L1 Point Research Articles

Distorted Magnetic Flux Ropes within Interplanetary Coronal Mass Ejections

Magnetic flux ropes (MFRs) at the center of interplanetary coronal mass ejections (ICMEs) are often characterized as simplistic cylindrical or toroidal tubes with field lines that twist around the cylinder or torus axis. Recent multipoint observations suggest that the overall geometry of these large-scale structures may be significantly more complex. As such, contemporary modeling approaches are likely insufficient to properly understand the global structure of any ICME. In an attempt to rectify this issue, we have developed a novel flux rope modeling approach that allows for the description of arbitrary distortions of the flux rope cross section or deformation of the magnetic axis. The resulting distorted MFR model is a fully analytic model that can be used to describe a complex geometry and is numerically efficient enough to be used for event reconstructions. To demonstrate the usefulness of our approach, we focus on a specific implementation of our model and apply it to an ICME event that was observed in situ on 2023 April 23 at the L1 point by the Wind spacecraft and also by the STEREO-A spacecraft, which was 10.°2 further east and 0.°9 south in heliographic coordinates. We demonstrate that our model can accurately reconstruct each observation individually and also gives a fair reconstruction of both events simultaneously using a multipoint reconstruction algorithm, which results in a geometry that is inconsistent with a cylindrical or toroidal approximation.

SOTHE: SOlar-terrestrial habitability explorer

Among more than 5000 exoplanets discovered up to now, around 60 are believed to be potentially habitable. The Sun-Earth system provides a unique example based on which detailed insights into the properties, formation, evolution, and thus habitability of exoplanets could be gained. However, simultaneous observation of the Sun as a star and the Earth as an exoplanet has been rare. In this paper, we introduce the SOlar-Terrestrial Habitability Explorer (SOTHE) to be deployed to the Sun-Earth L1 point. SOTHE will carry a science payload comprising four instruments to obtain the integrated spectra of the whole solar disk and the whole sunlit Earth at the same time, together with images of the Earth at 11 unique passbands from UV to NIR and the local plasma and magnetic field parameters at the L1 point. The core scientific goal of SOTHE is to understand key characteristics related to the habitability of the Sun-Earth system and provide a unique baseline for exploring habitable exoplanets, especially Earth-like planets around Sun-like stars.

SOHO SWAN Lyα Models Supporting LRO LAMP: 2008–2023

The Lunar Reconnaissance Orbiter Lyman-Alpha Mapping Project (LAMP) has been mapping the Moon since its launch in 2009. Faint ultraviolet illumination of the lunar dark side includes light from stars and from hydrogen Lyα emissions, mostly attributed to sunlight scattered by hydrogen atoms near the Sun with a smaller contribution from the whole Galaxy. Models of the lunar illumination by time-dependent Lyα photons have allowed the LAMP team to map polar shadowed craters suspected of harboring water ice and other volatiles. This paper describes the model that provides daily all-sky Lyα maps tuned by comparisons with all-sky Lyα maps from the SOlar and Heliospheric Observatory Solar Wind ANisotropy Experiment stationed at the Sun–Earth L1 point.

New Transient Co-orbital Asteroids of Venus

Venus has no known natural satellites but has 5 known co-orbitals. These are objects trapped in a 1:1 mean-motion resonance with Venus. Co-orbital configurations include retrograde satellite orbits (RS), tadpole orbits (T) around the Lagrangian equilibrium points L4 or L5, and horseshoe orbits around both L4 and L5 (H). At high eccentricity or inclination, co-orbital configurations may also involve compounds of T and RS (T-RS, T-RS-T), H and RS (H-RS) orbits, or transitions between different co-orbital modes. Here we identify asteroids in 2 RS, 1 L4-tadpole, 2 H-RS, and 2 T-RS orbits, as well as 8 additional asteroids in possible temporary co-orbital status. Although the majority of these objects do not yet have well-characterized orbits, 2020 CL1, and 2020 SB do and are very likely to be new co-orbital asteroids. With the new candidates, Venus would have a population of 20 co-orbital asteroids, comparable to those of Mars and Earth.

Forecasting Geoffective Events from Solar Wind Data and Evaluating the Most Predictive Features through Machine Learning Approaches

This study addresses the prediction of geomagnetic disturbances by exploiting machine learning techniques. Specifically, the Long Short-term Memory recurrent neural network, which is particularly suited for application over long time series, is employed in the analysis of in situ measurements of solar wind plasma and magnetic field acquired over more than one solar cycle, from 2005 to 2019, at the Lagrangian point L1. The problem is approached as a binary classification aiming to predict 1 hr in advance a decrease in the SYM-H geomagnetic activity index below the threshold of −50 nT, which is generally regarded as indicative of magnetospheric perturbations. The strong class imbalance issue is tackled by using an appropriate loss function tailored to optimize appropriate skill scores in the training phase of the neural network. Beside classical skill scores, value-weighted skill scores are then employed to evaluate predictions, suitable in the study of problems, such as the one faced here, characterized by strong temporal variability. For the first time, the content of magnetic helicity and energy carried by solar transients, associated with their detection and likelihood of geoeffectiveness, were considered as input features of the network architecture. Their predictive capabilities are demonstrated through a correlation-driven feature selection method to rank the most relevant characteristics involved in the neural network prediction model. The optimal performance of the adopted neural network in properly forecasting the onset of geomagnetic storms, which is a crucial point for giving real warnings in an operational setting, is finally showed.

Ultrasound-guided retromammillary injections in dogs: a feasibility, descriptive and anatomical study

ObjectiveTo evaluate the feasibility of an ultrasound-guided technique targeting the medial branches of the dorsal ramus of the spinal nerves (DRSN) by injecting a dye solution at the caudal aspect of the base of lumbar mammillary processes [i.e. the retromammillary (RM) space]. Study designFeasibility, descriptive, anatomical study. AnimalsEleven canine cadavers. MethodsUsing anatomical dissections, the relationship between the mammillary processes and the branches of the DRSN of the thoracolumbar and lumbar spine was studied in two cadavers. Subsequently, ultrasound-guided RM injections were administered in nine cadavers, randomly assigned to low volume (LV; 0.01 mL kg–1) of a dye solution at multiple points from L3 to L6 on one side, and high volume (HV; 0.4 mL kg–1) at a single L4 point on the contralateral side. Gross anatomical dissections were immediately performed after the injections. The RM injections were feasible if ultrasonographic landmarks were identifiable in at least 80% of cases, and 80% of LV injections showed medial branch staining. A one-sample binomial test was used for testing feasibility. ResultsThe medial branches emerged shortly after the DRSN exited the intervertebral foramen and traveled towards the caudal aspect of the base of the mammillary process, which served as the target injection point. With LV, 36 out of 36 (100%) injected medial branches were stained, meeting the criteria of feasibility (p < 0.001). The median (range) number of stained medial branches per cadaver were 4 (4–4) and 2 (1–3), with LV and HV, respectively. Although no lateral branches were stained with LV, 1 (0–2) was stained with HV. Neither ventral branch staining nor epidural spread was noted in any cadaver. Conclusions and clinical relevanceUltrasound-guided RM injections are feasible and allow for selective staining of the medial branch of the DRSN in canine cadavers at the lumbar spine.

Temperature mapping methods for thermoelastic analyses of the ARIEL spacecraft payload module

The ARIEL mission is a European space project that aims to detect exoplanets with a spacecraft orbiting around the L2 point of the Sun-Earth system. The main payload consists of a Cassegrain telescope composed of mirrors that reflect and concentrate the incoming light from the deep space observations to finally guide it to the detectors. As in many other space missions, a dedicated complex assessment is established during the design phase to evaluate the impact on the optical performance caused by thermoelastic effects, which involves the coordinated work of the thermal, structural, and optical engineers. Despite that well-known and standardized processes and tools are established separately in each involved area, there is a lack of standardization about the way of exchanging the data between them, where additional calculations are required in some cases. This work focuses on the temperature mapping, which is the intermediate step between thermal and structural analyses, where temperatures are transferred to the structural model. The main difficulty of this process is related to the differences in modelling methods and approaches between both models, being necessary the development of an adequate algorithm to find the most accurate transfer of temperatures. This paper shows two different options for temperature mapping, detailing the proposed flowcharts. One of these methods requires the performance of an additional thermal conductive analysis, where a new improved procedure has been implemented in this work to solve some computational issues that made its application for large models difficult or even unfeasible. Both temperature mapping methods have been applied to the payload module of the ARIEL spacecraft, comparing the output results in terms of temperatures, stresses, forces, and displacements to evaluate their differences.

Trajectory tracking PID passivity-based control of spacecraft formation flying around Sun-Earth L2 point in the port-Hamiltonian framework

Spacecraft formation flying for interferometric observations around the 2nd Lagrange point in the Sun-Earth system (SEL2) is currently focal point in deep space exploration research, which demands high precision in relative position control of spacecraft. This paper proposes the relative motion dynamics of satellite formations around the L2 point in the port-Hamiltonian framework, and establishes a high-precision nonlinear dynamics model. PID passivity-based control (PID-PBC) is widely used in engineering. However, existing methods of PID-PBC cannot address the trajectory tracking issues in port-Hamiltonian systems. Utilizing the contraction properties of the port-Hamiltonian system, this paper proposes the trajectory tracking PID-PBC (tPID-PBC) approach, effectively resolving trajectory tracking issues for formation dynamics around L2 point in port-Hamiltonian framework. The paper details explicit solutions of the Partial Differential Equations (PDE) for the tPID-PBC method and its controller structure, and references the trajectories of interferometric observation formations, to verify the method’s effectiveness through numerical simulation. The presented control approach is applicable across generic port-Hamiltonian systems, offering substantial theoretical value.

Further Study of the Relationship between Transient Effects in Energetic Proton and Cosmic Ray Fluxes Induced by Coronal Mass Ejections

The study and better understanding of energetic transient phenomena caused by disturbances occurring on our Sun are of great importance, primarily due to the potential negative effects those events can have on Earth’s environment. Here, we present the continuation of our previous work on understanding the connection between disturbances in the flux of energetic particles induced in the near-Earth environment by the passage of interplanetary coronal mass ejections and related Forbush decrease events. The relationship between the shape of fluence spectra of energetic protons measured by the instruments on the SOHO/ERNE probe at Lagrange point L1, Forbush decrease parameters measured by the worldwide network of neutron monitors, and coronal mass ejection parameters measured in situ is investigated. Various parameters used to characterize transient phenomena and their impact on the heliosphere, provided by the WIND spacecraft, were utilized to improve the accuracy of the calculation of the associated energetic proton fluence. The single and double power laws with exponential rollover were used to model the fluence spectra, and their effectiveness was compared. Correlation analysis between exponents used to characterize the shape of fluence spectra and Forbush decrease parameters is presented, and the results obtained by the two models are discussed.

SODA - a tool to predict storm induced orbit decays for low Earth orbiting satellites

Due to the rapidly increasing technological progress in the last decades, the issue of space weather and its influences on our everyday life gains more and more importance. Today, satellite-based navigation plays a key role in aviation, logistics and transportation systems. With the strong rise of the current solar cycle 25 the number and intensity of solar eruptions increased. The forecasting tool SODA (Satellite Orbit DecAy) is based on an interdisciplinary analysis of space geodetic observations and solar wind in situ measurements. It predicts the effect of coronal mass ejections from their in-situ measured counterparts (ICME) on the altitude of low Earth orbiting satellites at 490 km with a lead time of about 20 hours. Additionally, it classifies the severeness of the expected geomagnetic storm in the form of the Space Weather G–scale from the National Oceanic and Atmospheric Administration (NOAA). For the establishment and validation of SODA, we examined 360 ICME events over a period of 21 years. Appropriated variations in the thermospheric neutral mass density, were derived mainly from measurements of the Gravity Recovery and Climate Experiment (GRACE) satellite mission. Related changes in the interplanetary magnetic field component Bz were investigated from real-time measurements using data from spacecraft located at the Lagrange point L1. The analysis of the ICME induced orbit decays and the interplanetary magnetic field showed a strong correlation as well as a time delay between the ICME and the associated thermospheric response. The derived results are implemented in the real- forecasting tool SODA, which integrated in the Space Safety Program Ionospheric Weather Expert Service Center; I.161 of the Space Agency (ESA).

Cislunar [formula omitted] and [formula omitted] axial orbits and their applications

Cislunar L4 or L5 axial orbit families are continuous asymmetrical periodic orbits from the figure-8 orbit around L4 or L5 Lagrange point of the Earth–Moon system to the halo-family around the Moon. They provide special locations of lunar relay satellites for the lunar south pole due to their offset locations. In this paper, we investigate the orbital characters and applications of cislunar L4 and L5 axial orbits. A construction method of cislunar L4 and L5 axial orbit families is proposed according to their topological feature in the torus space. Then, lunar relay performances, including coverage and eclipse, are analyzed for different cislunar L4 and L5 axial orbits. Numerical computation indicates that 3:1 resonant L4 and L5 axial orbits are the optimal options in terms of the stability, coverage and eclipse avoidance. Lunar relay performances of a two-satellite constellation deployed in these orbits are compared with that in a near rectilinear halo orbit (NRHO). Numerical results show that the constellation of axial orbits can provide longer contact duration to the lunar equator and southern hemisphere than that of the NRHO. Finally, a station-keeping strategy and a transfer design of cislunar L4 and L5 axial orbits are developed, and their fuel costs are studied.

Global cloud optical depth daily variability based on DSCOVR/ EPIC observations

When investigating the potential effects of cloud changes on climate, the interday and intraday variabilities should be distinguished. Historically, studies have focused on the long-term cloud changes, and the intraday cycles of cloud properties have been mostly ignored partly owing to the limited availability of global datasets to study higher frequency variabilities. In this regard, DSCOVR’s vantage point at the Lagrange L1 point overcomes the temporal limitations of polar orbiters as well as the limited spatial views of geostationary satellites, allowing characterization of the daytime variability of cloud properties using a single sensor. In previous analyses, we used DSCOVR’s EPIC instrument to characterize the diurnal cycles of cloud height and cloud fraction; here, we expand on previous studies to additionally investigate the variability of cloud optical thickness. We observe a recurring diurnal pattern of cloud optical thicknesses for different latitudinal zones that reaches a maximum around noon regardless of the underlying surface. Once we separate the clouds based on their optical thickness into optically thin (0–3), intermediate (3–10), and thick (10–25), we find that these cloud classes follow different optical thickness diurnal cycles on the global scale. We further explore these differences by combining the evolution of cloud fraction and optical thickness of each group to obtain the diurnal evolution of cloud-fraction-weighted optical depths.

Validation of EUHFORIA cone and spheromak coronal mass ejection models

We present validation results for calculations of arrival times and geomagnetic impact of coronal mass ejections (CMEs) using the cone and spheromak CME models implemented in EUropean Heliospheric FORecasting Information Asset (EUHFORIA). Validating numerical models is crucial for ensuring their accuracy and performance with respect to real data. We compared CME plasma and magnetic field signatures measured in situ by satellites at the L1 point with the simulation output of EUHFORIA. The validation of this model was carried out using two datasets in order to ensure a comprehensive evaluation. The first dataset focuses on 16 CMEs that arrived at Earth, offering specific insights into the model's accuracy in predicting arrival time and geomagnetic impact. Meanwhile, the second dataset encompasses all CMEs observed over eight months within Solar Cycle 24, regardless of whether or not they arrived at Earth, covering periods of both solar minimum and maximum activity. This second dataset enables a more comprehensive evaluation of the model's predictive precision in term of CME arrivals and misses. Our results show that EUHFORIA provides good estimates in terms of arrival times, with root mean square error (RMSE) values of 9 hours. Regarding the number of correctly predicted ICME arrivals and misses, we find a 75&lt;!PCT!&gt; probability of detection in a 12 hour time window and 100&lt;!PCT!&gt; probability of detection in a 24 hour time window. The geomagnetic impact forecasts measured by the $K_p$ index provide different degrees of accuracy ranging from 31&lt;!PCT!&gt; to 69&lt;!PCT!&gt;. These results validate the use of cone and spheromak CMEs for real-time space weather forecasting.

Design of a Cislunar space navigation constellation based on special long-period orbits

This paper proposes a method for designing a navigation constellation in the Cislunar space. Firstly, the dynamic characteristics of the Cislunar space were analyzed. Northern Halo orbits and southern Halo orbits around L1 and L2 libration point are designed. Then, based on the invariant manifold theory, the homoclinic low-energy transfer trajectories of L1 Halo orbits and the low-energy heteroclinic transfer trajectories between L1 and L2 Halo orbits are provided respectively. Afterthat, two types of special long-period orbits are attained for the constellation design. Based on the geometric dilution of precision and the minimum number of visible satellites, design requirements for two parts are given. Next, two navigation constellation configurations are proposed. Lastly, simulations are conducted on the performance of two constellation configurations with different number of satellites. Compared to constellations in one orbit, constellations that configured in two orbits require fewer satellites to meet the design requirements. In different lunar transfer orbits, the performance of the dual orbit constellation was validated.

Exploitation of the Number of Return Echoes for DTM Extraction from Point Clouds Acquired by LiDAR UAS DJI Zenmuse L1

Abstract. Following the enormous technological developments of LiDAR (Light Detection And Ranging) sensors, it is currently easier to find them commercially in the UA (Uncrewed Aerial Systems) sector. In particular, with the Zenmuse L1 by DJI (Dà-Jiāng Innovations) the market has grown globally, mainly due to the compactness of the product that is easily compatible with UAS. The L1 sensor can record up to three returns of the emanating signal, so it can acquire a larger amount of points, such as those below the vegetation. Therefore, in addition to the geometric information of the points, the Zenmuse L1 point clouds also provide other information, such as the number of echo returns from 1 to 3. This data could be exploited to improve the automatic extraction of the digital terrain model (DTM) from the point clouds, hopefully leading to the avoidance of manual correction. This research aims to focus on evaluating whether the addition of the return number feature can affect the identification of the ground points through different computational methods and can improve the time efficiency of state-of-the-art algorithms.

The Vigil Magnetometer for Operational Space Weather Services From the Sun‐Earth L5 Point

AbstractSevere space weather has the potential to cause significant socio‐economic impact and it is widely accepted that mitigating this risk requires more comprehensive observations of the Sun and heliosphere, enabling more accurate forecasting of significant events with longer lead‐times. In this context, it is now recognized that observations from the L5 Sun‐Earth Lagrange point (both remote and in situ) would offer considerable improvements in our ability to monitor and forecast space weather. Remote sensing from L5 allows for the observation of solar features earlier than at L1, providing early monitoring of active region development, as well as tracking of interplanetary coronal mass ejections through the inner heliosphere. In situ measurements at L5 characterize the solar wind's geoeffectiveness (particularly stream interaction regions), and can also be ingested into heliospheric models, improving their performance. The Vigil space weather mission is part of the ESA Space Safety Program and will provide a real‐time data stream for space weather services from L5 following its anticipated launch in the early 2030s. The interplanetary magnetic field is a key observational parameter, and here we describe the development of the Vigil magnetometer instrument for operational space weather monitoring at the L5 point. We summarize the baseline instrument capabilities, demonstrating how heritage from science missions has been leveraged to develop a low‐risk, high‐heritage instrument concept.

Lagrange points and regionally conserved quantities

Lagrange points are the equilibrium points within a restricted three-body system, epitomized by the Trojan asteroids near the L4 and L5 points of the Sun–Jupiter system. They also play a crucial role in some space missions, including the James Webb Space Telescope which is located at the Sun–Earth L2 point. While the existence of five Lagrange points is a well-known feature of the restricted three-body problem, the equations describing the precise location of all five points are not extensively documented. This work presents a derivation of all Lagrange points using polar coordinates and a new normalization scheme that offers a simpler interpretation of solutions compared to prior analyses. A subtle issue concerning the treatment of angular momentum in the potential formulation of this problem is addressed and resolved. The supplementary material to this work contains additional mathematical details and discussion.

Evaluation of Regio Temporalis in 3 Steps in Terms of Interventional Procedures.

Regio temporalis is a site where botulinum neurotoxin is applied for various medical reasons, such as migraine, bruxism, and myofascial pain syndrome. The region is also one of the target regions in flap surgery. This study aimed to define the region topographically. In addition, it was aimed to reveal the intramuscular nerve distribution of the temporalis.11 fixed cephalus (cadaver head) and 2 fresh cephalus were used. The lateral canthus of the eye was marked as point A, and the middle of the ear tragus as point B. The transverse and vertical distances of the branching point of the superficial temporal artery to the A and B points were measured. Transverse distances of the superficial temporal artery and superficial temporal vein to A and B points were measured. The muscle was examined in 5 equal parts (L0-L1-L2-L3-L4), and each part's vertical muscle and tendon lengths were examined. Intramuscular nerve density was demonstrated by applying the modified Sihler staining to fresh temporalis'. Superficial temporal artery had an average transverse distance of 8.56±1.9mm in women and 12.56±1.94mm in men from the middle of the ear tragus. The artery was 64.21±5.59mm posterior in females and 63.48±6.53mm in males from the lateral canthus of the eye. Our study determined that the branching point of the superficial temporal artery was below the upper level of the arcus zygomaticus in 10% of cases and above it in 90% of cases. In our study, the L2 point had the highest vertical muscle length at 45.67mm, while the L3 point had the highest vertical tendon length at 41.25mm. The point where the muscle length had the highest ratio with 1.49 compared to the tendon length, was the L2 point. The temporalis' for which the modified Sihler staining was applied was examined in 5 quadrants. It was determined that the nerve densities were in the second and third quadrants from anterior to posterior. The distance of superficial landmarks to neurovascular structures is extremely important in interventions to the regio temporalis. Considering the average distances given in our study is important in avoiding damage in surgical procedures and not injecting into vascular structures. The point where the muscle length had the highest ratio of 1.49 compared to the tendon length was the L2 point. The area in line with this point is the most suitable area for injection. The L2 point is also the most suitable area for injection as it has the highest muscle length. Since the nerve densities were observed in the modified Sihler staining applied temporalis' 2 and 3 quadrants from anterior to posterior, botulinum neurotoxin injections to these areas will give more effective results.

Magnetopause location modeling using machine learning: inaccuracy due to solar wind parameter propagation

An intrinsic limitation of empirical models of the magnetopause location is a predefined magnetopause shape and assumed functional dependences on relevant parameters. We overcome this limitation using a machine learning approach (artificial neural networks), allowing us to incorporate general, purely data-driven dependences. For the training and testing of the developed neural network model, a data set of about 15,000 magnetopause crossings identified in the THEMIS A-E, Magion 4, Geotail, and Interball-1 satellite data in the subsolar region is used. A cylindrical symmetry around the direction of the impinging solar wind is assumed, and solar wind dynamic pressure, interplanetary magnetic field magnitude, cone angle, clock angle, tilt angle, and corrected Dst index are considered as parameters. The effect of these parameters on the magnetopause location is revealed. The performance of the developed model is compared with other empirical magnetopause models. Finally, we demonstrate and discuss the inaccuracy of magnetopause models due to the inaccurate information about the impinging solar wind parameters based on measurements near the L1 point. This inaccuracy imposes a theoretical limit on the precision of magnetopause predictions, a limit that our model closely approaches.

Decretion disc size in Be/X-ray binaries depends upon the disc aspect ratio

ABSTRACT With three-dimensional hydrodynamical simulations we show that the size of the decretion disc and the structure of the accretion flow on to the neutron star in a Be/X-ray binary strongly depends upon the disc aspect ratio, H/R. We simulate a Be star disc that is coplanar to the orbit of a circularly or moderately eccentric neutron star companion, thereby maximizing the effects of tidal truncation. For low-disc aspect ratio, H/R ≲ 0.1, the disc is efficiently tidally truncated by the neutron star. Most material that escapes the Roche lobe of the Be star is accreted by the neutron star through tidal streams. For larger disc aspect ratio, the outflow rate through the Be star disc is higher, tidal truncation becomes inefficient, the disc fills the Roche lobe and extends to the orbit of the companion. Some material escapes the binary as a gas stream that begins near the L2 point. While the accretion rate on to the neutron star is higher, the fraction of the outflow that is accreted by the neutron star is smaller. Low-density Be star discs are expected to be approximately isothermal, such that H/R increases with radius. Tidal truncation is therefore weaker for larger separation binaries, and lower mass primaries.