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1.
A method for a kinematic analysis of stellar radial velocities using spherical harmonics is proposed. This approach does not depend on the specific kinematic model and allows both low-frequency and high-frequency kinematic radial velocity components to be analyzed. The possible systematic variations of distances with coordinates on the celestial sphere that, in turn, are modeled by a linear combination of spherical harmonics are taken into account. Theoretical relations showing how the coefficients of the decomposition of distances affect the coefficients of the decomposition of the radial velocities themselves have been derived. It is shown that the larger the mean distance to the sample of stars being analyzed, the greater the shift in the solar apex coordinates, while the shifts in the Oort parameter A are determined mainly by the ratio of the second zonal harmonic coefficient to the mean distance to the stars, i.e., by the degree of flattening of the spatial distribution of stars toward the Galactic plane. The distances to the stars for which radial velocity estimates are available in the CRVAD-2 catalog have been decomposed into spherical harmonics, and the existing variations of distances with coordinates are shown to exert no noticeable influence on both the solar motion components and the estimates of the Oort parameter A, because the stars from this catalog are comparatively close to the Sun (no farther than 500 pc). In addition, a kinematic component that has no explanation in terms of the three-dimensional Ogorodnikov-Milne model is shown to be detected in the stellar radial velocities, as in the case of stellar proper motions. 相似文献
2.
Chuikova N. A. Rodionova Zh. F. Maksimova T. G. Grishakina E. A. 《Solar System Research》2019,53(3):161-171
The harmonic and statistical analysis of lunar terrain altitudes has been performed based on the procedure developed by the authors. The explanations for the displacements of the Moon's figure relative to the center of mass and for the shift of the major equatorial axis relative to the earthward direction have been given. The maps have been plotted for the density anomalies in the near-surface layers of the Moon that correspond to mascons (with negative correlation between the field and terrain mainly for N= 10, 11) and other variants of links between the gravitational field and terrain (with positive correlation between the field and terrain). It has been shown that the harmonics of the degree N= 5–9 mainly correspond to the isostatic compensation of the terrain in the near-surface layers of the crust; the low harmonics (N< 5) correspond to the isostatic compensation of the terrain in the deeper layers, while the harmonics of the degrees N > 11 may indicate the presence of tension in the crust generated by small structures of the terrain. Based on the maps, possible locations of deposits of volatile elements (mainly on the far side of the Moon and in the northern cir-cumpolar region) and other natural resources have been determined.
相似文献3.
M. Bahmanabadi A. Anvari M. Khakian Ghomi D. Purmohammad J. Samimi M. Lamehi Rachti 《Experimental Astronomy》2002,13(1):39-57
We have studied Extensive Air Showers (EAS) with two small arraysof 1 m2 scintillation detectors inTehran, 1200 m above sea level.The distribution of air showersin zenith and azimuth angles has been studied and a cosnΘdistribution with n = 7.2±0.2 was obtained for zenith angledistribution. An asymmetry has been observed in the azimuthaldistribution of EAS of cosmic rays because of magnetic field ofthe Earth. Amplitudes of the first and the second harmonics ofobserved distribution depend on zenith angle as A
I ≈ (0.02 + 0.35 sin2Θ)±0.02, and A
II ≈ (0.03 + 0.42 sin4Θ)±0.03. Meanwhile, the uncertainties arising from the instrument, transit location of shower particles in the scintillator and fluctuations in the shower front have been calculated. 相似文献
4.
D. G. King-Hele 《Planetary and Space Science》1986,34(12):1319-1328
The orbit of the satellite 1971-30B (Tournesol rocket) has been determined from more than 2000 observations at 34 epochs spaced at 8-day intervals between March and November 1978 when the orbit was experiencing 15th-order resonance. The variations in the orbital inclination, which was near 46.4°, and in the eccentricity, which was near 0.01, have been analysed to determine values of six lumped harmonics of order 15. In view of the fact that the orbit passed through resonance quite rapidly, the results are very satisfactory: the standard deviations of the lumped harmonics correspond to accuracies between 1 and 3 cm in geoid height. 相似文献
5.
D.G. King-Hele 《Planetary and Space Science》1985,33(10):1145-1153
The satellite 1967-11G, which had an orbital inclination of 40°, passed through the 14th-order resonance with the Earth's gravitational field in 1974. The changes in its orbital inclination at resonance have been analysed to obtain values for four lumped 14th-order harmonics in the geopotential, with accuracies equivalent to about 5 cm in geoid height. Analysis of the eccentricity was also attempted, but did not yield useful results.As no previous satellite analysed at 14th-order resonance has had an inclination near 40°, the results have proved to be valuable in determining individual 14th-order harmonics in the geopotential. 相似文献
6.
We study the effect of systematic variations in stellar parallaxes over the celestial sphere on the results of a kinematic analysis of stellar proper motions. Our approach is based on the representation of stellar parallaxes by scalar spherical harmonics and on the decomposition of stellar proper motions into a system of vector spherical harmonics. We derive theoretical relations that relate the coefficients of the decomposition of stellar proper motions into toroidal and spheroidal harmonics to the coefficients of the decomposition of stellar parallaxes into scalar spherical harmonics. We have established that the systematic variations of parallaxes over the celestial sphere distort all parameters of the linear Ogorodnikov-Milne model and can be responsible for the appearance of beyond-the-model harmonics. We have performed a kinematic analysis of the proper motions of blue-white and red giants based on Hipparcos data. The parallaxes of blue-white giants show a strong dependence on Galactic latitude (with predominant contraction along the Galactic equator). In contrast, the deviations of the parallaxes from the mean for red giants are localized only in two regions of the celestial sphere. For these samples, the effect of parallax variations over the celestial sphere on kinematic parameters has turned out to be comparable to their rms errors. The global solutions performed using both samples have revealed strong beyond-the-model kinematic effects described by second-order toroidal harmonics and third-order spheroidal harmonics. Using the solutions performed separately in the northern and southern Galactic hemispheres, we have established that not the systematic variations of parallaxes over the celestial sphere but the retardation of Galactic rotation with increasing distance of stars from the principal Galactic plane is mainly responsible for the appearance of these harmonics. Based on these samples of stars, we have estimated the magnitude of the vertical Galactic rotation velocity gradient to be 18.0±2.9 and 22.7±2.2 km s?1 kpc?1, respectively. 相似文献
7.
Huang Guangs LI 《Solar physics》1987,114(2):363-373
A theoretical analysis of electron-cyclotron maser instabilities indicates that the distribution function of non-thermal electrons influences millisecond radio spikes in solar flares, and that a hollow beam distribution is more likely than a loss-cone distribution. The restrictions of classical theories of cyclotron resonant absorption are discussed and a formula is derived for the absorption coefficient near the resonant frequency. Finally, the computations show that for typical coronal parameters, the growth rates of the fundamental of fast extraordinary modes are much faster than those of their second harmonics; and because the directional angle of the fundamental is smaller, its resonant absorption may be neglected. Moreover, the band-width of the fundamental is consistent with observation of radio spikes; therefore, we claim that the millisecond radio spikes in the decimetric range are composed mainly of fundamentals of the fast extraordinary modes. The second harmonics of fast extraordinary modes may be generated for directions near to the vertical to the magnetic field, but it is impossible to observe both fundamental and second harmonics in the same direction. 相似文献
8.
Will J. Percival 《Monthly notices of the Royal Astronomical Society》2005,356(3):1168-1176
The real-space power spectrum of L * galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov chain Monte Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a spherical harmonics decomposition of the 2dFGRS overdensity field (described in a previous paper) with 16 real-space power spectrum values and linear redshift-space distortion parameter β( L * , 0) . The recovered marginalized band powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17-dimensional likelihood hypersurface in order to allow the likelihood to be quickly estimated given a set of model band powers and β( L * , 0). The likelihood surface is not well approximated by a multivariate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band power has a Gaussian distribution in a combination of the band power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and we use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full spherical harmonics procedure. All of the data are made publicly available (from http://www.roe.ac.uk/~wjp/ ), enabling the spherical harmonics decomposition of the 2dFGRS of Percival et al. to be easily used as a cosmological constraint. 相似文献
9.
The line shape of the non-thermal O(1D) 6300 Å emission is calculated using the two population model of Schmitt, Abreu and Hays (Planet. Space Sci.29, 1095, 1981). The calculated line shapes simulate observations made from a space platform at different zenith angles and altitudes. The non-thermal line shapes observed at zenith angles other than the local vertical have been obtained by using the Addition theorem for spherical harmonics of a Legendre polynomial expansion of the non-thermal population distribution function. 相似文献
10.
Astronomy Letters - The technique of spherical harmonics, both scalar and vector ones, has long been applied to analyze the astronomical data on a sphere, for example, in the representation of... 相似文献
11.
An accurate theory of the rotation of the Moon has been constructed by numerical integration. All direct perturbations on the Moon's rotational motion have been analysed. The requirements of the current observational accuracy are such that some improvements had to be added to the theoretical models. First, the gravitational figure of the Moon has been developed up to the fifth degree harmonics. Second, mutual potential effects between the figure of the Moon and the figure of the Earth have been expanded farther up. The direct action of planets must be taken into account, its effects being very small but not always negligible. The physical librations resulting of planetary effects and Earth-Moon figure-figure interactions are presented in this paper. 相似文献
12.
Hans G. Walter 《Celestial Mechanics and Dynamical Astronomy》1970,2(3):389-397
A comparison is drawn between the expansion of the potential in spherical harmonics on the one hand and in ellipsoidal harmonics on the other, with the objective of associating the spherical and ellipsoidal gravity coefficients of the Earth's potential.For this purpose the properties of orthogonality of the Lamé functions of the first kind have been tailored to this subject of investigation and become instrumental in establishing the mathematical expressions which relate the two classes of gravity coefficients to each other. In deriving the elements of the transition matrices elliptic integrals have been encountered whose reduction to the three kinds of canonical elliptic integrals is discussed.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969. 相似文献
13.
In this paper, models of the static pointing errors and their correction of an altazimuth telescope are discussed, and a stable model with a small number of basic parameters is given. Compared with the common spherical harmonics model, the present model is not sensitive to the distribution of observing data and has a much higher correction accuracy. The residuals from this model follow the normal distribution in statistics. It can meet the need of precise orbit determination. 相似文献
14.
The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained. 相似文献
15.
Doreen M.C. Walker 《Planetary and Space Science》1974,22(3):391-402
Cosmos 359 rocket 1970-65D, was launched on 22 August 1970 into an orbit inclined at 51·2° to the Equator, with an initial perigee height of 209 km: it decayed on 6 October 1971 after a lifetime of 410 days. The orbit has been determined at 42 epochs during the lifetime, using the RAE orbit refinement program, PROP, with over 2600 observations. Observations from the Hewitt cameras at Malvern and Edinburgh were available for 10 of the 42 orbits.Ten values of density scale height, at heights between 185 and 261 km, have been determined from analysis of the variations in perigee height.Upper-atmosphere zonal winds and 15th-order harmonics in the geopotential have been evaluated from the changes in orbital inclination. The average atmospheric rotation rate, for heights near 220 km, is found to be 1·04 rev/day; but there are striking departures from the average, with well-established values of 1·30, 0·75, 1·35 and 0·95 over four successive 75-day intervals. The changes in inclination at the 15th-order resonance in November 1970 give values of lumped 15th-order harmonics, which will provide equations for evaluating coefficients of order 15 and even degree (16,18,…) and also show that useful results on the geopotential can be obtained from satellites with perigee as low as 200 km. 相似文献
16.
M. Bahgat El-Shaarawy 《Earth, Moon, and Planets》1989,47(3):217-230
In a series of papers, the equilibrium configurations of highly rotating fluid bodies have been derived. The deformation of these inhomogeneous self-gravitating fluid, of arbitrary internal structure are due to centrifugation potential. These level surfaces are expressed in terms of fourth-order sectorial harmonics.In this paper, the main equations of the problem — such as the surface of the distorted body, the gravitational potential at an arbitrary point and the disturbing potential — have been expanded to the fourth-order in terms of the even-order sectorial harmonics.This work will hereafter be referred to as Paper I. 相似文献
17.
In the present work the data of three different neutron monitoring stations, Deep River, Tokyo and Inuvik located at different
geomagnetic cutoff rigidities and altitudes has been harmonically analysed for the period 1980–1993, 1980–1990 and 1981–1993
respectively to investigate for a comparative study of diurnal, semi-diurnal and tri-diurnal anisotropies in cosmic ray (CR)
intensity in connection with the change in IMF Bz component and solar wind velocity on 60 quietest days. It is observed that
the amplitude of first harmonic is highly anti-correlated to the solar wind velocity during the period of high-speed solar
wind stream (HSSWS) epoch on quiet days for three neutron monitor stations at different geomagnetic rigidity thresholds. During
quiet days the amplitude of all the three harmonics significantly deviates on the onset of HSSWS epoch, whereas the direction
of the anisotropy of all the three harmonics remains time invariant at three different cut off rigidity stations. The amplitude
as well as the direction of anisotropy of all the three harmonics does not have time variation characteristics associated
with Bz component of IMF on geo-magnetically most quiet days. 相似文献
18.
E. Evangelidis 《Astrophysics and Space Science》1978,56(1):255-269
The behavioyr of a force-free field has been studied in a Reissner-Nordström metric. An expansion in tensor harmonics of even-odd parity reduced the radial equations in a differential equation of the Sturm-Liouville system which was solved asymptotically in a conveniently defined space coordinate. Further, it has been possible to regularize the singular behaviour of the Reissner-Nordström metric at the event horizon and the modified metric to be given explicitly. 相似文献
19.
Halil Kirbiyik 《Astrophysics and Space Science》1989,153(2):289-296
A model of first-generation intermediate mass star of 5M
with no metals has been considered. The vibrational instability of this model has been investigated. The model, in question, burns helium in the core. Calculations have been performed for the first and second harmonics as well as for the fundamental mode. The model has been found to be vibrationally stable toward radial pulsations. 相似文献
20.
B. P. Kondratyev 《Solar System Research》2011,45(1):60-74
A flexible and informative vector approach to the problem of physical libration of the rigid Moon has been developed in which
three Euler differential equations are supplemented by 12 kinematic ones. A linearized system of equations can be split into
an even and odd systems with respect to the reflection in the plane of the lunar equator, and rotational oscillations of the
Moon are presented by superposition of librations in longitude and latitude. The former is described by three equations and
consists of unrestricted oscillations with a period of T
1 = 2.878 Julian years (amplitude of 1.855″) and forced oscillations with periods of T
2 = 27.201 days (15.304″), one stellar year (0.008″), half a year (0.115″), and the third of a year (0.0003″) (five harmonics
altogether). A zero frequency solution has also been obtained. The effect of the Sun on these oscillations is two orders of
magnitude less than that of the Earth. The libration in latitude is presented by five equations and, at pertrubations from
the Earth, is described by two harmonics of unrestricted oscillations (T
5 ≈ 74.180 Julian years, T
6 ≈ 27.347 days) and one harmonic of forced oscillations (T
3 = 27.212 days). The motion of the true pole is presented by the same harmonics, with the maximum deviation from the Cassini
pole being 45.3″. The fifth (zero) frequency yields a stationary solution with a conic precession of the rotation axis (previously
unknown). The third Cassini law has been proved. The amplitudes of unrestricted oscillations have been determined from comparison
with observations. For the ratio $
\frac{{\sin I}}
{{\sin \left( {I + i} \right)}} \approx 0.2311
$
\frac{{\sin I}}
{{\sin \left( {I + i} \right)}} \approx 0.2311
, the theory gives 0.2319, which confirms the adequacy of the approach. Some statements of the previous theory are revised.
Poinsot’s method is shown to be irrelevant in describing librations of the Moon. The Moon does not have free (Euler) oscillations;
it has oscillations with a period of T
5 ≈ 74.180 Julian years rather than T ≈ 148.167 Julian years. 相似文献