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1.
New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k
2)1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia 相似文献
2.
Sandro Da Silva Fernandes 《Celestial Mechanics and Dynamical Astronomy》1995,62(4):305-321
Some classic expansions of the elliptic motion — cosmE and sinmE — in powers of the eccentricity are extended to highly eccentric orbits, 0.6627...<e<1. The new expansions are developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients are given in terms of the derivatives of Bessel functions with respect to the eccentricity. The expansions have the same radius of convergence (e*) of the extended solution of Kepler's equation, previously derived by the author. Some other simple expansions — (a/r), (r/a), (r/a) sinv, ..., — derived straightforward from the expansions ofE, cosE and sinE are also presented. 相似文献
3.
E. V. Glushkova S. E. Koposov I. Yu. Zolotukhin Yu. V. Beletsky A. D. Vlasov S. I. Leonova 《Astronomy Letters》2010,36(2):75-85
Automated search for star clusters in J, H, K
s
data from 2MASS catalog has been performed using the method developed by Koposov et al. (2008). We have found and verified
153 new clusters in the interval of the galactic latitude −24° < b < 24°. Color excesses E(B − V), distance moduli and ages were determined for 130 new and 14 yet-unstudied known clusters. In this paper, we publish a catalog
of coordinates, diameters, and main parameters of all the clusters under study. A special web-site available at has been developed to facilitate dissemination and scientific usage of the results. 相似文献
4.
S. Chatterjee 《Journal of Astrophysics and Astronomy》1991,12(4):269-280
We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above
the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m0)m−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v2(m)> ∼ m−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field
Kz, in terms of confluent hypergeometric functions, the limiting trends being Kz∼z for z →0, while Kz
→ constant for z → infinity. We also study the behaviour of < |z(m)|2>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|2>∼ mt-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested
that observation of < |z(m)|2> can be used as a probe to findx and hence obtain information about the mass spectrum. 相似文献
5.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1982,84(1):53-71
In this paper of the series, the expansions of the functionsH
1,H
2, andH
3 will be established analytically and computationally form positive integer,q any real number and , are both positive <1. Full recursive computational algorithms with their numerical results will also be included. 相似文献
6.
Bernard De Saedeleer 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):239-268
This paper is a contribution to the Theory of the Artificial Satellite, within the frame of the Lie Transform as canonical
perturbation technique (elimination of the short period terms). We consider the perturbation by any zonal harmonic J
n
(n ≥ 2) of the primary on the satellite, what we call here the complete zonal problem of the artificial satellite. This is quite useful for primaries with symmetry of revolution. We give an analytical formula to compute directly the first
order averaged Hamiltonian. The computation is carried out in closed form for all terms, avoiding therefore tedious expansions
in the eccentricity or in any anomaly; this feature makes the averaging process, not only valid for all kind of elliptic trajectories
but at the same time it yields the averaged Hamiltonian in a very short and compact way. The formula allows us to now skip
the averaging process, which means an asymptotic gain of a factor 3n/2 regarding the computational cost of the n
th
zonal. Our analytical formulae have been widely checked, by comparison on one hand with published works (Brouwer, 1959) (which
contained results for particular zonal harmonics, let’s say typically from J
2 to J
8), and on the other hand with the results of 3 symbolic manipulation software, among which the MM (standing for ‘Moon’s series
Manipulator’), which has already been used and described in (De Saedeleer B., 2004). Additionally, the first order generator
associated with this transformation is given into the same closed form, and has also been validated. 相似文献
7.
Konstantin V. Kholshevnikov Sergei L. Kurdubov 《Celestial Mechanics and Dynamical Astronomy》2004,89(1):83-96
According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us
call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has
proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate
cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center,
etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present
paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the
convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is
demonstrated by means of a computer assisted proof.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1986,125(2):259-298
In this paper of the series, we arrive at the end of the second step of our regularization approach, and in which, elliptic expansions in terms of the sectorial variables
j
(i)
introduced by the author in Paper IV (Sharaf, 1982b) to regularize the highly oscillating perturbation force of some orbital systems will be established analytically and computationally for the thirteenth, fourteenth, fifteenth, and sixteenth categories according to our adopted scheme of presentation drawn up in Paper V (Sharaf, 1983). For each of the elliptic expansions belonging to a category, literal analytic expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computations, and numerical results are included to provide test examples for constructing computational algorithms. Finally, the second and the last collection of completed elliptic expansion will be given in Appendix B, such that, the materials of Appendix A of Paper VIII (Sharaf, 1985b) and those of Appendix B of the present paper provide the reader with the elliptic expansions in terms of
j
(i)
so explored for the second step of our regularization approach. 相似文献
9.
Mohamed Adel Sharaf 《Astrophysics and Space Science》1985,116(2):251-283
In this paper of the series, elliptic expansions in terms of the sectorial variables
j
(i)
introduced by the author in Paper IV (Sharaf, 1982) to regularize the highly oscillating perturbation force of some orbital systems will be established analytically and computationally for the ninth, tenth, eleventh, and twelfth categories according to our adopted scheme of presentation drawn up in Paper V (Sharaf, 1983). For each of the elliptic expansions belonging to a category, literal analytical expressions for the coefficients of its trigonometric series representation are established. Moreover, some recurrence formulae satisfied by these coefficients are also established to facilitate their computation, and numerical results are included to provide test examples for constructing computational algorithms. Finally, the first collection of completed elliptic expansions in terms of
j
(i)
so explored will be given in Appendix A for the guidance of the reader. 相似文献
10.
Stochastic temperatures and turbulence are characterized by average velocities u
th
and < u
turb
> ≡ u
0 and fluctuations u¢th {u'_{th}} and u′ (<u′ > = 0). Thus, the Doppler width of a line also has a fluctuating component Dl¢D \Delta {\lambda '_D} . Observed spectra correspond to the radiative flux averaged over time and over a star’s surface, <Hλ>. Usually, only the average velocities u
th
and u
0 are taken into account in photospheric models and these yield the Doppler width DlD(0) \Delta \lambda_D^{(0)} of a line in the customary way. The fluctuations Dl¢D \Delta {\lambda '_D} mean that near a line center the average absorption coefficient < αλ > is larger than the usual αλ, which depends only on the average velocities u
th
and u
0. This enhances the absorption line near the center and is not explained by the photospheric models. This new statistical
effect depends on the wavelength of the line. A comparison of observed lines with model profiles yields an estimate for the
average level of fluctuations in the Doppler width, h =
á | Dl¢D |
ñ