首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 46 毫秒
1.
4颗卫星情况的几何优化法修正   总被引：6，自引：0，他引：6  
在GPS定位与导航中,用户可以通过选择至少4颗可见卫星的观测,得到测站位置和站钟差信息,卫星相对于测站的几何关系直接影响到定位和导航的精度,考虑用4颗卫星进行定位,在当前有一定的现实意义,在KihaLra等人工作的基础上对四面体的性质进行了深入讨论,推导了4颗可见卫星构成四面体体积的计算公式,实例分析证明该计算公式更合理、更精确。  相似文献   

2.
In astrophysical studies of Solar System bodies, the measured values of the linear polarization degree Pobs and the position angle of the polarization plane θ are usually considered relative to the plane orthogonal to the scattering plane; and the resulting quantities are designated as Pr and θr, respectively. Parameters of the phase curve of polarization Pr = f(α) serve for determining the physical characteristics of grains composing the regolith surfaces of such bodies as, for example, the Moon, Mercury, asteroids, and planetary satellites, or the polydisperse media, such as cometary comae and tails. In this paper it has been shown that the error in the polarization degree grows \({\sigma _{{P_r}}}\) due to the error \({\sigma _{{\theta _{obs}}}}\) in determining the position angle. The interrelations between these errors were obtained, and the conditions, under which the values of the linear polarization degree Pr relative to the orthogonal system can be used to analyze the phase dependences of polarization, were formulated.  相似文献   

3.
In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133–160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one-to-one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits \( b_1 \Delta \varpi + b_2 \Delta \varOmega \), forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that \({>}20\) and \({>}40\%\) of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with \(b_1+|b_2|\le 3\) persist, while even higher-order resonances, up to \(b_1+|b_2|\ge 7\), survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.  相似文献   

4.
In this paper, we consider the elliptic collinear solutions of the classical n-body problem, where the n bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion is called an elliptic Euler–Moulton collinear solution. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic Euler–Moulton collinear solution of n-bodies splits into \((n-1)\) independent linear Hamiltonian systems, the first one is the linearized Hamiltonian system of the Kepler 2-body problem at Kepler elliptic orbit, and each of the other \((n-2)\) systems is the essential part of the linearized Hamiltonian system at an elliptic Euler collinear solution of a 3-body problem whose mass parameter is modified. Then the linear stability of such a solution in the n-body problem is reduced to those of the corresponding elliptic Euler collinear solutions of the 3-body problems, which for example then can be further understood using numerical results of Martínez et al. on 3-body Euler solutions in 2004–2006. As an example, we carry out the detailed derivation of the linear stability for an elliptic Euler–Moulton solution of the 4-body problem with two small masses in the middle.  相似文献   

5.
We present the results of observations of the Galilean moons of Jupiter carried out at the Normal Astrograph of the Pulkovo Observatory in 2016?2017. We obtained 761 positions of the Galilean moons of Jupiter in the system of the Gaia DR1 catalog (ICRF, J2000.0) and 854 differential coordinates of the satellites relative to each other. The mean errors in the satellites’ normal places and the corresponding root-mean-square deviations are εα = 0.0020′′, εδ = 0.0027′′, σα = 0.0546′′, and σδ = 0.0757′′. The equatorial coordinates of the moons are compared to the motion theories of planets and satellites. On average, the (O–C) residuals in the both coordinates relative to the motion theories are less than 0.031′′. The best agreement with observations is achieved by a combination of the EPM2015 and V. Lainey-V.2.0|V1.1 motion theories, which yields the average (O–C) residuals of approximately 0.02″. Peculiarities in the behavior of the (O–C) residuals and error values in Ganymede have been noticed.  相似文献   

6.
We describe the properties of Mini-MegaTORTORA (MMT-9) nine-channel wide-field optical sky monitoring system with subsecond temporal resolution. This instrument can observe sky areas as large as 900 deg2, perform photometry in three filters close to Johnson BV R system and polarimetry of selected objects or areas with 100–300 deg2 sizes. The limiting magnitude of the system is up to V = 11m for 0.1 s temporal resolution, and reaches V = 15m in minute-long exposures. The system is equipped with a powerful computing facility and dedicated software pipeline allowing it to perform automatic detection, real-time classification, and investigation of transient events of different nature located both in the near- Earth space and at extragalactic distances. The objects routinely detected by MMT-9 include faint meteors and artificial Earth satellites.We discuss astronomical tasks that can be solved using MMT-9, and present the results of the first two years of its operation. In particular, we report the parameters of the optical flare detected on June 25, 2016, which accompanied the gamma-ray burst GRB160625B.  相似文献   

7.
In this paper, we have investigated linear and nonlinear propagation of kinetic Alfven waves in which the electrons have been assumed to follow generalized (\(r,q\)) distribution. We have shown that (\(r,q\)) distribution gives us most of the distributions observed in space plasmas. We have varied the flatness parameter \(r\) and the tail parameter \(q\) to explore the linear and nonlinear propagation characteristics of kinetic Alfven waves. We have also discussed the limiting cases. It has been shown that our results agree well with Fast and Freja observations of the nonlinear kinetic Alfven waves. An important feature of our study is the formation of rarefactive solitary structures. It has been shown that this result cannot be obtained with Maxwellian distribution and that it agrees well with the observations of Fast and Freja satellites.  相似文献   

8.
The paper considers a digital modeling complex for the attitude control system of the Auriga Earth remote sensing small spacecraft. Mathematical models of measuring and executive devices are described. The results of spacecraft orbital attitude tests are presented.  相似文献   

9.
The influence of active processes on the Sun and their response on the dynamics of Earth’s artificial satellites has been investigated. The relationship between the characteristics of solar activity and variations of the periods P of the orbital motion of Earth’s artificial satellites has been found. These variations mainly indicate the variations in the Earth’s atmosphere density caused by solar activity (index F10.7) and geomagnetic activity (ΣKp index). High values of the correlation coefficients between P and F10.7 (–0.77…–0.91) and between P and ΣKp (–0.67…–0.89) exhibit significant effect of solar and geomagnetic activity on the orbital periods of satellites.  相似文献   

10.
The effects of solid and ocean tides have been computed on the right ascension of the ascending node of the two LAGEOS and LARES satellites and on the argument of pericenter of LAGEOS II. Their effects—together with the possible mis-modeling related to systematic errors in the estimate of the tidal coefficients, especially in the case of ocean tides—are quite important to be well established for the key role of the LAGEOS satellites, as well as of the newly LARES, in space geodesy and geophysics as well as in fundamental physics measurements. In the case of the measurement of the Lense–Thirring effect, the mis-modeling of long-period tides may mimic a secular effect on the cited orbital elements, thus producing a degradation in the measurement of the relativistic precession. A suitable combination of the orbital elements of the three satellites can help in avoiding the effects of the long-period tides of degree \(\ell =2\) (as for the Lunar solid tides with periods of 18.6 and 9.3 years) and \(\ell =4\), but other long-period tides, as the ocean \(K_1\) tide, which has the same periodicities of the right ascension of the ascending node \(\varOmega \) of the satellites, may strongly influence the measurement, especially if it is performed over a relatively short time span. These results are particularly important in the case of LARES, since they are new and because of the role that the orbit of LARES, and especially of its ascending node right ascension, will have in a new measurement of the Lense–Thirring effect by the joint analysis of its orbit with that of the two LAGEOS.  相似文献   

11.
The motion of a point mass in the J 2 problem is generalized to that of a rigid body in a J 2 gravity field. The linear and nonlinear stability of the classical type of relative equilibria of the rigid body, which have been obtained in our previous paper, are studied in the framework of geometric mechanics with the second-order gravitational potential. Non-canonical Hamiltonian structure of the problem, i.e., Poisson tensor, Casimir functions and equations of motion, are obtained through a Poisson reduction process by means of the symmetry of the problem. The linear system matrix at the relative equilibria is given through the multiplication of the Poisson tensor and Hessian matrix of the variational Lagrangian. Based on the characteristic equation of the linear system matrix, the conditions of linear stability of the relative equilibria are obtained. The conditions of nonlinear stability of the relative equilibria are derived with the energy-Casimir method through the projected Hessian matrix of the variational Lagrangian. With the stability conditions obtained, both the linear and nonlinear stability of the relative equilibria are investigated in details in a wide range of the parameters of the gravity field and the rigid body. We find that both the zonal harmonic J 2 and the characteristic dimension of the rigid body have significant effects on the linear and nonlinear stability. Similar to the classical attitude stability in a central gravity field, the linear stability region is also consisted of two regions that are analogues of the Lagrange region and the DeBra-Delp region respectively. The nonlinear stability region is the subset of the linear stability region in the first quadrant that is the analogue of the Lagrange region. Our results are very useful for the studies on the motion of natural satellites in our solar system.  相似文献   

12.
Consider a system of two rigid, massive bodies interacting according to their mutual gravitational attraction. In a relative equilibrium motion, the bodies rotate rigidly and uniformly about a fixed axis in \({\mathbb {R}}^3\). This is possible only for special positions and orientations of the bodies. After fixing the angular momentum, these relative equilibrium configurations can be characterized as critical points of a smooth function on configuration space. The goal of this paper is to use Morse theory and Lusternik–Schnirelmann category theory to give lower bounds for the number of critical points when the angular momentum is sufficiently large. In addition, the exact number of critical points and their Morse indices are found in the limit as the angular momentum tends to infinity.  相似文献   

13.
In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth–Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the \(L_{1}\) and \(L_{2}\) points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.  相似文献   

14.
Observational results are presented for Jupiter and its Galilean moons from the Normal Astrograph at Pulkovo Observatory in 2013–2015. The following data are obtained: 154 positions of the Galilean satellites and 47 calculated positions of Jupiter in the system of the UCAC4 (ICRS, J2000.0) catalogue; the differential coordinates of the satellites relative to one another are determined. The mean errors of the satellites’ normal places in right ascension and declination over the entire observational period are, respectively: εα = 0.0065″ and εδ = 0.0068″, and their standard deviations are σα = 0.0804″ and σδ = 0.0845″. The equatorial coordinates are compared with planetary and satellite motion theories. The average (O–C) residuals in the two coordinates relative to the motion theories are 0.05″ or less. The best agreement with the observations is achieved by a combination of the EPM2011m and V. Lainey-V.2.0|V1.1 motion theories; the average (O–C) residuals are 0.03″ or less. The (O–C) residuals for the features of the positions of Io and Ganymede are comparable with measurement errors. Jupiter’s positions calculated from the observations of the satellites and their theoretical jovicentric coordinates are in good agreement with the motion theories. The (О–С) residuals for Jupiter’s coordinates are, on average, 0.027″ and–0.025″ in the two coordinates.  相似文献   

15.
Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi-periodic cycles via re-inversing of the proper ultra-elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.  相似文献   

16.
A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy–Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4–0.45 in eccentricity and 40–45\(^\circ \) in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy–Wiltshire solution in curvilinear coordinates is also presented.  相似文献   

17.
The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites.  相似文献   

18.
Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein–Infeld–Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.  相似文献   

19.
We study the temporal intensity profile, or pulse shape, of cosmic ray ground-level enhancements (GLEs) by calculating the rise \(( \tau_{\mathrm{r}})\) and decay \((\tau_{\mathrm{d}})\) times for a small subset of all available events. Although these quantities show very large inter-event variability, a linear dependence of \(\tau_{ \mathrm{d}} \approx 3.5 \tau_{\mathrm{r}}\) is found. We interpret these observational findings in terms of an interplanetary transport model, thereby including the effects of scattering (in pitch-angle) as these particles propagate from (near) the Sun to Earth. It is shown that such a model can account for the observed trends in the pulse shape, illustrating that interplanetary transport must be taken into account when studying GLE events, especially their temporal profiles. Furthermore, depending on the model parameters, the pulse shape of GLEs may be determined entirely by interplanetary scattering, obscuring all information regarding the initial acceleration process, and hence making a classification between impulsive and gradual events, as is traditionally done, superfluous.  相似文献   

20.
In this paper, we found some new anisotropic charged models admitting generalized polytropic equation of state with spherically symmetry. An analytic solution of the Einstein–Maxwell field equations is obtained through the transformation introduced by Durgapal and Banerji (Phys. Rev. D 27:328, 1983). The physical viability of solutions corresponding to polytropic index \(\eta =1/2\), \(2/3\), 1, 2 is analyzed graphically. For this, we plot physical quantities such as radial and tangential pressure, anisotropy, speed of sound which demonstrated that these models achieve all the considerable physical conditions required for a relativistic star. Further, it is mentioned here that previous results for anisotropic charged matter with linear, quadratic and polytropic equation of state can be retrieved.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号