共查询到20条相似文献，搜索用时 406 毫秒
1.
In this paper, an efficient iterative method of arbitrary integer order of convergence ≥ 2 has been established for solving
the hyperbolic form of Kepler’s equation. The method is of a dynamic nature in the sense that, moving from one iterative scheme
to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge
of the initial guess. A property which avoids the critical situations between divergent and very slow convergent solutions
that may exist in other numerical methods which depend on initial guess. Computational Package for digital implementation
of the method is given and is applied to many case studies. 相似文献
2.
In this paper, we developed statistical method for distance determination of a stellar group. The method depends on the assumption that, the stars scatter around a mean magnitude in a Gaussian distribution. The mean apparent magnitude of the stars is then expressed in terms of the frequency function of the apparent magnitudes, so as to correct for observational incompleteness at the faint end. The problem reduces to the solution of a highly transcendental equation for a given apparent magnitude parameter α. Computational algorithm of the method is illustrated and the numerical solutions of the basic equation are given for some values of α . 相似文献
3.
In this paper, an efficient iterative method of arbitrary positive integer order of convergence 2 will be established for the two-body universal initial value problem. The method is of dynamic nature in the sense that, on going from one iterative scheme to the subsequent one, only additional instruction is needed. Moreover, which is the most important, the method does not need any a priori knowledge of the initial guess. A property which avoids the critical situations between divergent to very slow convergent solutions, that may exist in other numerical methods which depend on initial guess. Some applications of the method are also given. 相似文献
4.
Laura Stumpf 《Celestial Mechanics and Dynamical Astronomy》1999,74(2):95-109
The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of . 相似文献
5.
In the present paper, an efficient iterative method of arbitrary integer order of convergent ≥2 based on the homotopy continuation techniques for the solution of the initial value problem of space dynamics using the universal Y functions is presented. The method is of dynamic nature in the sense that, ongoing from one iterative scheme to the subsequent one, only additional instruction is needed. Most importantly, the method does not need any prior knowledge of the initial guess. This is a property which avoids the critical situations between divergent to very slow convergent solutions that may exist in other numerical methods which depend on initial guesses. A computational package for digital implementation of the method is given, together with numerical applications for elliptic, hyperbolic, and parabolic orbits. The accuracy of the results for all orbits is O(10–16). (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
《New Astronomy》2003,8(1):15-21
In this paper, a general method is developed for the determination of cosmic distances. The method is based on the assumption that the members of a cosmic group scatter around a mean absolute magnitude in a Gaussian distribution. The basic formula of the method is obtained as a least-squares fit of the solution of a highly transcendental equation as a function of a given apparent magnitude parameter α. For each range of α, the precision criteria of this formula, and also the absolute relative uncertainty in the derived distance, are very satisfactory. Some illustrative examples of the usages of the method are included. 相似文献
7.
R. Armellin M. Lavagna A. Ercoli-Finzi 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):391-405
The aero-gravity assist maneuver is here proposed as a tool to improve the efficiency of the gravity assist as, thanks to the interaction with the planetary atmospheres, the angular deviation of the velocity vector can be definitely increased. Even though the drag reduces the spacecraft velocity, the overall Δυ gain could be remarkable whenever a high lift-to-drag vehicle is supposed to fly. Earlier studies offer simplified approaches according to both the dynamics modeling and the atmospheric trajectory constraints. In this paper a 3D dynamical model is adopted and a more realistic L/D performance for the hypersonic vehicle is assumed. Some relevant aspects related to the multidisciplinary design have been considered such as heating rates and structural loads bounding. Comparisons between in and out of plane maneuvering have been performed by assuming, as control variables, either the angle of attack or the bank angle, respectively. The optimal control problem has been solved by selecting a direct method approach. The dynamics has been transcribed into a set of non-linear constraints and the arising non-linear programming problem has been solved with a sequential quadratic programming solver. To gain the global optimum convergence the initial guess has been supplied by solving the same problem by a direct shooting technique and a genetic optimizer. 相似文献
8.
The results of a comprehensive study of the Galactic open cluster NGC 2323 (M50) are presented. The positions of stars to
a limiting magnitude {ie74-1} in a {ie74-2} area centered on the cluster were measured on six plates from the Pulkovo normal
astrograph with a maximum epoch difference of 60 yr. The measurements were performed with the Pulkovo “Fantasy” automated
measuring system upgraded in 2010. The corresponding areas from the USNO-A2.0, USNO-B1, and 2MASS catalogues were used as
additional plates. As a result, the relative proper motions of stars were obtained with a root-mean-square error of 5.85 mas
yr−1. A catalogue of UBV and JHK magnitudes for objects in the investigated area was compiled from available published resources. The astrometric selection
of cluster members was made by the maximum likelihood method. A high individual cluster membership probability of a star (P ≥ 80%) served as the first selection criterion. The position of a star on the photometric color-magnitude (V ∝ (B-V), J ∝ (J-K)) diagrams of the cluster was considered as the second criterion. The position of an object on the color-color ((U-B)-(B-V), (J-H)-(J-K)) diagrams served as the third criterion. On the basis of these criteria, it was established that 508 stars are members of
NGC 2323. These data were used to refine the physical parameters of the cluster: the mean reddening {ie74-3}, the true distance
modulus {ie74-4}, and the cluster age of about 140 Myr from the grid of isochrones computed by the Padova group for solar
chemical composition. Two tables contain the catalogues of proper motions and photometry for stars in the area. The luminosity
and mass functions were constructed. The cluster membership of red and blue giants, variable, double, and multiple stars was
considered. The position of the cluster center was improved: {ie74-5}, δ = −08°20′16″(2000.0). 相似文献
9.
Reza Raymond Karimi Daniele Mortari 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):167-180
A novel approach for initial orbit determination based on multiple angles-only observations is presented. The proposed technique
is iterative and uses Lagrangian coefficients, f and g. The proposed method does not show singularity for the coplanar cases. In addition, the method is capable of handling multiple
observations, providing higher accuracy, whereas the level of the algorithm complexity and processor running time remain almost
invariant. The technique presented is compared with the Double r-iteration and Gauss’ methods using data corrupted by noise to simulate true measurements. Results show that the proposed
method is a valid alternative to the classical methods of orbit determination. 相似文献
10.
The cross-correlation function of solar p modes in a time – distance analysis changes with travel distance (or travel time). The exponential decrease in the amplitude
of the cross-correlation function with travel distance has been interpreted as the dissipation of solar p-mode power and used to determine the lifetimes of high-degree p modes. It is found that the width of the cross-correlation function increases with travel distance. We interpret the increase
in width as the dispersion of the wave packet in a time – distance analysis. The dispersion would also cause a decrease in
amplitude and affect the determination of lifetimes. We include the dispersion effect in the determination of lifetimes of
high-degree p modes in a time – distance analysis and find that the derived lifetime increases significantly compared with the previous
study for degree less than 400. 相似文献
11.
This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bézier curves. Optimal control point coordinates are first shown to be
linear with respect to orbit eccentricity for any eccentric anomaly range. This property yields the development of a piecewise
(e.g., 3, 4) solving technique providing accuracies better than 10−13 degree for orbit eccentricity e ≤ 0.99. The proposed method does not require large pre-computed discretization data, but instead solves a cubic/quadratic
algebraic equation and uses a single final Halley iteration in only a few lines of code. The method still provides accuracies
better than 10−5 degree for the near parabolic worst case (e = 0.9999) with very small mean anomalies (M < 0.0517 deg). The complexity of the proposed algorithm is constant, independent of the parameters e and M. This makes the method suitable for extensive orbit propagations.
Presented at the 7th Dynamics and Control of Systems and Structures in Space Conference, July 18–22, 2006, Greenwich, England. 相似文献
12.
M. Rejkuba 《Astrophysics and Space Science》2012,341(1):195-206
Globular clusters are among the first objects used to establish the distance scale of the Universe. In the 1970-ies it has been recognized that the differential magnitude distribution of old globular clusters is very similar in different galaxies presenting a peak at M V ∼−7.5. This peak magnitude of the so-called Globular Cluster Luminosity Function has been then established as a secondary distance indicator. The intrinsic accuracy of the method has been estimated to be of the order of ∼0.2 mag, competitive with other distance determination methods. Lately the study of the Globular Cluster Systems has been used more as a tool for galaxy formation and evolution, and less so for distance determinations. Nevertheless, the collection of homogeneous and large datasets with the ACS on board HST presented new insights on the usefulness of the Globular Cluster Luminosity Function as distance indicator. I discuss here recent results based on observational and theoretical studies, which show that this distance indicator depends on complex physics of the cluster formation and dynamical evolution, and thus can have dependencies on Hubble type, environment and dynamical history of the host galaxy. While the corrections are often relatively small, they can amount to important systematic differences that make the Globular Cluster Luminosity Function a less accurate distance indicator with respect to some other standard candles. 相似文献
13.
14.
M. Prato M. Piana J. C. Brown A. G. Emslie E. P. Kontar A. M. Massone 《Solar physics》2006,237(1):61-83
We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I(∊)) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct
the corresponding differential emission measure (ξ(T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here
we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ(T) from measurements of I(∊) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (
[`(F)]\overline{F}
(E)) from I(∊) and the second, to recover ξ(T) from
[`(F)]\overline{F}
(E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization
theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective
in recovering δ-like forms of ξ(T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-law-like forms. Therefore,
we introduce a restoration approach whereby the low-energy part of
[`(F)]\overline{F}
(E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy
part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested
by using simulated
[`(F)]\overline{F}
(E) derived from a priori known forms of ξ(T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). 相似文献
15.
The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into
the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution
space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter
after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter),
which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain
(x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε =
0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce
the density parameter, say to ε = 10−6, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary.
The stability of all members of each and all families computed was calculated and presented in this paper for both the large
solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by
stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied
by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections.
All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received,
consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including
their stability and is available at request. It is concluded that approximation of the general solution of this system is
straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties. 相似文献
16.
Photoelectric Vilnius seven-color photometry is presented and analyzed for a sample of 24 red giant branch and clump stars
in the open cluster NGC 7789. For each star we have determined photometric spectral type, absolute magnitude, interstellar
reddening, effective temperature, metallicity, and surface gravity. From averages over the stars in the sample we find the
mean reddening to the cluster E
Y−V
= 0.21± 0.02 (s.d.), or E
B−V
= 0.25, and the apparent distance modulus (m−M)
V
= 12.21± 0.10 (s.d.), which yield a distance of 1840 pc. The mean overall metallicity is found to be [Fe/H] = −0.18± 0.09
(s.d.). The clump stars, on average, appear to be slightly more metal-rich than the other red giants, which is most probably
caused by evolutionary changes of carbon and nitrogen molecular bands falling in the photometric passbands. A difference in
mass between the two groups of stars has also been detected, which suggests that the clump stars might have undergone extra
mass loss before reaching their core He-burning phase of evolution. 相似文献
17.
A classical problem in the theory of radiative transfer is considered: calculating the radiation field within a plane scattering
atmosphere. The recently proposed albedo-shifting method is used to calculate the source function both in a semi-infinite
atmosphere and in an atmophere of finite optical depth, illuminated by parallel rays. The method enables one to “suppress”
scattering and obtain iterative solutions of the integral equation for the source function in only a few direct lambda iterations,
even when the average number of photon scatterings in the atmosphere is very large.
Translated from Astrofizika, Vol. 42, No. 4, pp. 485–500, October–December, 1999. 相似文献
18.
P. K. Manoharan 《Solar physics》2006,235(1-2):345-368
Knowledge of the radial evolution of the coronal mass ejection (CME) is important for the understanding of its arrival at
the near-Earth space and of its interaction with the disturbed/ambient solar wind in the course of its travel to 1 AU and
further. In this paper, the radial evolution of 30 large CMEs (angular width > 150∘, i.e., halo and partial halo CMEs) has been investigated between the Sun and the Earth using (i) the white-light images of
the near-Sun region from the Large Angle Spectroscopic Coronagraph (LASCO) onboard SOHO mission and (ii) the interplanetary scintillation (IPS) images of the inner heliosphere obtained from the Ooty Radio Telescope (ORT). In the LASCO field of view at heliocentric
distances R≤30 solar radii (R⊙), these CMEs cover an order of magnitude range of initial speeds, VCME≈260–2600 km s−1. Following results have been obtained from the speed evolution of these CMEs in the Sun–Earth distance range: (1) the speed
profile of the CME shows dependence on its initial speed; (2) the propagation of the CME goes through continuous changes,
which depend on the interaction of the CME with the surrounding solar wind encountered on the way; (3) the radial-speed profiles
obtained by combining the LASCO and IPS images yield the factual view of the propagation of CMEs in the inner heliosphere
and transit times and speeds at 1 AU computed from these profiles are in good agreement with the actual measurements; (4)
the mean travel time curve for different initial speeds and the shape of the radial-speed profiles suggest that up to a distance
of ∼80 R⊙, the internal energy of the CME (or the expansion of the CME) dominates and however, at larger distances, the CME's interaction
with the solar wind controls the propagation; (5) most of the CMEs tend to attain the speed of the ambient flow at 1 AU or
further out of the Earth's orbit. The results of this study are useful to quantify the drag force imposed on a CME by the
interaction with the ambient solar wind and it is essential in modeling the CME propagation. This study also has a great importance
in understanding the prediction of CME-associated space weather at the near-Earth environment. 相似文献
19.
According to the optimal control theory, the optimal control problem of the low-thrust tra jectory can be converted into a solution of nonlinear two- point boundary-value problem (TPBVP). To solve the TPBVP, the repeated random guesses for the initial costate variables and iterative computations are needed. In order to enhance the convergence of the iterations, we select an appropriate performance index, and then linearize the equations of the TPBVP around a Keplerian orbit. For multi-revolution transfers, instead of the multi- revolution Lambert tra jectory, multiple segmented Keplerian arcs are used to ensure the effectiveness of the linearization. The method is totally automatic with multiple iterations. With this method, we can get the results within 3 ∼ 5 iterations, and the random guess of the initial costates is unnecessary. Finally by the iterative optimization of the performance index, a better control strategy approaching to the bang-bang control is obtained. 相似文献
20.
We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based
on the material available for an observer, for example relative positions at a given time of the couple in the “plane of sky”,
namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination
is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one
hand, the geometric problem is solved using the first Kepler’s law from a single observing run and, on the other hand, dynamical
parameters are then inferred from the fit of the Kepler’s equation. At last, the final stage consists in determining the main
physical parameters involved in the secular evolution of the system, that is the spin axis and the J2 parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too
restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by
a non-linear least-squares Levenberg–Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful
to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto–Charon system parameters from
observations collected in the literature since 1980. 相似文献