Charged Satellite Research Articles

Perturbations of Zonal and Tesseral Harmonics on Frozen Orbits of Charged Satellites

The objective of this research is to address the issue of frozen orbits in charged satellites by incorporating geopotential zonal harmonics up to J6 and the initial tesseral harmonics. The employed model starts from the first normalized Hamiltonian to calculate specific sets of long-term frozen orbits for charged satellites. To explore the frozen orbits acquired, a MATHEMATICA CODE is developed. The investigation encompasses extensive variations in orbit altitudes by employing the orbital inclination and argument of periapsis as freezing parameters. The determined ranges ensuring frozen orbits are derived from the generated figures. Three-dimensional presentations illustrating the freezing inclination in relation to eccentricity, argument of periapsis, and semi-major axis parameters are presented. Additional three-dimensional representations of the phase space for the eccentricity vector and its projection onto the nonsingular plane are examined. In all investigated scenarios, the impacts of electromagnetic (EM) field perturbations on the freezing parameters of a charged satellite are demonstrated.

The frozen orbits of the charged satellites under zonal harmonics perturbation

In the present work, the problem of frozen orbits of a charged satellite around the Earth is treated. The geopotential is considered as oblate body up to J6 zonal harmonics. The first normalized Hamiltonian is utilized so as to compute families of the long-term frozen orbits for a charged satellite in the concerned model using the Lie transform method. Since the mathematical model of the problem is complicated, the Hamilton canonical equations have been solved numerically. Our numerical investigation of the considered dynamical system reveals no frozen orbits can be obtained for orbits with perigee point lies on the equator g∈0.0°, 0.180°. But, in the neighbouhood of these orbits, equilibria for a very nearly circular orbits as well as equatorial HEO exist. Our results reflected the remarkable effects of the electromagnetic perturbations on the frozen orbit dynamics, especially for the medium and high Earth orbits. Investigating charged satellites carrying different electronic charges, the phase space (I,e) is noticeably changed near the equilibria g=n(180°),n=0,1. It is observed also that a very little change in the amount of charge carried by the satellite, gives rise to a change in the phase space especially for the nearly circular orbits that have inclinations in between the two roots of critical of inclinations.

Dynamics of electrified jets in electrohydrodynamic atomization

An electrified jet ejected from a meniscus (or Taylor cone) can further disintegrate into fine drops with different modes in electrohydrodynamic atomization (EHDA). This process has been applied into many fields because of controllable production of highly charged and monodispersed drops. However, both stable and unstable electrified jets are encountered in EHDA, usually depending on liquid physical properties and operating parameters. A series of electrified jets are visualized and the transient breakup dynamics are analyzed within an electric field. According to the geometry forms of drops or/and jets emitted from the end of a needle, periodic dripping, pulsating-jet, stable-jet, and unstable jet are clearly classified. The operating parameters versus spraying modes are also discussed, especially for propylene glycol and n-octanol. The initial velocity from the Taylor cone, jet breakup length, jet position, and the size separation effect are deeply studied. The jet velocity is significantly accelerated by electric stresses and good agreement with predicted value. The jet breakup length increases sharply as liquid flow rate increasing and slowly increases as electric potential increasing, except for small liquid flow rate where bullet cone occurs. The jet ejection point varies and gradually deflects off needle axis with an increase in electric potential. The ‘size separation effect’ can help improve the quality of printing by removed highly charged satellite drops.

SENTINEL-2 IMAGERY FOR MAPPING AND MONITORING IMPERVIOUSNESS IN URBAN AREAS

Abstract. Nowadays there is need to take the action to find out the innovative solutions to reduce the negative effects of climate change in urban areas. Cities face multiple challenges in water management and flood protection at local scale, especially given an uncertain future climate and a rapidly growing population. The density of impervious surfaces (roofs and pavement) is a key element in evaluating hydrologic processes and occurring the surface runoff – the major component of water cycle in urban catchment. Satellite imagery are powerful and up-to-date data for estimation human impact on urban space. It is also highlighted the possibility of using those results in urban development studies according to adaptation cities to climate change. The Copernicus SENTINEL constellation brings out the potential to provide high quality and free of charge satellites images that enable to estimate parameters related to urban structure and imperviousness. Multitemporal Sentinel-2 data are widely used to calculate the indices for urban sprawl. The normalized difference built-up index (NDBI) and normalized difference vegetation index (NDVI), indicators providing information on urban heat Island effect, are useful for change detection of imperviousness percentage in urban areas. The main objective of this research is fusion of multi-temporal and multi-resolution SENTINEL-2 MSI data for developing a new, innovative approach for improving water management in urban catchments at local scale provide valuable input data for hydrological model. The results obtained were compared by quantitative comparison with Imperviousness HRL of Copernicus Program, visual comparison with OpenStreetMap data as well as qualitative comparison with the high resolution Planet’s.

Charged Satellite Drop Avoidance in Electrohydrodynamic Dripping.

The quality of electrohydrodynamic jet (e-jet) printing is crucially influenced by the satellite drop formed when the primary drop detaches from the meniscus. If the satellite drop falls onto the substrate, the patterns on the substrate will be contaminated. The electric charge carried by the satellite drop leads to more complex satellite/meniscus interaction than that in traditional inkjet printing. Here, we numerically study the formation and flight behavior of the charged satellite drop. This paper discovered that the charge relaxation time (CRT) of the liquid determines the electric repulsion force between the satellite drop and meniscus. The satellite drop will merge with the meniscus at long CRT, and fail to merge and deteriorate the printing quality at short CRT. The simulations are adopted to discover the mechanism of generation and flight behavior of charged satellite drops. The results show that the critical CRT decreases with the dielectric constant of the liquid and the supplied flow rate. Namely, for small dielectric constant and fixed CRT, the satellite drop is less likely to merge with the meniscus, and for high flow rate, the satellite drop is prone to merge with the meniscus due to the delay of necking thread breakup. These results will help to choose appropriate parameters to avoid the satellite drop from falling onto the substrate.

Characteristics of Polar Wind Flows at Altitudes of about 20000 km

The problem of the outflow of ionospheric plasma into the magnetosphere is considered. In particular, the phenomenon of the polar wind observed in the polar cap is studied. The study of this phenomenon is complicated by the fact that the field-alined velocities of individual ions are small, and therefore, the electric field of the positively charged satellite prevents their measurement. This paper examines the measurements carried out on the Interball-2 satellite at altitudes of ~20000 km and compares them with the results of simulations within the framework of the GSM TIP model. It has been demonstrated the GSM TIP model well describes the outflow of H+ ions from the ionosphere to the magnetosphere in the polar cap.

Modelling of charged satellite motion in Earth’s gravitational and magnetic fields

In this work Lagrange’s planetary equations for a charged satellite subjected to the Earth’s gravitational and magnetic force fields are solved. The Earth’s gravity, and magnetic and electric force components are obtained and expressed in terms of orbital elements. The variational equations of orbit with the considered model in Keplerian elements are derived. The solution of the problem in a fully analytical way is obtained. The temporal rate of changes of the orbital elements of the spacecraft are integrated via Lagrange’s planetary equations and integrals of the normalized Keplerian motion obtained by Ahmed (Astron. J. 107(5):1900, 1994).

Influence of the electric induction drag on the orbit of a charged satellite moving in the ionosphere (solution by the method of the average value)

The secular effects of the electric induction drag on the orbit of a charged satellite moving in the ionosphere are examined by the method of average values. The first solutions are obtained under the assumption of non-rotation of the Earth; the second solutions are obtained assuming rotation of the Earth. In the first case the semi-major axis exhibits secular variation, but the other orbital elements exhibit no secular variation. In the second case both semi-major axis and eccentricity exhibit secular variation, but the other orbital elements exhibit no secular variation. It can be shown that the semi-major axis is contracted due to the action of the electric induction drag if the satellite has enough charge in the ionosphere. The eccentricity is decreased gradually with time, but its variation is very small for the case of a rotating Earth. An example is presented in which the secular effects of the electric induction drag on the orbits of a charged satellite are calculated. The numerical results are given in Table 1 and a discussion of them is presented in Table 2.

Periodic solutions for rotational motion of an axially symmetric charged satellite

Periodic solutions for rotational motion of an axially symmetric charged satellite

Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques

The attitude dynamics of a rigid artificial satellite subject to a gravity gradient and Lorentz torques in a circular orbit are considered. Lorentz torque is developed on the basis of the electrodynamic effects of the Lorentz force acting on the charged satellite's surface. We assume that the satellite is moving in a Low Earth Orbit in the geomagnetic field, which is considered to be a dipole. Our model of torque due to the Lorentz force is developed for an artificial satellite with a general shape, and the nonlinear differential equations of Euler are used to describe its attitude orientation. All equilibrium positions are determined and conditions for their existence are obtained. The numerical results show that the charge q and radius ρ0 of the center of charge for the satellite provide a certain type of semi-passive control for the attitude of the satellite. The technique for this kind of control would be to increase or decrease the electrostatic screening on the satellite. The results obtained confirm that the change in charge can affect the magnitude of the Lorentz torque, which can also affect control of the satellite. Moreover, the relationship between magnitude of the Lorentz torque and inclination of the orbit is investigated.

J192013 帯電衛星を用いたスペースデブリ除去に関する研究([J192]ロボティクスと宇宙)

J192013 帯電衛星を用いたスペースデブリ除去に関する研究([J192]ロボティクスと宇宙)

Spacecraft Formation Flying Dynamics and Control Using the Geomagnetic Lorentz Force

The motion of a charged satellite subjected to the Earth’s magnetic field is considered. The Lorentz force, which acts on a charged particle when it is moving through a magnetic field, provides a new concept of propellantless electromagnetic propulsion. A dynamic model of a charged satellite, including the effect of the Lorentz force in the vicinity of a circular or an elliptic orbit, is derived and its application to formation flying is considered. Based on Hill–Clohessy–Wiltshire equations and Tschauner–Hempel equations, analytical approximations for the relative motion in Earth orbit are obtained. The analysis based on the linearized equations shows the controllability of the system by stepwise charge control. The sequential quadratic programming method is applied to solve the orbital transfer problem of the original nonlinear equations in which the analytical solutions cannot be obtained. A strategy to reduce the charge amount using sequential quadratic programming is also developed.

Mechanism of half-frequency electric dipole spin resonance in double quantum dots: Effect of nonlinear charge dynamics inside the singlet manifold

Electron dynamics in quantum dots manifests itself in spin-flip spectra through electric dipole spin resonance (EDSR). Near a neutrality point separating two different singlet charged states of a double quantum dot, charge dynamics inside a $2\ifmmode\times\else\texttimes\fi{}2$ singlet manifold can be described by a $1/2$ pseudospin. In this region, charge dynamics is highly nonlinear and strongly influenced by flopping its soft pseudospin mode. As a result, the responses to external driving include first and second harmonics of the driving frequency and their Raman satellites shifted by the pseudospin frequency. In EDSR spectra of a spin-orbit couplet doublet dot, they manifest themselves as charge satellites of spin-flip transitions. The theory describes gross features of the anomalous half-frequency EDSR in spin blockade spectra [E. A. Laird et al., Semicond. Sci. Techol. 24, 064004 (2009)].

Attitude dynamics of a pendulum-shaped charged satellite

In this paper, we investigate the possibility of the use of the Lorentz force, which acts on charged satellite when it is moving through the magnetic field, as a means of satellite attitude control. We first derive the equations of attitude motion of charged satellite and then investigate the stability of the motion. Finally we propose an attitude control method using the Lorentz force. Our method requires moderate charge level for future Lorentz-augmented satellite.

Influence of geomagnetic field on the motion of low satellites

The first aim of the present work is to compute a more accurate and recent model for the Earth’s magnetic field. The second aim is to determine the effects of the Earth’s magnetic field on the motion of a charged artificial satellite to evaluate the variations of the orbital elements of the satellite due to these effects. The magnetic field and its variation with time have been studied at different heights, longitudes and latitudes. The geomagnetic field is considered as a multiple potential field and the electrical charge of the satellite is assumed to be constant. A new computer code has been constructed to follow the components of the magnetic field in spherical harmonic models. The Gauss equations are solved numerically. The results concentrate on the computation of the numerical values of orbital perturbation for the case of a low Earth satellite. RS-1 satellite and space craft gravity probe B (GPB) are chosen as cases of studies for a detailed numerical analysis.

Моделирование измерений тепловых ионов Н+ на заряженном спутнике с учетом температурной анизотропии

The mass-spectrometer model of thermal ionospheric ions measurements was considered in case of charged satellite. Hyperboloid device characteristics onboard Interball-2 satellite was used for mathematical model of measurements. It was shown that angular ion distribution function changed due to temperature anisotropy and it can be interprets by different ways. Positive satellite potential increases these effects.

New Synchronous Orbits Using the Geomagnetic Lorentz Force

The Lorentz-augmented orbits concept provides propellantless electromagnetic propulsion without a tether, using the interaction between an electrostatically charged satellite and the Earth's magnetic field to provide a useful thrust. New types of Earth-synchronous orbits are found from equations governing the motion of satellites experiencing the Lorentz force in orbit. The equations of motion for such a spacecraft are derived based on a simplified magnetic field model, in which the dipole is aligned with true north. For a polar-orbiting satellite, a constant electrical charge can create arbitrary changes in the right-ascension angle. This method allows for single-orbit repeat-groundtrack low-Earth-orbit satellites. Analytical expressions for changes in orbital elements due to Lorentz forces are verified by numerical simulation for the polar and equatorial cases. In the equatorial case, manipulation of the longitude of perigee by constant electrostatic charge is possible. Perigee movement also allows for the creation of an Earth-synchronous type of orbit. The case of a dipole field, for which the north pole is not aligned with true north, is also examined. Feedback control using only the Lorentz force for actuation is shown to stabilize this general case.

Charge distribution consequences of the magnetic order in TbB6

AbstractThe antiferromagnetic state of TbB6 has been investigated by way of magnetostriction and X‐ray scattering measurements on a single crystal. The magnetostriction data reveal a well defined tetragonal symmetry lowering and a weak volume increase below TN . The X‐ray scattering investigation shows charge satellites, related to the 〈${1 \over 2}$00〉 and 〈${1 \over 2}$${1 \over 2}$0〉 wave vectors stars. The 〈${1 \over 2}$00〉 satellites are characteristic of exchange displacement waves, similar to those observed in GdB6, whereas the 〈${1 \over 2}$${1 \over 2}$0〉 ones could result as well from 4f multipolar scattering. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earth’s oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellite’s rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.

P–f mixing in CeSb, studied by resonant X-ray scattering

X-ray magnetic scattering experiments have been performed in CeSb at the Ce and Sb L edges. In the non-resonant regime, we observe charge satellites reflecting the lattice modulation associated with the periodicity of paramagnetic Γ 8 planes. At the Ce L 2 edge we observe strong magnetic resonances, due to the antiferromagnetic stacking of the ferromagnetic Γ 7. The study at the Sb L 1 edge shows a magnetic dipole resonance, which supports the model of strong p–f mixing, used to explain the origin of the long-range magnetic order of CeSb.