Lagrangian Point L1 Research Articles

Lunar occultations events from the Earth–Moon equilateral Lagrangian point: simulations and scientific potential

ABSTRACT Recently, a novel idea has been proposed to use a spacecraft orbiting closely around the L4 or L5 Lagrangian points of the Earth–Moon system as a vantage location for astronomical observations under unique and advantageous conditions, e.g. to investigate the Solar corona or Kordylewski clouds. In this paper, we explore the scientific advantages of this configuration to observe lunar occultations. By using simulations based on actual orbital parameters and detector performance, we find that even a telescope as small as 10 cm in a L4 orbit would enable better light-curve sampling and higher angular resolution than from ground, and open up at the same time new spectral windows such as e.g. in the UV. We focus in particular on angular diameter measurements, which we find would be possible at the 100 $\mu$as level even at magnitudes normally considered faint in the context of ground-based LOs. Considerable benefits would also be afforded in the area of small separation binary objects, not just in terms of angular resolution but also by the capability of L4-based observations to repeat an LO scan of a source at multiple different position angles. Additional science cases would be made possible by the high time resolution intrinsic to the LO technique and the access to UV wavelengths. On-board data pipeline codes already exist, greatly simplifying the automatic pre-processing and the data transfer requirements.

Forecasting Geomagnetic Storm Disturbances and Their Uncertainties Using Deep Learning

AbstractSevere space weather produced by disturbed conditions on the Sun results in harmful effects both for humans in space and in high‐latitude flights, and for technological systems such as spacecraft or communications. Also, geomagnetically induced currents (GICs) flowing on long ground‐based conductors, such as power networks, potentially threaten critical infrastructures on Earth. The first step in developing an alarm system against GICs is to forecast them. This is a challenging task given the highly non‐linear dependencies of the response of the magnetosphere to these perturbations. In the last few years, modern machine‐learning models have shown to be very good at predicting magnetic activity indices. However, such complex models are on the one hand difficult to tune, and on the other hand they are known to bring along potentially large prediction uncertainties which are generally difficult to estimate. In this work we aim at predicting the SYM‐H index characterizing geomagnetic storms multiple‐hour ahead, using public interplanetary magnetic field (IMF) data from the Sun‐Earth L1 Lagrange point and SYM‐H data. We implement a type of machine‐learning model called long short‐term memory (LSTM) network. Our scope is to estimate the prediction uncertainties coming from a deep‐learning model in the context of forecasting the SYM‐H index. These uncertainties will be essential to set reliable alarm thresholds. The resulting uncertainties turn out to be sizable at the critical stages of the geomagnetic storms. Our methodology includes as well an efficient optimization of important hyper‐parameters of the LSTM network and robustness tests.

Technical Overview and Prospect of India’s First Solar Mission - Aditya L1 Spacecraft

The Aditya-L1 mission represents a significant milestone in solar research, aimed at unlocking the mysteries of our closest star, the Sun. This paper provides an overview of the mission's objectives, scientific instruments, and key findings. By placing a spacecraft in a Lagrangian point L1 orbit, Aditya-L1 offers an unprecedented vantage point for continuous solar observations. The primary scientific goals include studying the Sun's dynamic atmosphere, monitoring solar variability, and enhancing our understanding of space weather and its impact on Earth. The paper discusses the advanced instrumentation onboard, such as the Visible Emission Line Coronagraph (VELC), the Solar Ultraviolet Imaging Telescope (SUIT), and the Aditya Solar Wind Particle Experiment (ASPEX), highlighting their contributions to solar science. Furthermore, this paper presents early results and insights obtained from Aditya-L1's observations, shedding light on solar phenomena, solar eruptions, and their influence on Earth's space environment. The Aditya-L1 mission stands as a testament to international collaboration and technological advancements, poised to reshape our understanding of the Sun and its profound effects on our solar system.

Linear stability of elliptic relative equilibria of four-body problem with two infinitesimal masses

In this paper, we consider the elliptic relative equilibria of four-body problem with two infinitesimal masses. The most interesting case occurs when the two small masses tend to the same Lagrangian point L4 (or L5). In [20], Xia showed that there exist four central configurations: two of them are non-convex, and the other two are convex. We prove that the elliptic relative equilibria raised from the non-convex central configurations are always linearly unstable, while for the elliptic relative equilibria raised from the convex central configurations, the conditions of linear stability with respect to the parameters are provided.

Effect of Space Radiation on Transition-Edge Sensor Detectors Performance

The Athena mission and its X-ray Integral Field Unit (X-IFU) instrument will be positioned at the Sun-Earth Lagrange point L1, where it will be subject to particles from the solar wind with energy below 0.1 MeV, and from galactic cosmic rays and solar flares with energies up to hundreds of MeV for protons and GeVs for heavier ions. Some of these particles will go through the satellite and hit the focal plane assembly and hence the detectors. These detectors will be TES (Transition-edge sensor) microcalorimeters, flown for the first time in such an environment. In order to ensure the performance of this type of detector throughout the duration of such a mission, it is critical to study the impact of the radiation on their behavior. Indeed, although a lot of reference material exist for semiconductor-based photodetectors such as CCDs and CISs, little is currently known about the impact of radiation on TES detectors. These energetic events could cause local heating or damage to the detectors and affect their performance. In this work, we describe how we designed a test campaign to assess the impact of L1 radiation on TES detectors for Athena/X-IFU-like missions and present the results of the tests, for a maximum dose of 4.3 krad(Si)). Analysis includes assessing changes in the pulse shapes and energy resolution of the detectors measured at 55 mK after several radiation dose steps performed at 4 K.

Jovian Periodicities (~10 h, ~40, 20, 15 min) at ACE, Upstream from the Earth’s Bow Shock, on 25–27 November 2003

It is known that Jovian radio and high energy electron emissions are observed near Earth. The question we address in this study is whether the quasi-periodic ~10 h and ~40/15–20 min (QP-10 h, QP-40/15–20 min) energetic particle and magnetic field periodicities observed by Ulysses during its distant encounter with Jupiter in 2003 were also detectable as far as the Earth’s orbit. Surprisingly, we found that at the end of the extreme 2003 Halloween events, during times of a highly disturbed Jovian magnetosphere, as inferred from strong bKOM radio emissions observed by Ulysses, and a magnetic connection of Earth with the Jovian magnetosphere, as suggested by simulation results of the interplanetary magnetic field (IMF), the ACE satellite observed, between at least 25–27 November 2013 at the Lagrangian Point L1 (LPL1), all the characteristic Jovian periodicities. In particular, by using high-time resolution data (1/5 min), we found, for the first time, quasi-permanent electron, and magnetic field QP-10/5 h, QP-40 min and QP-15/20 data variations at LPL1 for at least three days. These observations reasonably suggest that low energy (~50–~300 keV) Jovian electrons reached the Earth’s environment; the observations examined extend the lowest energy limit of the Jovian electron spectrum from 200 keV to ~50 keV. In addition, the ACE satellite observed an impressive series of QP-10/5 h energetic (≤0.05 MeV) ion bursts (EIBs) with strong cross-field intensity gradients at the onset/decay phase of the events and energy-dependent field aligned anisotropy suggesting ion streaming in the anti-sunward direction during their main phase. A comparison of simultaneously obtained measurements by ACE at the LPL1 and by Geotail upstream from the bow shock and in the magnetosphere suggests that the QP-10/5 h EIBs are inconsistent with the concept of a terrestrial origin. On the contrary, the observations indicate that the series of QP-10/5 h EIBs on 25–27 November 2003 was a spatial effect caused by the ~10/5 h quasi-periodic approach of a large-scale sheet to the Earth’s environment. The source of the ion population forming the QP-10/5 h sharp EIBs seems most probably Jovian ions accumulated in the interplanetary space, although a solar ion contribution is possible. Based on the above results, it is reasonable to suggest that the observed QP-10 h, QP-40 min and QP-15/20 periodicities are due to Jovian influence. Further research is needed to study the cause of the QP-10/5 h EIBs. This study presents new data which extend our view on the influence of the QP-10 h/QP-40/QP-15/20 min Jovian emissions from the outer to the inner heliosphere at 1 AU.

The energetic storm particle events of 3 November 2021

Observations of energetic particles at interplanetary shocks are important to study acceleration mechanisms and their connection with magnetohydrodynamic turbulence. Energetic storm particle (ESP) events are increases in proton fluxes that occur locally at the passage time of interplanetary shocks. These events are more dangerous when they are superimposed on the solar energetic particles (SEPs) produced by the eruption of flares and/or CME-driven shocks propagating from the corona to the interplanetary space. We considered ESP events occurring in association with SEPs on 3 November 2021. We used proton fluxes provided by Solar Orbiter (located at 0.85 AU) in the energy range of 30 keV–82 MeV, by Wind at energies from 70 keV to 72 MeV, and ACE in the range from 40 keV to 5 MeV (both located at the Lagrangian point L1, close to 1 AU along the Sun-Earth direction). In order to broaden the range of analyzed energies (40 keV - 72 MeV), we combine these data with the proton fluxes from the SOHO spacecraft, also located at L1. We analyzed the ESP event and fitted the proton energy spectra at both locations with several distributions to shed light on the mechanisms leading to the acceleration of energetic particles. We also investigated the turbulent magnetic field fluctuations around the shock. The obtained ESP spectra, best reproduced by the so-called double power law function, the spectral differences at the two locations, and the shock features (quasi-parallel geometry, enhanced downstream turbulence) suggest that diffusive shock acceleration is responsible for acceleration of low energy particles, whereas stochastic acceleration contributes to the (re) acceleration of high energies ones.

Breakdown of homoclinic orbits to L3 in the RPC3BP (II). An asymptotic formula

The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies are coplanar, one has the Restricted Planar Circular 3-Body Problem (RPC3BP). In rotating coordinates, it can be modeled by a two degrees of freedom Hamiltonian, which has five critical points called the Lagrange points L1,…,L5.The Lagrange point L3 is a saddle-center critical point which is collinear with the primaries and beyond the largest of the two. In this paper, we obtain an asymptotic formula for the distance between the stable and unstable manifolds of L3 for small values of the mass ratio 0<μ≪1. In particular we show that L3 cannot have (one round) homoclinic orbits.If the ratio between the masses of the primaries μ is small, the hyperbolic eigenvalues of L3 are weaker, by a factor of order μ, than the elliptic ones. This rapidly rotating dynamics makes the distance between manifolds exponentially small with respect to μ. Thus, classical perturbative methods (i.e. the Melnikov-Poincaré method) can not be applied.The obtention of this asymptotic formula relies on the results obtained in the prequel paper [10] on the complex singularities of the homoclinic of a certain averaged equation and on the associated inner equation.In this second paper, we relate the solutions of the inner equation to the analytic continuation of the parameterizations of the invariant manifolds of L3 via complex matching techniques. We complete the proof of the asymptotic formula for their distance showing that its dominant term is the one given by the analysis of the inner equation.

Prediction Capability of Geomagnetic Events from Solar Wind Data Using Neural Networks

Multiple neural network architectures, with different structural composition and complexity, are implemented in this study with the aim of providing multi-hour-ahead warnings of severe geomagnetic disturbances, based on in situ measurements of the solar wind plasma and magnetic field acquired at the Lagrangian point L1. First, a statistical analysis of the interplanetary data was performed to point out which are the most relevant parameters to be provided as input to the neural networks, and a preprocessing of the data set was implemented to face its heavy imbalance (the Earth’s magnetosphere is in fact mostly at rest). Then, neural networks were tested to evaluate their performance. It turned out that, in a binary classification problem, recurrent approaches are best at predicting critical events both 1 and 8 hr in advance, achieving a balanced accuracy of 94% and 70%, respectively. Finally, in an attempt at multistep prediction of the criticality of future geomagnetic events from 1–8 hr ahead, more complex neural networks, built by merging the different types of basic convolutional and recurrent architectures, have been shown to outperform single-step and state-of-the-art approaches with a balanced accuracy of at least 70%. Interestingly, the accuracy peaks at 4 hr, corresponding to the waiting time between the detection of solar drivers at L1 and the onset of the geomagnetic storm (as previously obtained by statistical investigations), suggesting that on average this is the time the Earth’s magnetosphere takes to react to the solar event.

Direct Lyapunov Method in the Problem of Ensuring the Stability of a Compact Minimum Set of a Dynamic System and the Formation of a Halo-Orbit Near the Lagrange Point L2

The efficiency of using the direct Lyapunov method for ensuring the stability of motion in compact invariant sets of finite-dimensional dynamical systems is shown. In the linear model of the restricted three-body problem, the possibility of ensuring the asymptotic stability of the periodic motion of a spacecraft (SC) in the vicinity of the collinear Lagrange point L2 using light pressure forces without the consumption of the working fluid is considered. The required area of control surfaces is estimated depending on the mass of the SC.

Space weather investigation Frontier (SWIFT)

The Space Weather Investigation Frontier (SWIFT) mission will aim at making major discoveries on the three-dimensional structure and dynamics of heliospheric structures that drive space weather. The focus will be on Interplanetary Coronal Mass Ejections (ICMEs) that originate from massive expulsions of plasma and magnetic flux from the solar corona. They cause the largest geomagnetic storms and solar energetic particle events, threatening to endanger life and disrupt technology on Earth and in space. A big current problem, both regarding fundamental solar-terrestrial physics and space weather, is that we do not yet understand spatial characteristics and temporal evolution of ICMEs and that the existing remote-sensing and in-situ observatories are not suited for resolving multi-layered and evolutionary structures in these massive storm drivers. Here, we propose a groundbreaking mission concept study using solar sail technology that, for the first time, will make continuous, in-situ multi-point observations along the Sun-Earth line beyond the Lagrange point L1 (sub-L1). This unique position, in combination with L1 assets, will allow distinguishing between local and global processes, spatial characteristics, temporal evolution, and particle energization mechanisms related to ICMEs. In addition, measurements of the magnetic field in earthbound ICMEs and their sub-structures from the SWIFT location will double the current forecasting lead-times from L1. This concept also paves the way for missions with increasingly longer forecasting lead-times, addressing NASA and NOAA’s space weather goals, as set forth by the Decadal Survey. The objective of this communication is to inform the community of the ongoing effort, including plans to further develop the mission concept, supported by the Heliophysics Flight Opportunities Studies (HFOS) program under NASA’s Research Opportunities in Space and Earth Sciences (ROSES).

Direct Lyapunov Method in the Problem of Ensuring the Stability of a Compact Minimum Set of a Dynamic System and the Formation of a Halo-Orbit Near the Lagrange Point L2

Direct Lyapunov Method in the Problem of Ensuring the Stability of a Compact Minimum Set of a Dynamic System and the Formation of a Halo-Orbit Near the Lagrange Point L2

The Origin of Extremely Nonradial Solar Wind Outflows

The origin of nonradial solar wind flows and their effect on space weather are poorly understood. Here we present a detailed investigation of 12 nonradial solar wind events during solar cycles 23–24, covering the period 1995–2017. In all these events the azimuthal flow angles of the solar wind exceed 6° as measured at the L1 Lagrangian point of the Sun–Earth system, for periods of 24 hr. In addition, all the events were selected during periods when coronal mass ejections (CMEs) and/or corotating interaction regions (CIRs) were absent. For most of the events, the near-Earth solar wind density was <5 cm−3 for periods exceeding 24 hr, similar to the well-known “solar wind disappearance events” wherein near-Earth solar wind densities dropped by two orders of magnitude for periods exceeding 24 hr. The solar source regions determined for all the cases were found to be associated with active region–coronal hole (AR–CH) pairs located around the central meridian. Further, the dynamical evolution of the source regions, studied using both the Extreme-ultraviolet Imaging Telescope and the Michelson Doppler Imager, showed a clear reduction in the CH area accompanied by the emergence of new magnetic flux regions. This dynamic evolution in the AR–CH source regions eventually disturbed the stable CH configurations, thereby giving rise to the extremely nonradial solar wind outflows. We discuss, based on our results, a possible causative mechanism for the origin of these highly nonradial flows that were not associated with either CMEs or CIRs.

Embrace through the universe: Sound design with cosmic muons and the parameters of solar wind

Although humans are destined to live in a world of chaos, there is also hidden beauty within it. Analogically, this implies that there can be a creative way of living through the exploration of the unknown. Considering humans are part of the dynamism of the whole universe that consists of matter and energy, what would it be like if they could feel being embraced through the universe? Having continuous dialogues with the organizer throughout the planning phase, an artistic performance with the sounds of the universe is presented at the cultural event Connected Ink 2021 in Tokyo. This performance is entitled Life, the Universe and Everything in homage to The Hitchhiker's Guide to the Galaxy by Douglas Adams. In this paper, the background, concepts, physics, sound design, and the process and result of the project are discussed in collaboration with artists, sound designers, and experimental physicists. Regarding the sound design, it had been developed, in part, based on what the authors have shown through the preliminary sound the installation: Particle Post – Letters from the Universe in 2019, through which the signals from cosmic muons that are captured by a scintillation detector are poetically designed. Transforming imperceivable elements of the universe into an appreciable form in a poetic manner is one of the crucial essences of the authors' research and practice. With this, we believe that we could approach the wonders of the universe aesthetically. Hence, imperceivable elements such as cosmic muons and the parameters of solar wind (density, speed, and temperature in particular) captured from the satellite DSCOVR orbiting the L1 Lagrange point, are brought into the audio system in almost real time. Five iron fuurin, Japanese wind bells, ring triggered by cosmic muons that constantly arrive on Earth, while the stylized sounds of solar wind surround the large space at the venue. Consequently, these two different kinds of ‘wind’ sounds create harmony within the space, hoping to create a similar harmony through the bodies and minds of the audience as well. This project also signifies the value of genuine dialogue and communication with the purpose of deepening an interdisciplinary collaboration and opening up further creation.

PINE-RT: An operational real-time plasmasphere model

The plasmasphere is a region of cold and dense plasma around the Earth, corotating with the Earth. Its plasma density is very dynamic under the influence of the solar wind and it influences several processes such as the GPS navigation, the surface charging of the satellites and the propagation and growth of plasma waves. In this manuscript, we present a new machine-learning model of the equatorial plasma density depending only on the Kp index and the solar-wind properties at the L1 Lagrange point. We call this model PINE-RT as it has been inspired by the recently-introduced PINE (Plasma density in the Inner magnetosphere Neural network-based Empirical) model and it has been developed to run in real-time (RT) in the context of the PAGER project. This project is an EU Horizon 2020 project aiming at forecasting the threats of satellite charging as a consequence of the solar activity 1–2 days ahead. In PAGER, the Kp index and the solar-wind properties at L1 are the inputs which are made available for the plasmasphere modeling. We report here the detailed derivation of the PINE-RT model and its validation and comparison with two state-of-the-art machine-learning and physics-based models. The model is currently running in real-time and its predictions are publicly available.

Dust as a solar shield

We revisit dust placed near the Earth–Sun L1 Lagrange point as a possible climate-change mitigation measure. Our calculations include variations in grain properties and orbit solutions with lunar and planetary perturbations. To achieve sunlight attenuation of 1.8%, equivalent to about 6 days per year of an obscured Sun, the mass of dust in the scenarios we consider must exceed 1010 kg. The more promising approaches include using high-porosity, fluffy grains to increase the extinction efficiency per unit mass, and launching this material in directed jets from a platform orbiting at L1. A simpler approach is to ballistically eject dust grains from the Moon’s surface on a free trajectory toward L1, providing sun shade for several days or more. Advantages compared to an Earth launch include a ready reservoir of dust on the lunar surface and less kinetic energy required to achieve a sun-shielding orbit.

The dynamics of co-orbital giant exomoons – applications for the Kepler-1625 b and Kepler-1708 b satellite systems

ABSTRACT Exomoons are a missing piece of exoplanetary science. Recently, two promising candidates were proposed, Kepler-1625 b-I and Kepler-1708 b-I. While the latter still lacks a dynamical analysis of its stability, Kepler-1625 b-I has already been the subject of several studies regarding its stability and origin. Moreover, previous works have shown that this satellite system could harbour at least two stable massive moons. Motivated by these results, we explored the stability of co-orbital exomoons using the candidates Kepler-1625 b-I and Kepler-1708 b-I as case studies. To do so, we performed numerical simulations of systems composed of the star, planet, and the co-orbital pair formed by the proposed candidates and another massive body. For the additional satellite, we varied its mass and size from a Mars-like to the case where both satellites have the same physical characteristics. We investigated the co-orbital region around the Lagrangian equilibrium point L4 of the system, setting the orbital separation between the satellites from θmin = 30° to θmax = 90°. Our results show that stability islands are possible in the co-orbital region of Kepler-1708 b-I as a function of the co-orbital companion’s mass and angular separation. Also, we identified that resonances of librational frequencies, especially the 2:1 resonance, can constrain the mass of the co-orbital companion. On the other hand, we found that the proximity between the host planet and the star makes the co-orbital region around Kepler-1625 b-I unstable for a massive companion. Finally, we provide TTV profiles for a planet orbited by co-orbital exomoons.

Space probe of the gravitational constant G

The empirical Gravitational constant G is of fundamental interest in metrology, Newtonian physics, and the field equations in General Relativity, particle physics, geophysics, and astrophysics. The precise value of G has yet to be known with the desired level of accuracy. In the 233 years since Cavendish, hundreds of experiments sought more accurate results but produced inconsistent results. Although they have had much more advanced supporting technology, past experiments have mostly stayed the same from the Cavendish approach. This paper shows that a different method is feasible to enhance the accuracy of G. A sphere made of metal with a large uniform mass density having a channel through the center with a bead oscillating back and forth in a simple-harmonic fashion. Monitoring the positions of the bead experimentally and comparing the predictions of the channel model will allow refining the value of G. The study develops a gravitational force function for the bead in a channeled sphere to provide more accuracy in the prediction of the bead's motion. This study determines that the best place to perform future gravitation constant experiments is in space far away from interfering effects. A near-perfect place is likely to be in outer space at the Sun-Earth Lagrange point L1, located about 1.5 million kilometers from the Earth on a line toward the Sun where other probes reside. It is estimated that three to six significant figures may be added to the current value of G.

First polarimetric evidence of the existence of the Kordylewski Dust Cloud at the L4 Lagrange point of the Earth–Moon system

ABSTRACT In 1961, Kordylewski found two bright patches near the L5 Lagrange point of the Earth–Moon system. This referred to an accumulation of dust particles, later called as Kordylewski dust cloud (KDC). In spite of the photographic observation of the L5 KDC by Kordylewski and its visual (naked-eyed) or photometric confirmation by others, some astronomers assumed that the KDC cannot exist, because the gravitational perturbation of the Sun may disrupt the stabilizing effect of the triangular Lagrange points L4 and L5 of the Earth and Moon. In 2017, the L5 KDC was observed in two consecutive nights by ground-based imaging polarimetry. So far the L5 KDC has been detected 16 times and the L4 KDC only 5 times. Contrary to the visually, photometrically, and polarimetrically documented existence of the L5 KDC, a polarimetric proof does not exist for the L4 KDC. On 2022 July 3, we were able to detect the polarization signals of the L4 KDC, furthermore on 2021 October 31 we detected polarimetrically again the L5 KDC. In this work, we present the first polarimetric evidence of the existence of the L4 KDC, and corroborate polarimetrically the existence of the L5 KDC for the third time.

Probing cosmic inflation with theLiteBIRDcosmic microwave background polarization survey

AbstractLiteBIRD, the Lite (Light) satellite for the study of B-mode polarization and Inflation from cosmic background Radiation Detection, is a space mission for primordial cosmology and fundamental physics. The Japan Aerospace Exploration Agency (JAXA) selected LiteBIRD in May 2019 as a strategic large-class (L-class) mission, with an expected launch in the late 2020s using JAXA’s H3 rocket. LiteBIRD is planned to orbit the Sun–Earth Lagrangian point L2, where it will map the cosmic microwave background polarization over the entire sky for three years, with three telescopes in 15 frequency bands between 34 and 448 GHz, to achieve an unprecedented total sensitivity of $2.2\, \mu$K-arcmin, with a typical angular resolution of 0.5○ at 100 GHz. The primary scientific objective of LiteBIRD is to search for the signal from cosmic inflation, either making a discovery or ruling out well-motivated inflationary models. The measurements of LiteBIRD will also provide us with insight into the quantum nature of gravity and other new physics beyond the standard models of particle physics and cosmology. We provide an overview of the LiteBIRD project, including scientific objectives, mission and system requirements, operation concept, spacecraft and payload module design, expected scientific outcomes, potential design extensions, and synergies with other projects.