Lagrange Point

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Gabor Horvath - One of the best experts on this subject based on the ideXlab platform.

  • why was the kordylewski dust cloud observed more frequently at the l5 Lagrange Point than at l4 asymmetry of the particle capture at the triangular Lagrange Points of the earth moon system
    Icarus, 2021
    Co-Authors: Judit Slizbalogh, Balint Erdi, Daniel Horvath, Gabor Horvath
    Abstract:

    Abstract In 1961, the Polish astronomer, Kazimierz Kordylewski found dust clouds around the triangular Lagrange Points L4 and L5 of the Earth-Moon system. After this discovery, several astronomers observed the Kordylewski dust clouds (KDCs) with photometry or ground-based imaging polarimetry, altogether 21 times. Remarkably, the L5 KDC has been detected three times (16) more than the L4 one (5). This may be due to varying sky and/or astronomical conditions during the KDC observations; for example, the Sun and Moon must be deep enough below the horizon, and the atmosphere must be as aerosol-free as possible. To reveal an additional possible physical reason for the asymmetric frequency of KDC observations, we performed computer simulations. We determined the particle capture at the L4 and L5 Points in a 28-day period before the 21 published KDC observations. We found that the L5 Point had by maximum 9% larger particle capture than L4, depending on the date of observation. We propose that this bias of the particle capture may be one of the reasons why the KDC has been observed more frequently around the L5 Lagrange Point than around L4.

  • celestial mechanics and polarization optics of the kordylewski dust cloud in the earth moon Lagrange Point l5 i three dimensional celestial mechanical modelling of dust cloud formation
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: Judit Slizbalogh, Andras Barta, Gabor Horvath
    Abstract:

    Since the discovery in 1772 of the triangular Lagrange Points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies around these Points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 Points of the Earth and Moon may be empty due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski found two bright patches near the L5 Point, which may refer to an accumulation of interplanetary particles. Since that time this formation is called the Kordylewski dust cloud (KDC). Until now only a very few computer simulations studied the formation and characteristics of the KDC. To fill this gap, we investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1860000 times separately. We mapped the size and shape of the conglomeratum of particles not escaped from the system sooner than an integration time of 3650 days around L5. Polarimetric observations of a possible KDC around L5 are presented in the second part of this paper.

Judit Slizbalogh - One of the best experts on this subject based on the ideXlab platform.

  • why was the kordylewski dust cloud observed more frequently at the l5 Lagrange Point than at l4 asymmetry of the particle capture at the triangular Lagrange Points of the earth moon system
    Icarus, 2021
    Co-Authors: Judit Slizbalogh, Balint Erdi, Daniel Horvath, Gabor Horvath
    Abstract:

    Abstract In 1961, the Polish astronomer, Kazimierz Kordylewski found dust clouds around the triangular Lagrange Points L4 and L5 of the Earth-Moon system. After this discovery, several astronomers observed the Kordylewski dust clouds (KDCs) with photometry or ground-based imaging polarimetry, altogether 21 times. Remarkably, the L5 KDC has been detected three times (16) more than the L4 one (5). This may be due to varying sky and/or astronomical conditions during the KDC observations; for example, the Sun and Moon must be deep enough below the horizon, and the atmosphere must be as aerosol-free as possible. To reveal an additional possible physical reason for the asymmetric frequency of KDC observations, we performed computer simulations. We determined the particle capture at the L4 and L5 Points in a 28-day period before the 21 published KDC observations. We found that the L5 Point had by maximum 9% larger particle capture than L4, depending on the date of observation. We propose that this bias of the particle capture may be one of the reasons why the KDC has been observed more frequently around the L5 Lagrange Point than around L4.

  • celestial mechanics and polarization optics of the kordylewski dust cloud in the earth moon Lagrange Point l5 i three dimensional celestial mechanical modelling of dust cloud formation
    Monthly Notices of the Royal Astronomical Society, 2018
    Co-Authors: Judit Slizbalogh, Andras Barta, Gabor Horvath
    Abstract:

    Since the discovery in 1772 of the triangular Lagrange Points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies around these Points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 Points of the Earth and Moon may be empty due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski found two bright patches near the L5 Point, which may refer to an accumulation of interplanetary particles. Since that time this formation is called the Kordylewski dust cloud (KDC). Until now only a very few computer simulations studied the formation and characteristics of the KDC. To fill this gap, we investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1860000 times separately. We mapped the size and shape of the conglomeratum of particles not escaped from the system sooner than an integration time of 3650 days around L5. Polarimetric observations of a possible KDC around L5 are presented in the second part of this paper.

S. Balachandar - One of the best experts on this subject based on the ideXlab platform.

  • self induced temperature correction for inter phase heat transfer in euler Lagrange Point particle simulation
    Journal of Computational Physics, 2019
    Co-Authors: Kai Liu, Mandar Lakhote, S. Balachandar
    Abstract:

    Abstract In a two-way coupled Euler-Lagrange simulation, particles are approximated as Point sources and their momentum and energy exchange with the surrounding flow are modeled through Point-particle force and heat transfer models. As the particle size increases and approaches the Eulerian grid, the feedback force and heat transfer become large and strongly affect the local flow at the particle location. The fluid velocity and temperature computed in the EL simulation when interpolated to the particle location will be substantially different from the corresponding undisturbed values. In this work we will follow the approach pursued in Balachandar et al. (2018) [1] for self-induced velocity correction to develop an analogous correction procedure for self-induced temperature. We obtain analytical solutions for the self-induced thermal perturbation for a steady uniform cross flow past a Gaussian filtered heat source under both steady and unsteady conditions. The analytical results are extended to finite Peclet number using numerical simulations. The resulting quasi-steady and unsteady models are tested with a simple problem of exponential thermal evolution against the corresponding EL simulation results. We also provide a simple criterion for when the self-induced temperature correction is needed in an Euler-Lagrange simulation.

  • self induced velocity correction for improved drag estimation in euler Lagrange Point particle simulations
    Journal of Computational Physics, 2019
    Co-Authors: S. Balachandar, Mandar Lakhote
    Abstract:

    Abstract In Euler–Lagrange (EL) simulations the force on each particle is obtained from a Point-particle model, which is then coupled back to the fluid momentum. The feedback force modifies the flow at the particle location and it is important to evaluate the resulting self-induced velocity disturbance, since the Point-particle models are based on the undisturbed flow. An exact solution of the Oseen's equation for flow generated by a steady Gaussian feedback force was obtained, which along with the corresponding finite Reynolds number numerical simulations, provided a steady model for the self-induced velocity disturbance. The unsteady problem of a time dependent Gaussian feedback force was then theoretically investigated in the zero Reynolds number limit. The corresponding finite Reynolds number unsteady results were obtained using companion numerical simulations. Based on these results an unsteady model for predicting the self-induced velocity disturbance was developed. The two main non-dimensional quantities affecting the self-induced velocity disturbance are the Reynolds number based on Gaussian width Re σ and the non-dimensional feedback force F ˜ . The resulting self-induced velocity correction model is general and can be applied in a variety of EL Point-particle simulations, with the time history of Re σ and F ˜ as input. The quasi-steady and unsteady versions of the model were tested in the context of a freely settling particle. The unsteady model was shown to predict the self-induced velocity disturbance to reasonable accuracy for a wide range of Reynolds and Stokes numbers. Issues pertaining to practical implementation and limitations are discussed.

Mandar Lakhote - One of the best experts on this subject based on the ideXlab platform.

  • self induced temperature correction for inter phase heat transfer in euler Lagrange Point particle simulation
    Journal of Computational Physics, 2019
    Co-Authors: Kai Liu, Mandar Lakhote, S. Balachandar
    Abstract:

    Abstract In a two-way coupled Euler-Lagrange simulation, particles are approximated as Point sources and their momentum and energy exchange with the surrounding flow are modeled through Point-particle force and heat transfer models. As the particle size increases and approaches the Eulerian grid, the feedback force and heat transfer become large and strongly affect the local flow at the particle location. The fluid velocity and temperature computed in the EL simulation when interpolated to the particle location will be substantially different from the corresponding undisturbed values. In this work we will follow the approach pursued in Balachandar et al. (2018) [1] for self-induced velocity correction to develop an analogous correction procedure for self-induced temperature. We obtain analytical solutions for the self-induced thermal perturbation for a steady uniform cross flow past a Gaussian filtered heat source under both steady and unsteady conditions. The analytical results are extended to finite Peclet number using numerical simulations. The resulting quasi-steady and unsteady models are tested with a simple problem of exponential thermal evolution against the corresponding EL simulation results. We also provide a simple criterion for when the self-induced temperature correction is needed in an Euler-Lagrange simulation.

  • self induced velocity correction for improved drag estimation in euler Lagrange Point particle simulations
    Journal of Computational Physics, 2019
    Co-Authors: S. Balachandar, Mandar Lakhote
    Abstract:

    Abstract In Euler–Lagrange (EL) simulations the force on each particle is obtained from a Point-particle model, which is then coupled back to the fluid momentum. The feedback force modifies the flow at the particle location and it is important to evaluate the resulting self-induced velocity disturbance, since the Point-particle models are based on the undisturbed flow. An exact solution of the Oseen's equation for flow generated by a steady Gaussian feedback force was obtained, which along with the corresponding finite Reynolds number numerical simulations, provided a steady model for the self-induced velocity disturbance. The unsteady problem of a time dependent Gaussian feedback force was then theoretically investigated in the zero Reynolds number limit. The corresponding finite Reynolds number unsteady results were obtained using companion numerical simulations. Based on these results an unsteady model for predicting the self-induced velocity disturbance was developed. The two main non-dimensional quantities affecting the self-induced velocity disturbance are the Reynolds number based on Gaussian width Re σ and the non-dimensional feedback force F ˜ . The resulting self-induced velocity correction model is general and can be applied in a variety of EL Point-particle simulations, with the time history of Re σ and F ˜ as input. The quasi-steady and unsteady versions of the model were tested in the context of a freely settling particle. The unsteady model was shown to predict the self-induced velocity disturbance to reasonable accuracy for a wide range of Reynolds and Stokes numbers. Issues pertaining to practical implementation and limitations are discussed.

Roger J P Angel - One of the best experts on this subject based on the ideXlab platform.

  • feasibility of cooling the earth with a cloud of small spacecraft near the inner Lagrange Point l1
    Proceedings of the National Academy of Sciences of the United States of America, 2006
    Co-Authors: Roger J P Angel
    Abstract:

    If it were to become apparent that dangerous changes in global climate were inevitable, despite greenhouse gas controls, active methods to cool the Earth on an emergency basis might be desirable. The concept considered here is to block 1.8% of the solar flux with a space sunshade orbited near the inner Lagrange Point (L1), in-line between the Earth and sun. Following the work of J. Early [Early, JT (1989) J Br Interplanet Soc 42:567–569], transparent material would be used to deflect the sunlight, rather than to absorb it, to minimize the shift in balance out from L1 caused by radiation pressure. Three advances aimed at practical implementation are presented. First is an optical design for a very thin refractive screen with low reflectivity, leading to a total sunshade mass of ≈20 million tons. Second is a concept aimed at reducing transportation cost to $50/kg by using electromagnetic acceleration to escape Earth's gravity, followed by ion propulsion. Third is an implementation of the sunshade as a cloud of many spacecraft, autonomously stabilized by modulating solar radiation pressure. These meter-sized “flyers” would be assembled completely before launch, avoiding any need for construction or unfolding in space. They would weigh a gram each, be launched in stacks of 800,000, and remain for a projected lifetime of 50 years within a 100,000-km-long cloud. The concept builds on existing technologies. It seems feasible that it could be developed and deployed in ≈25 years at a cost of a few trillion dollars, <0.5% of world gross domestic product (GDP) over that time.