, while those with a unilateral fluorine substituent exhibit nematic and SmA phases. Moreover, an increase in the length of the alkoxy chain results in an expanded mesophase temperature range. This study demonstrates that the presence of a fluorine substituent and the incorporation of an NO2 group in the molecular structure result in an increase in dielectric permittivity, DC conductivity, dielectric anisotropy, and birefringence.

Inverse estimation of tensile shear strength from fracture surface images using deep learning

To improve the long-term durability of adhesive joints, it is important to analyse the fracture surface and identify the fracture factors. Although conventional optical observation methods are simple and widely used, they were limited to qualitative discussions. In this study, an inverse estimation method utilising deep learning was investigated to clarify the quantitative relationship between the tensile shear strength and the fracture surface of single lap joints immersed in water. The deep learning analysis revealed that the tensile shear strength could be estimated from the fracture surface images with very high accuracy, indicating a strong quantitative correlation between the fracture surface images and the residual tensile shear strength. Grad-CAM indicated that the deep learning model could estimate the residual tensile shear strength by observing from the topology and colour of the remaining adhesive.

Siliceous deposition in limestone-marl alternations of the Yangtze Carbonate platform during the Permian Chert Event

During the Permian Chert Event (PCE), limestone-marl alternations (LMAs), contemporaneously developing in the Yangtze region with chert-mudstone alternations, differed from typical LMAs by their enrichment in authigenic siliceous components (quartziferous components and Mg-phyllosilicates). However, the factors driving the transition from distal chert deposits to proximal siliceous-rich carbonate deposits remain unclear, and the genesis of authigenic siliceous components is puzzling. Resolving these issues could provide a deeper understanding of the paleoclimate and paleoenvironment during the PCE. Optical and SEM observations and geochemical analyses revealed that Si4+, derived from seawater, silica-secreting organisms, and terrigenous clasts, precipitated as authigenic quartziferous components under relatively acidic conditions, while it precipitated as Mg-phyllosilicates through reverse weathering by combining with the dissolved high-Mg calcites under relatively alkaline conditions. Through the facies division of LMAs, its variations describe relative and short-term sea-level fluctuations in the Yangtze Carbonate Platform (YCP). By integrating tendency comparisons and time series analyses of sea level fluctuations, continental weathering intensity, authigenic siliceous content, and relative proportions of quartz vs. Mg-phyllosilicates, four proxies exhibit covariation and similar astronomical signals, indicating that the high sea level period of the YCP, corresponding to intensified continental weathering, favored the deposition of authigenic siliceous components and reverse weathering. Because the facies variations encompass short eccentricity, obliquity, and precession cycles, sea level fluctuations are considered to have been influenced by Gondwana glaciation P3. The seawater in the continental shelf cooled and became rich in silica and nutrients under the effect of upwelling. Interglacial periods may trigger high sea levels and intensified continental weathering in the YCP, facilitating the influx of Si-rich eutrophic seawater and stimulating biological silica secretion by radiolarians. However, the direct precipitation of activated silica resulted in weakened reverse weathering. Consequently, the lithological transformation from distal to proximal areas during the PCE was attributed to differences in silica-secreting organism abundance, upwelling intensity, biological pump activity, reverse weathering intensity, OM abundance, pH conditions, and seawater temperature between the continental shelf and carbonate platform.

HYPSTAR: a hyperspectral pointable system for terrestrial and aquatic radiometry

Optical Earth observation satellites provide vast amounts of data on a daily basis. The top-of-atmosphere radiance measured by these satellites is usually converted to bottom-of-atmosphere radiance or reflectance which is then used for deriving numerous higher level products used for monitoring environmental conditions, climate change, stock of natural resources, etc. The increase of available remote sensing data impacts decision-making on both regional and global scales, and demands appropriate quality control and validation procedures. A HYperspectral Pointable System for Terrestrial and Aquatic Radiometry (HYPSTAR®) has been designed to provide automated, in-situ multiangular reflectance measurements of land and water targets. HYPSTAR-SR covers 380–1020 nm spectral range at 3 nm spectral resolution and is used at water sites. For land sites the HYPSTAR-XR variant is used with the spectral range extended to 1680 nm at 10 nm spectral resolution. The spectroradiometer has multiplexed radiance and irradiance entrances, an internal mechanical shutter, and an integrated imaging camera for capturing snapshots of the targets. The spectroradiometer is mounted on a two-axis pointing system with 360° range of free movement in both axes. The system also incorporates a stable light emitting diode as a light source, used for monitoring the stability of the radiometric calibration during the long-term unattended field deployment. Autonomous operation is managed by a host system which handles data acquisition, storage, and transmission to a central WATERHYPERNET or LANDHYPERNET server according to a pre-programmed schedule. The system is remotely accessible over the internet for configuration changes and software updates. The HYPSTAR systems have been deployed at 10 water and 11 land sites for different periods ranging from a few days to a few years. The data are automatically processed at the central servers by the HYPERNETS processor and the derived radiance, irradiance, and reflectance products with associated measurement uncertainties are distributed at the WATERHYPERNET and LANDHYPERNET data portals.

LONEStar: The Lunar Flashlight Optical Navigation Experiment

This paper documents the results from the highly successful Lunar flashlight Optical Navigation Experiment with a Star tracker (LONEStar). Launched in December 2022, Lunar Flashlight (LF) was a NASA-funded technology demonstration mission. After a propulsion system anomaly prevented capture in lunar orbit, LF was ejected from the Earth-Moon system and into heliocentric space. NASA subsequently transferred ownership of LF to Georgia Tech to conduct an unfunded extended mission to demonstrate further advanced technology objectives, including LONEStar. From August to December 2023, the LONEStar team performed on-orbit calibration of the optical instrument and a number of different OPNAV experiments. This campaign included the processing of nearly 400 images of star fields, Earth and Moon, and four other planets (Mercury, Mars, Jupiter, and Saturn). LONEStar provided the first on-orbit demonstrations of heliocentric navigation using only optical observations of planets. Of special note is the successful in-flight demonstration of (1) instantaneous triangulation with simultaneous sightings of two planets with the LOST algorithm and (2) dynamic triangulation with sequential sightings of multiple planets.

Direct observation on the phase separation of polymer membrane embryos confined by microfluidics chips

In this paper, the growth of finger-like droplets inside various polymer membrane embryos induced by non-solvent phase separation (NIPS) is studied in details by using a standardized optical microscopic observation method. The boundary conditions of the phase separation are well-defined by microfluidics technology. The growth of finger-like droplets and Marangoni convection inside them are tracked and recorded by high-speed camera of sharp resolutions. Effects of the geometry of the membrane embryos (thickness/shape/size), humidity of the atmosphere and the viscosity of the embryos on the growth of finger-like droplets are systematically studied. Except the qualitative observations that are consistent to previous relative reports, more quantitative data are provided in this paper. The diffusing speed of the interface of the developing large droplets is measured by template matching algorithm. Strikingly, the time-dependent diffusing speed of the developing large droplets shows a wave-like declining pattern, which indicates that fluctuating boundary conditions are surrounding the membrane embryos. The Reynolds number of the flow inside the developing large droplets is estimated at the order of 10−5, the magnitude of which is 2 order smaller than that of a swimming sperm.

AI AND ANDROID APP BASED TOMATO PLANT DISEASE PREDICTION SYSTEM

Plant diseases are one of the grand challenges that face the agriculture sector worldwide. In the United States, crop diseases cause losses of one-third of crop production annually. Despite the importance, crop disease diagnosis is challenging for limited-resources farmers if performed through optical observation of plant leaves’ symptoms. Therefore, there is an urgent need for markedly improved detection, monitoring, and prediction of crop diseases to reduce crop agriculture losses. Computer vision empowered with Machine Learning (ML) has tremendous promise for improving crop monitoring at scale in this context. This paper presents an ML-powered mobile-based system to automate the plant leaf disease diagnosis process. The developed system uses Convolutional Neural networks (CNN) as an underlying deep learning engine for classifying 38 disease categories. We collected an imagery dataset containing 96,206 images of plant leaves of healthy and infected plants for training, validating, and testing the CNN model. The user interface is developed as an Android mobile app, allowing farmers to capture a photo of the infected plant leaves. It then displays the disease category along with the confidence percentage. It is expected that this system would create a better opportunity for farmers to keep their crops healthy and eliminate the use of wrong fertilizers that could stress the plants. Finally, we evaluated our system using various performance metrics such as classification accuracy and processing time. We found that our model achieves an overall classification accuracy of 94% in recognizing the most common 38 disease classes in 14 crop species. Keywords: plant leaf diseases; agriculture; mobile app; convolutional neural networks (CNN); deep learning

Reinforcement-Learning-Based Robust Guidance for Asteroid Approaching

This paper presents a reinforcement-learning (RL)-based robust low-thrust guidance method for asteroid approaching under process uncertainties. Markov decision processes with stochastic dynamics are formulated for RL. To overcome the problem of low terminal accuracy in RL-based transfer trajectory design, robust zero-effort-miss/zero-effort-velocity (R-ZEM/ZEV) guidance is proposed. Originally, an eigenvalue-related term is defined according to the stability conditions of the ZEM/ZEV feedback system and chosen as the learning parameter, which can significantly improve the robustness of the agent to process uncertainties under the low-thrust magnitude constraint. Moreover, the navigation performance of the asteroid approaching is modeled via the Fisher information matrix and incorporated in the reward function design, which enables optimizing the optical observation performance together with the propellant cost. Thereafter, the proximal policy optimization is adopted to train an RL agent that can efficiently deal with the uncertainties. The effectiveness and efficiency of the proposed method are validated through simulations of a low-thrust spacecraft approaching the asteroid Bennu. The promising results indicate that the proposed method can not only deal with various uncertainties efficiently and autonomously but can also guarantee high terminal accuracy.

Exploiting Turmeric’s Coloring Capability to Develop a Functional Pigment for Wood Paints: Sustainable Coloring Process of Polyamide 11 Powders and Their Strengthening Performance

Currently, the wood coatings industry is focusing on creating unique, vibrant finishes using new functional pigments. Simultaneously, there is a growing adoption of eco-friendly bio-based materials, reflecting trends in other sectors and supporting the circular economy. Thus, the aim of this study is to unveil a straightforward, cost-effective, and notably sustainable process for exploiting the coloring potential of turmeric powder and coloring polyamide 11-based fillers, employed as multifunctional pigments for wood coatings. Through the incorporation of this additive into a wood paint, the study demonstrates its dual effect of enhancing the aesthetics of the final composite layer while leveraging the beneficial protective properties inherent to polyamide 11. The impact of these additives on sample aesthetics is assessed through optical observations, as well as measurements of color, gloss, and surface roughness. The strengthening contribution of the functional pigment is evaluated using the Taber abrasion resistance test, static friction coefficient measurements, and Buchholz surface hardness test. Finally, the aesthetic consistency of the bio-based filler and the coloring efficiency of the sustainable process are tested by subjecting the samples to aggressive conditions, including the UV-B chamber exposure test, cold liquids resistance tests, and water uptake test. Ultimately, the study illustrates how this functional bio-based pigment not only provides sufficient protection but also meets current eco-requirements, thereby contributing to the sustainability of the wood coatings industry.

Testing particle acceleration in blazar jets with continuous high-cadence optical polarization observations

Variability can be the pathway to understanding the physical processes in astrophysical jets. However, the high-cadence observations required to test particle acceleration models are still missing. Here we report on the first attempt to produce continuous, $>24$ hour polarization light curves of blazars using telescopes distributed across the globe, following the rotation of the Earth, to avoid the rising Sun. Our campaign involved 16 telescopes in Asia, Europe, and North America. We observed BL Lacertae and CGRaBS J0211+1051 for a combined 685 telescope hours. We find large variations in the polarization degree and angle for both sources on sub-hour timescales as well as a $ rotation of the polarization angle in CGRaBS J0211+1051 in less than two days. We compared our high-cadence observations to particle-in-cell magnetic reconnection and turbulent plasma simulations. We find that although the state-of-the-art simulation frameworks can produce a large fraction of the polarization properties, they do not account for the entirety of the observed polarization behavior in blazar jets.

The important role of diatomite on multifunctional modified separator of Li-S battery

The commercial applications of lithium-sulfur (Li-S) batteries are limited by decreased cycling performance caused by the shuttle effect of polysulfides, slower kinetic reaction rates, and lithium anode dendrites. This study demonstrates the important role of diatomite (DT) in regulating cycle performance of modified separator for Li-S batteries. A multifunctional separator (Co/NC/DT) with DT as a carrier assembled high loading cobalt nanocluster is prepared. The N-doped carbon is immobilized via Si-N bond between DT and N-doped carbon. The depth profiles of XPS indicate that the ratio of pyrrolic N to pyridinic N of Co/NC/DT reaches 5.31 at the etching of 100 nm versus 0.83 for Co/NC at surface, which suggesting that mainly N species is pyrrolic N after the addition of DT. Theoretical calculations confirm that cobalt nanoclusters grown on pyrrolic N-doped carbon have a lower adsorption energy for active materials compared to that on pyridinic N-doped carbon and can reduce the energy barrier, especially only 0.09 eV for reduction from Li2S6 to Li2S4. In-situ X-ray diffraction analysis confirms Co/NC/DT can effectively promote formation of Li2S. Lithium anode in-situ optical microscopy observation shows the modified separator could reduce lithium dendrites effectively. Li-S battery assembled with the modified separator can reach an initial capacity of 1331.3 mAh g−1 at 0.2 C and cycle 1500 cycles at 1.0 C with a decay of only 0.039% per cycle. Through regulation of DT, Co/NC/DT accelerates the conversion from long-chain sulfur to short-chain sulfur and Li+ transfer rate, resulting in improving cycling performance.

Uncovering the hetero-hydrophobic attraction between the basal planes of molybdenite and talc under flotation conditions

The very close natural floatability of molybdenite and talc has been traditionally believed as the main reason for their separation problem. However, the interactions between the basal and edge planes of the two platy minerals remain unclear. Here the hydrophobic attraction between the basal planes was proposed as the dominating factor for that problem. Flotation tests in both single and mixed mineral systems were conducted using carboxymethyl cellulose (CMC) as talc depressant and sodium isobutyl xanthate (SIBX) as molybdenite collector. Zeta potential distribution, contact angle, in situ optical microscope observation, EDLVO calculation and surface energy analysis were applied to reveal the surfacial actions between the basal and edge planes of molybdenite and talc. Molybdenite and talc showed obvious floatability difference in single mineral system, however, their separation efficiency met with big decline in mixed mineral system. Zeta potential results demonstrated that, in the presence of CMC and SIBX, negatively charged particles of molybdenite and talc aggregated rather than electrostatically repulsed and dispersed. The contact angle and particle adhesion results showed a certain degree of selective attraction between the basal planes of molybdenite and talc. The EDLVO calculation suggested the attractive interactions were ranked as: Mb(basal)-Tlc(edge) > Mb(basal)-Tlc(basal) ≈ Mb(edge)-Tlc(edge) > Mb(edge)-Tlc(basal). The surface energy calculation pointed out that the fundamental reason for the separation problem was exactly the hetero-hydrophobic attraction between their basal planes.

A systematic first-principles investigation of the structural, electronic, mechanical, optical, and thermodynamic properties of Half-Heusler ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn) for spintronics and optoelectronics applications.

This paper is the first to look at the structural, electronic, mechanical, optical, and thermodynamic properties of the ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn) half-Heusler (HH) using DFT based first principles method. The lattice parameters that we have calculated are very similar to those obtained in prior investigations with theoretical and experimental data. The positive phonon dispersion curve confirm the dynamical stability of ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn). The electronic band structure and DOS confirmed that the studied materials ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn) are direct band gap semiconductors. The investigation also determined significant constants, including dielectric function, absorption, conductivity, reflectivity, refractive index, and loss function. These optical observations unveiled our compounds potential utilization in various electronic and optoelectronic device applications. The elastic constants were used to fulfill the Born criteria, confirming the mechanical stability and ductility of the solids ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn). The calculated elastic modulus revealed that our studied compounds are elastically anisotropic. Moreover, ANiX (ASc, Ti, Y, Zr, Hf; XBi, Sn) has a very low minimum thermal conductivity (Kmin), and a low Debye temperature (θD), which indicating their appropriateness for utilization in thermal barrier coating (TBC) applications. The Helmholtz free energy (F), internal energy (E), entropy (S), and specific heat capacity (Cv) are determined by calculations derived from the phonon density of states.

Contribution of landmark-tracking data to the estimation of the gravity field and rotation parameters of 311P/PANSTARRS for the incoming Tianwen-2 space mission

311P/PANSTARRS is one of the two targets of the Chinese asteroid exploration mission Tianwen-II. The estimation of the gravity field and rotation parameters is an important part of the mission. Optical landmark observations directly record the relative relationship between the asteroid and probe. For this purpose, we investigate the role of the addition of landmark observations to radio-tracking data in achieving precise orbit determination and deriving the physical parameters of 311P. More specifically, we use a linear re-weighting fusion scheme to aggregate these two heterogeneous data to determine 311P's gravitational field and rotational parameters. Our results show that landmark observations enhance parameter estimation drastically. We conduct extensive experiments to understand how to optimize the use of landmark observations. Besides, we find that the upper bound error on 311P ephemeris for estimating a 2nd-degree gravity field model is 5 km.

Schlieren measurements of shock train flow fields in a supersonic cylindrical isolator at Mach 2

In a supersonic cylindrical isolator at Mach 2, the structures and frequency characteristics of shock train flow fields were experimentally studied by the schlieren measurement method. According to the design principle of parallel light through schlieren windows in a cylindrical duct, a high-precision conformal optical window pair was designed and integratively processed before. Based on a self-built pipeline structure with conformal windows in a direct-connect wind tunnel under adjustable back-pressure conditions, the shock surfaces in a cylindrical isolator at Mach 2 were first captured by the schlieren method. Then, the schlieren photographs were corrected by a nonlinear image transformation algorithm for the restoration of real shock train structures, and the experimental results were compared with numerical simulation results quantitatively. Finally, the shock train positions were calculated by an image recognition algorithm to analyze the self-excited oscillation frequency characteristics of shock train structures. The methods and experiments in this study enriched optical observation methods of supersonic flows through non-rectangular cross-section isolators in scramjet.Graphical abstract

Orbit determination from one position vector and a very short arc of optical observations

In this paper, we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1$$\\end{document} and a very short arc (VSA) of optical observations A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{A}_2$$\\end{document}. Using the conservation laws of the two-body dynamics, we write the problem as a system of 8 polynomial equations in 6 unknowns. We prove that this system is generically consistent, namely, for a generic choice of the data P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document}, it always admits solutions in the complex field, even when P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document} do not correspond to the same celestial body. The consistency of the system is shown by deriving a univariate polynomial v\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {v}$$\\end{document} of degree 8 in the unknown topocentric distance at the mean epoch of the observations of the VSA. Through Gröbner bases theory, we also show that the degree of v\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {v}$$\\end{document} is minimum among the degrees of all the univariate polynomials solving this problem. Even though we can find solutions to our problem for a generic choice of P1,A2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{P}_1, \\mathcal{A}_2$$\\end{document}, most of these solutions are meaningless. In fact, acceptable solutions must be real and have to fulfill other constraints, including compatibility with Keplerian dynamics. We also propose a way to select or discard solutions taking into account the uncertainty in the data, if present. The proposed orbit determination method is relevant for different purposes, e.g., the computation of a preliminary orbit of an Earth satellite with radar and optical observations, the detection of maneuvres of an Earth satellite, and the recovery of asteroids which are lost due to a planetary close encounter. We conclude by showing some numerical tests in the case of asteroids undergoing a close encounter with the Earth.

The VISTA Variables in the Vía Láctea eXtended (VVVX) ESO public survey: Completion of the observations and legacy

The ESO public survey VISTA Variables in the V\'ia L\'actea (VVV) surveyed the inner Galactic bulge and the adjacent southern Galactic disk from $2009-2015$. Upon its conclusion, the complementary VVV eXtended (VVVX) survey has expanded both the temporal as well as spatial coverage of the original VVV area, widening it from $562$ to $1700$ sq. deg., as well as providing additional epochs in s $ filters from $2016-2023$. With the completion of VVVX observations during the first semester of 2023, we present here the observing strategy, a description of data quality and access, and the legacy of VVVX. VVVX took sim \,$2000$ hours, covering about 4<!PCT!> of the sky in the bulge and southern disk. VVVX covered most of the gaps left between the VVV and the VISTA Hemisphere Survey (VHS) areas and extended the VVV time baseline in the obscured regions affected by high extinction and hence hidden from optical observations. VVVX provides a deep $JHK_ s $ catalogue of $ point sources, as well as a s $ band catalogue of sim \,$10^7$ variable sources. Within the existing VVV area, we produced a $5D$ map of the surveyed region by combining positions, distances, and proper motions of well-understood distance indicators such as red clump stars, RR Lyrae, and Cepheid variables. In March 2023 we successfully finished the VVVX survey observations that started in 2016, an accomplishment for ESO Paranal Observatory upon 4200 hours of observations for VVV+VVVX. The VVV+VVVX catalogues complement those from the Gaia mission at low Galactic latitudes and provide spectroscopic targets for the forthcoming ESO high-multiplex spectrographs MOONS and 4MOST.