We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means o...We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits,Lyapunov exponents,and Poincarémaps.Based on several periodic orbits with different sizes and shapes,they are encoded systematically with two letters or four letters for two different sets of parameters.The periodic orbits outside the attractor with complex topology are discovered by accident.In addition,the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively.In this process,the rule of orbital period changing with parameters is also investigated.The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.展开更多
By analytically solving the equation of azimuthal null geodesics for spherical photon trajectories, a parametric representation of the corresponding segment of the orbit is obtained. The solution parameter is the lati...By analytically solving the equation of azimuthal null geodesics for spherical photon trajectories, a parametric representation of the corresponding segment of the orbit is obtained. The solution parameter is the latitude coordinate. The dependences of the orbital radius on the black hole spinning parameter and the angle of inclination of its plane with respect to the rotation axis are calculated for flat circular non-equatorial orbits. It is proved that all spherical photon trajectories in the Kerr spacetime are unstable, as well as equatorial ones, and the critical photon orbits in the Schwarzschild metric.展开更多
Even after extensive research in Quantum Mechanics, we are still unable to visualize instant-to-instant motion of an electron in hydrogen atom. That is because in QM treatment, potential energy term has been mistakenl...Even after extensive research in Quantum Mechanics, we are still unable to visualize instant-to-instant motion of an electron in hydrogen atom. That is because in QM treatment, potential energy term has been mistakenly assumed to be time-independent instead of depending on the instant-to-instant varying position of the orbiting electron [1]. This has led to wrong and weird solutions for the electron motion in hydrogen atom. Before the advent of wave mechanics, Sommerfeld model of elliptical electron orbits was able to explain most features of hydrogen spectra, except for the features associated with electron spin and magnetic moment interactions. However, the Sommerfeld elliptical orbits were of kinematic origin and could not provide visualization of instant-to-instant dynamic motion of the orbiting electron. Contrary to the QM perspective, we find that central core of the electron behaves as a classical particle while its electrostatic field behaves as a wave phenomenon. As such an electron under Coulomb force moves strictly in accordance with Newtonian laws of motion. In this paper, we develop dynamic electron orbits in hydrogen atom by using energy and angular momentum conservation principle in central force field. We have shown that during photon emission, angular momentum of the orbiting electron is changed by ħ due to recoil action. This may be the origin of various quantization rules. During emission of a photon, elliptical orbit transitions are also computed and plotted. Orbit transition time is of the order of 10<sup>-16</sup> seconds. We have extended this methodology to compute electron orbits in hydrogen molecular bond and computed the H<sub>2</sub> bond energy.展开更多
The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and freque...The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and frequency of the wireless signal between different receivers.Therefore,ground monitoring stations need to be equipped with more than two antenna receiving stations,and multiple satellites should be able to simultaneously relay the distress signal from the target source in order to achieve the geolocation function.However,when the ground receiving system has only one antenna receiving station,or the target source is in a heavily obscured environment,the ground side is unable to receive the forwarded signals from multiple satellites at the same time,which will make it impossible to locate.To address these problems,in this paper,a time-sharing single satellite geolocations method based on different orbits is proposed for the first time.This method uses one or several low-earth orbit satellites(LEO)and mediumearth orbit satellites(MEO)in the visible area,and the receiving station only needs one pair of receiving antennas to complete the positioning.It can effectively compensate for the shortcomings of the traditional TDOA using the same moment and have better positioning accuracy compared with the single satellite in the same orbit.Due to the limited experimental conditions,this paper tests the navigation satellite using different orbit time-sharing single satellite geolocations,and proves that the positioning method has high positioning accuracy and has certain promotion and application value.展开更多
We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In ...We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.展开更多
We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of plan...We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.展开更多
Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around...Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.展开更多
High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbita...High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.展开更多
This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primar...This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.展开更多
We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic or...We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of (h is energy constant;μ is mass ratio of the two primaries;are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.展开更多
A practical method is proposed to search for periodic orbits of elongated asteroids.The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters,and th...A practical method is proposed to search for periodic orbits of elongated asteroids.The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters,and then implement local iterations to obtain the real orbits over an asteroid in the polyhedral model.In this paper the dipole and polyhedral models,and list detailed procedures of the searching method are introduced.A planar single lobe orbit is presented to evaluate the effectiveness of the method,with the asteroid 216 Kleopatra of the triple asteroid system as a representative elongated body.By applying the above method,ten families of periodic orbits around Kleopatra are identified and discussed with respect to their orbital stabilities and periods.One sample of the sombrero orbit is checked by calculating 1000 hours to examine its orbital behavior.Besides the above orbits,the intriguing head-surrounding orbit is also analyzed.展开更多
For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node...For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guaran-tee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained.展开更多
In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimen...In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.展开更多
Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits...Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits are exponentially unstable,the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories.The inhibit force transforms the unstable component to a stable ...展开更多
We present a numerical method for efficiently detecting unstable periodic orbits(UPO’s)embedded in chaotic attractors of high-dimensional systems.This method,which we refer to as subspace fixed-point iteration, locat...We present a numerical method for efficiently detecting unstable periodic orbits(UPO’s)embedded in chaotic attractors of high-dimensional systems.This method,which we refer to as subspace fixed-point iteration, locates fixed points of Poincare maps using a form of fixed-point iteration that splits the phase space into appropriate subspaces.In this paper,among a number of possible implementations,we primarily focus on a subspace method based on the Schmelcher-Diakonos(SD)method that selectively locates UPO’s by varying a stabilizing matrix,and present some applications of the resulting subspace SD method to hyperchaotic attractors where the UPO’s have more than one unstable direction.展开更多
We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characteriza...We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of Einstein field Equations even in the case of a static weak field. However, both theories have a common limit corresponding to the case in which the alien concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well as an infinite set of LRL vectors, result all from one vector. The hodograph is a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle for bound motion.展开更多
In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The...In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).展开更多
In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbi...In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.展开更多
The lifetime of a lunar satellite orbit is constrained by the non-spherical nature of the Moon’s gravity field. The orbital lifetime of lunar orbits depends significantly on the initial conditions of the orbit. Right...The lifetime of a lunar satellite orbit is constrained by the non-spherical nature of the Moon’s gravity field. The orbital lifetime of lunar orbits depends significantly on the initial conditions of the orbit. Right ascension of ascending node (Ω) is one of the important orbital parameter affecting the orbital lifetime. In the present work we have analyzed the effect of Ω on the variation of lifetime with altitude for circular lunar orbits. It is found that at a particular initial altitude, a small increase in the altitude results in substantial increase in the orbital lifetime due to effect of the long periodic terms of Earth’s gravity on eccentricity and this transition altitude is different for different Ω. Further, it is observed that the variation of transition altitude with Ω follows a definite, but different trend for orbits with different inclinations. The transition altitude for polar orbits is found to be higher without the effect of Sun and Earth gravity. Variation of transition altitude with orbital inclination is also analyzed. Lifetimes of high altitude circular lunar orbits are analyzed and it is observed that at high altitudes lifetime decreases with altitude.展开更多
Conventional interpretation of the Einstein Equation has inconsistencies and contradictions, such as gravitational fields without energy, objects crossing event-horizons, objects exceeding the speed of light, and inco...Conventional interpretation of the Einstein Equation has inconsistencies and contradictions, such as gravitational fields without energy, objects crossing event-horizons, objects exceeding the speed of light, and inconsistency in scaling the speed of light and its factors. An isotropic metric resolves such problems by attributing energy to the gravitational field, in the Einstein Equation. This paper discusses symmetries of an isotropic metric, including scaling of physical quantities, the Lorentz transformation, covariant derivatives, and stress-energy tensors, and transitivity of this scaling between inertial reference frames. Force, charge, Planck’s constant, and the fine structure constant remain invariant under isotropic gravitational scaling. Gravitational scattering, orbital period, and precession distinguish between isotropic and Schwarzschild metrics. An isotropic metric accommodates quantum mechanics and improves models of black-holes.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12205257,11647085,and11647086)the Shanxi Province Science Foundation for Youths(Grant No.201901D211252)+1 种基金Fundamental Research Program of Shanxi Province(Grant No.202203021221095)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi of China(Grant Nos.2019L0505,2019L0554,and 2019L0572)。
文摘We use the variational method to extract the short periodic orbits of the Qi system within a certain topological length.The chaotic dynamical behaviors of the Qi system with five equilibria are analyzed by the means of phase portraits,Lyapunov exponents,and Poincarémaps.Based on several periodic orbits with different sizes and shapes,they are encoded systematically with two letters or four letters for two different sets of parameters.The periodic orbits outside the attractor with complex topology are discovered by accident.In addition,the bifurcations of cycles and the bifurcations of equilibria in the Qi system are explored by different methods respectively.In this process,the rule of orbital period changing with parameters is also investigated.The calculation and classification method of periodic orbits in this study can be widely used in other similar low-dimensional dissipative systems.
文摘By analytically solving the equation of azimuthal null geodesics for spherical photon trajectories, a parametric representation of the corresponding segment of the orbit is obtained. The solution parameter is the latitude coordinate. The dependences of the orbital radius on the black hole spinning parameter and the angle of inclination of its plane with respect to the rotation axis are calculated for flat circular non-equatorial orbits. It is proved that all spherical photon trajectories in the Kerr spacetime are unstable, as well as equatorial ones, and the critical photon orbits in the Schwarzschild metric.
文摘Even after extensive research in Quantum Mechanics, we are still unable to visualize instant-to-instant motion of an electron in hydrogen atom. That is because in QM treatment, potential energy term has been mistakenly assumed to be time-independent instead of depending on the instant-to-instant varying position of the orbiting electron [1]. This has led to wrong and weird solutions for the electron motion in hydrogen atom. Before the advent of wave mechanics, Sommerfeld model of elliptical electron orbits was able to explain most features of hydrogen spectra, except for the features associated with electron spin and magnetic moment interactions. However, the Sommerfeld elliptical orbits were of kinematic origin and could not provide visualization of instant-to-instant dynamic motion of the orbiting electron. Contrary to the QM perspective, we find that central core of the electron behaves as a classical particle while its electrostatic field behaves as a wave phenomenon. As such an electron under Coulomb force moves strictly in accordance with Newtonian laws of motion. In this paper, we develop dynamic electron orbits in hydrogen atom by using energy and angular momentum conservation principle in central force field. We have shown that during photon emission, angular momentum of the orbiting electron is changed by ħ due to recoil action. This may be the origin of various quantization rules. During emission of a photon, elliptical orbit transitions are also computed and plotted. Orbit transition time is of the order of 10<sup>-16</sup> seconds. We have extended this methodology to compute electron orbits in hydrogen molecular bond and computed the H<sub>2</sub> bond energy.
基金supported by National Science Foundation of China(No.91738201,U21A20450)。
文摘The main geolocation technology currently used in COSPAS-SARSAT system is TDOA/FDOA or three-star TDOA,the principle is to determine the location of the signal source by using the difference in arrival time and frequency of the wireless signal between different receivers.Therefore,ground monitoring stations need to be equipped with more than two antenna receiving stations,and multiple satellites should be able to simultaneously relay the distress signal from the target source in order to achieve the geolocation function.However,when the ground receiving system has only one antenna receiving station,or the target source is in a heavily obscured environment,the ground side is unable to receive the forwarded signals from multiple satellites at the same time,which will make it impossible to locate.To address these problems,in this paper,a time-sharing single satellite geolocations method based on different orbits is proposed for the first time.This method uses one or several low-earth orbit satellites(LEO)and mediumearth orbit satellites(MEO)in the visible area,and the receiving station only needs one pair of receiving antennas to complete the positioning.It can effectively compensate for the shortcomings of the traditional TDOA using the same moment and have better positioning accuracy compared with the single satellite in the same orbit.Due to the limited experimental conditions,this paper tests the navigation satellite using different orbit time-sharing single satellite geolocations,and proves that the positioning method has high positioning accuracy and has certain promotion and application value.
文摘We analyze the periodic orbits, quasi periodic orbits and chaotic orbits in the photo gravitational Sun-Saturn system incorporating actual oblateness of Saturn in the planar circular restricted three body problem. In this paper, we study the effect of solar radiation pressure on the location of Sun centered and Saturn centered orbits, its diameter, semi major axis and eccentricity by taking different values of solar radiation pressure q and different values of Jacobi constant “C”, and by considering actual oblateness of Saturn using Poincare surface of section (PSS) method. It is ob-served that by the introduction of perturbing force due to solar radiation pressure admissible range of Jacobi constant C decreases, it is also observed that as value of C decreases the number of islands decreases and as a result the number of periodic and quasi periodic orbits decreases.Fur-ther, the periodic orbits around Saturn and Sun moves towards Sun by decreasing perturbation due to solar radiation pressure q for a specific choice of Jacobi constant C. It is also observed that due to solar radiation pressure, semi major axis and eccentricity of Sun centered periodic orbit reduces, whereas, due to solar radiation pressure uniform change in semi major axis and eccen-tricity of Saturn centered periodic orbits is observed.
文摘We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.
基金Supported by JSPS and CNRS under the Japan-France Research Cooperative Programthe Grant-in-Aid for Scientific Research on Innovative Areas"Toward new frontiers:Encounter and synergy of state-of-the-art astronomical detectors and exotic quantum beams",JSPS/MEXT KAKENHI under Grant Nos JP18HO3692 and JP18H05462+1 种基金the National Key R&D Program of China(2018YFA0404403)the National Natural Science Foundation of China Nos 11775316,11535004,11875074 and 11875073
文摘Traditional "magic numbers" were once regarded as immutable throughout the nuclear chart. However, unexpected changes were found for unstable nuclei around N = 20. With both proton and neutron numbers around the magic number of 20, the neutron-rich ^(39)Cl isotope provides a good test case for the study of the quantumstate evolution across the major shell. In the present work, the negative parity states in ^(39)Cl are investigated through the β decay spectroscopy of 39 S. Newly observed γ transitions together with a new state are assigned into the level scheme of ^(39)Cl. The spin parity of 5/2^- for the lowest negative parity state in ^(39)Cl is reconfirmed using the combined γ transition information. These systematic observations of the negative parity states in ^(39)Cl allow a comprehensive comparison with the theoretical descriptions. The lowest 5/2^- state in ^(39)Cl remains exotic in terms of comparisons with existing theoretical calculations and with the neighboring isotopes having similar single-particle configurations. Further experimental and theoretical investigations are suggested.
基金supported by the National Key Research and Development Project(Grant No.2018YFB1900605)the Key Research Program of Chinese Academy of Sciences(Grant No.ZDRW-KT-2019-1).
文摘High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.
文摘This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.
文摘We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of (h is energy constant;μ is mass ratio of the two primaries;are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.
基金Supported by the National Natural Science Foundation of China(11602019)。
文摘A practical method is proposed to search for periodic orbits of elongated asteroids.The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters,and then implement local iterations to obtain the real orbits over an asteroid in the polyhedral model.In this paper the dipole and polyhedral models,and list detailed procedures of the searching method are introduced.A planar single lobe orbit is presented to evaluate the effectiveness of the method,with the asteroid 216 Kleopatra of the triple asteroid system as a representative elongated body.By applying the above method,ten families of periodic orbits around Kleopatra are identified and discussed with respect to their orbital stabilities and periods.One sample of the sombrero orbit is checked by calculating 1000 hours to examine its orbital behavior.Besides the above orbits,the intriguing head-surrounding orbit is also analyzed.
基金the French government under the No de dossier: 688028B
文摘For a satellite in an orbit of more than 1600 km in altitude, the effects of Sun and Moon on the orbit can’t be negligible. Working with mean orbital elements, the secular drift of the longitude of the ascending node and the sum of the argu-ment of perigee and mean anomaly are set equal between two neighboring orbits to negate the separation over time due to the potential of the Earth and the third body effect. The expressions for the second order conditions that guaran-tee that the drift rates of two neighboring orbits are equal on the average are derived. To this end, the Hamiltonian was developed. The expressions for the non-vanishing time rate of change of canonical elements are obtained.
文摘In contrast to the main stream of studying the chaotic behavior of a given map, constructing chaotic map has attracted much less attention. In this paper, we propose simple analytical method for constructing one dimensional continuous maps with certain specific periodic points.Further, we obtain results for the existence of chaotic phenomenon in the sense of Li and Yorke. Some examples are also analyzed using the proposed methods.
基金supported by the National Natural Science Foundation of China(10832004)the Fundamental Research Funds for the Central Universities(YWF-10- 02-049)
文摘Spacecrafts in periodic or quasi-periodic orbits near the collinear libration points are proved to be excellent platforms for scientific investigations of various phenomena.Since such periodic or quasi-periodic orbits are exponentially unstable,the station-keeping maneuver is needed. A station-keeping strategy which is found by an analytical method is presented to eradicate the dominant unstable component of the libration point trajectories.The inhibit force transforms the unstable component to a stable ...
文摘We present a numerical method for efficiently detecting unstable periodic orbits(UPO’s)embedded in chaotic attractors of high-dimensional systems.This method,which we refer to as subspace fixed-point iteration, locates fixed points of Poincare maps using a form of fixed-point iteration that splits the phase space into appropriate subspaces.In this paper,among a number of possible implementations,we primarily focus on a subspace method based on the Schmelcher-Diakonos(SD)method that selectively locates UPO’s by varying a stabilizing matrix,and present some applications of the resulting subspace SD method to hyperchaotic attractors where the UPO’s have more than one unstable direction.
文摘We show first that an orbit, which is naturally characterized by its eccentricity and semi-latus rectum, can equally be characterized by other sets of parameters, and proceed to determine mass-independent characterizations. The latter is employed to obtain the laws of equivalent orbits, which by definition have the same eccentricity and orbit’s parameter [1]. These laws relate the values of the same physical observables on two equivalent orbits to the corresponding total mass;they include the laws of velocity, angular velocity, radial velocity, areal velocity, acceleration, period, energy and angular momentum. Regardless of the share of the two bodies of a fixed total mass, the same relative orbit occurs for the same initial conditions. Moreover, the same orbit can be traced by different total masses but with different relative velocities. The concept of a gravitational field generated by a set of masses is shown to be meaningful only when the center of mass is not changed by the test mass. The associated concept of the “nothing”, which is an infinitesimal mass that allows for the property just mentioned to be fulfilled, is introduced and its orbits are determined. The perturbation of the nothing orbits due to its replacement by a finite mass is determined. It is proved that such a replacement can have a qualitative effect resulting in a “phase transition” of an orbit from unbound to bound, and that the nothing’s circular orbits cannot be occupied by any material body. The Galileo law of free fall, on which the equivalence principle hinges and which is exact only for “nothing-like” falling objects, is revised to determine the duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is demonstrated that Newton’s law of gravitation is not an approximation of Einstein field Equations even in the case of a static weak field. However, both theories have a common limit corresponding to the case in which the alien concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well as an infinite set of LRL vectors, result all from one vector. The hodograph is a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle for bound motion.
文摘In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).
文摘In the present work, the collinear equilibrium points of the restricted three-body problem are studied under the effect of oblateness of the bigger primary using an analytical and numerical approach. The periodic orbits around these points are investigated for the Earth-Moon system. The Lissajous orbits and the phase spaces are obtained under the effect of oblateness.
文摘The lifetime of a lunar satellite orbit is constrained by the non-spherical nature of the Moon’s gravity field. The orbital lifetime of lunar orbits depends significantly on the initial conditions of the orbit. Right ascension of ascending node (Ω) is one of the important orbital parameter affecting the orbital lifetime. In the present work we have analyzed the effect of Ω on the variation of lifetime with altitude for circular lunar orbits. It is found that at a particular initial altitude, a small increase in the altitude results in substantial increase in the orbital lifetime due to effect of the long periodic terms of Earth’s gravity on eccentricity and this transition altitude is different for different Ω. Further, it is observed that the variation of transition altitude with Ω follows a definite, but different trend for orbits with different inclinations. The transition altitude for polar orbits is found to be higher without the effect of Sun and Earth gravity. Variation of transition altitude with orbital inclination is also analyzed. Lifetimes of high altitude circular lunar orbits are analyzed and it is observed that at high altitudes lifetime decreases with altitude.
文摘Conventional interpretation of the Einstein Equation has inconsistencies and contradictions, such as gravitational fields without energy, objects crossing event-horizons, objects exceeding the speed of light, and inconsistency in scaling the speed of light and its factors. An isotropic metric resolves such problems by attributing energy to the gravitational field, in the Einstein Equation. This paper discusses symmetries of an isotropic metric, including scaling of physical quantities, the Lorentz transformation, covariant derivatives, and stress-energy tensors, and transitivity of this scaling between inertial reference frames. Force, charge, Planck’s constant, and the fine structure constant remain invariant under isotropic gravitational scaling. Gravitational scattering, orbital period, and precession distinguish between isotropic and Schwarzschild metrics. An isotropic metric accommodates quantum mechanics and improves models of black-holes.
