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1.
In non-resonant cases, a constant part coming from the perturbations can be easily separated from the observed mean mean motion, which can be called the perturbed part. An another part created by resonance must be separated from the observed mean motion in the case of the first three Galilean satellites. The determination of it gives better value of the semi-major axis.In this investigation, the analytical process is chosen to avoid a mixture of orders in successive expansions and integrations.The main terms entering in the computation of the libration are the great inequalities of the first three satellites. Each of them is introduced in the development by its eight components; while in Sampson's theory, only the great inequality of Satellite 2 is given by two components.The equations of motion used in this work are derived from Sagnier's theory.

Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.  相似文献   

2.
Satellite theory     
In this paper dynamical characteristics of satellites are outlined by classifying the satellites into three categories according to the values of the solar tidal factor (n/n)2 which is the disturbing factor due to the sun and the oblateness factor of the primary planetJ 2/a 2. For inner satellites (n/n)2 is much smaller thanJ 2/a 2 and there are several pairs among them, for which the mean motions are commensurable to each other, and for some of them secular accelerations in the mean longitudes have been detected. For outer satellites (n/n)2 is much larger and the solar perturbations are dominant. For intermediary satellites the motion of the pole of the orbital plane is not so simple as those of the satellites of the other categories.  相似文献   

3.
The aim of the present work is to compare photographic observations of the Galilean satellites of Jupiter with the theory developed by Sampson at the beginning of the century and corrected and implemented recently by Lieske.The comparisons between the observed and computed values give differences in geocentric angular distances of the order of 0.08 for modern observations (1968 to 1977) and of the order of 0.14 for older ones (1913 to 1928).These results lead to the suggestion that important long period defects still exist in the theory of Sampson-Lieske. This is not surprising, due to the difficulties of the computation of the long-period inequalities in mean longitudes, even in a first-order theory.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980  相似文献   

4.
In a previous paper (Stellmacher, 1981, hereafter mentioned as Paper I), we have given an algorithm for the construction of periodic orbits in a rotating frame, for satellites around an oblate planet. In the present paper, we apply this theory to the Mimas-Tethys case; we obtain the following results:
  1. Without resonance, it is possible to find a rotating system in which the solution is a periodic one. The angular velocity of this rotating frame is calculated as function of the masses of the two satellites.
  2. Including the resonant terms and assuming an exact commensurability of the implied frequencies, we demonstrate that the condition for periodic solutions in the rotating system as defined in (a) is: the initial position of the satellites at conjunction lies on an axis defined by (Ω1+Ω2)/2 or (Ω1+Ω2)/2 + π/2;Ω1 and Ω2 are the longitudes of the ascending nodes of the satellite's orbits. The solution still is a periodic one, thus all the conjunction occur in either axis.
  3. In the Mimas Tethys case there is only approximately commensurability between these frequencies. The two satellites are considered as oscillators whose amplitudes and phases are functions of time. The equation of the libration can be established; we find the usual form, but for each satellite the generating solution is a periodic solution (as defined in Paper I), but not a Keplerian one. It follows a determination of the masses which slightly differs from that given by Kozai (1957), when the same values of the observed quantities are used for calculations.
  4. The equation of the libration is: $$\ddot z + n_1^2 h^2 \sin z + n_1 q\dot z\sin z = 0$$
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5.
Résumé La transformation de Lyapunov transforme une équation de Hill en une autre qui occupe la même place dans la classification de Yakubovich.Soit (C) une solution périodique d'un système conservatif à deux degrés de liberté. D'après le principe de moindre action de Maupertuis (C) est l'image d'une géodésique ().Nous montrons que les équations aux variations au voisinage de (C) et de () sont réductibles à deux équations de Hill qui se correspondent par une transformation de Lyapunov.
The Lyapunov transformation of Hill's equation and his dynamic interpretation
The Lyapunov transformation carries Hill's equationÿ+F(t)y=0,F(t+T)=F(t) into another one which belongs to the same class in Yakubovich's classification.Let (C) be a closed trajectory of a Lagrangian conservative system with two degrees of freedom. By the Principle of Least action, we know that (C) is the image of a geodesic () of a certain two-dimensional surface ().We show that the two Hill equations associated with (C) and () are related by a certain Lyapunov transformation.

Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.  相似文献   

6.
It is shown that the application of the Chebyshev theory of approximation to the calculation of the orbit of a minor planet allows the production of a compact ephemeris, based on data gathered over only a short time, which is both accurate, and simple and rapid to produce. Adjustment of numerical data to fit observational results is readily performed. Using Clenshaw's algorithm, an ephemeris may even be worked out on a pocket calculator. Further applications of Chebyshev polynomials to the calculation of parameters usually obtainable only by interpolation of classical ephemerides, and to the calculation of minor planetary orbits from observations of short duration by an orbiting telescope are discussed.

Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.  相似文献   

7.
The period-growth dichotomy of the solar cycle predicts that cycle 21, the present solar cycle, will be of long duration (>133 mo), ending after July 1987. Bimodality of the solar cycle (i.e., cycles being distributed into two groups according to cycle length, based on a comparison to the mean cycle period) is clearly seen in a scatter diagram of descent versus ascent durations. Based on the well-observed cycles 8–20, a linear fit for long-period cycles (being a relatively strong inverse relationship that is significant at the 5% level and having a coefficient of determination r 2 0.66) suggests that cycle 21, having an ascent of 42 mo, will have a descent near 99 mo; thus, cycle duration of about 141 mo is expected. Like cycle 11, cycle 21 occurs on the downward envelope of the sunspot number curve, yet is associated with an upward first difference in amplitude. A comparison of individual cycle, smoothed sunspot number curves for cycles 21 and 11 reveals striking similarity, which suggests that if, indeed, cycle 21 is a long-period cycle, then it too may have an extended tail of sustained, low, smoothed sunspot number, with cycle 22 minimum occurring either in late 1987 or early 1988.  相似文献   

8.
We propose that the coronal source longitude and latitude of solar wind plasma can be estimated within 10°. Previous writers have argued that the solar wind in the ecliptic should originate near the equator and that a quasi-radial hypervelocity (QRH) approximation (constant radial flow) is valid beyond the magnetohydrodynamic critical points. We demonstrate that an extension of the QRH approximation (as if the solar wind flowed radially with constant velocity from the center of the Sun) yields a proper estimate of the high coronal source location at the release zone where the solar wind makes its transition to radial interplanetary flow. This extrapolated QRH (or EQRH) approximation succeeds because the two main corrections to this source estimate, coronal corotation and interplanetary acceleration, tend to cancel (the former correcting the source location eastward, the latter westward). Although this ideal spiral approximation was first suggested by Snyder and Neugebauer (1966), only recently has it been demonstrated that it relates a wide range of interplanetary plasma, magnetic field and energetic particle data to observed coronal magnetic structure. We estimate quantitatively the error in the EQRH approximation by comparison with steady-state streamlines predicted by azimuthally independent and dependent theoretical solutions to the steady-state plasma equations. We find the error in both cases 10° in longitude and therefore suggest that the EQRH approximation offers the means to relate observed solar initial conditions in the release zone directly to interplanetary measurements. If, in addition, the EQRH approximation also leads to agreement with low coronal structure, then there should be a straightforward correspondence to otherwise unobservable high coronal structure.  相似文献   

9.
A new analytical solution of the system of differential equations describing secular perturbations and long-period solar perturbations of mean orbits of outer satellites of giant planets was obtained. As distinct from other solutions, the solution constructed using von Zeipel’s method approximately takes into account, in the secular part of the perturbing function, the totality of fourth order with respect to the small parameter m of the ratio of the mean motions of the primary planet and the satellite. This enables us to describe more accurately the evolution of satellite orbits with large apocentric distances, which in the course of evolution may exceed the halved radius of the Hill sphere of the planet with respect to the Sun. Among these are the orbits of the two outermost Neptunian satellites N10 (Psamathe) and N13 (Neso). For these satellites, the parameter m amounts to 0.152 and 0.165, respectively. Different from a purely analytical solution, the proposed solution requires preliminary calculations for each satellite. More precisely, in doing so, we need to construct some simple functions to approximate more complex ones. This is why we use the phrase “constructive analytical.” To illustrate the solution, we compare it with the results of the numerical integration of the strict motion equations of the satellites N10 and N13 over time intervals 5–15 thousand years.  相似文献   

10.
A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent after -2 Jovian years, where is a constant and is the maximum initial deviation of each planet from its reference orbit.  相似文献   

11.
A physical mechanism for the production of solar flares   总被引：1，自引：0，他引：1  
The weakly ionized photospheric layer in the sunspot environment satisfies certain dynamo inequalities (Equations (11) and (13)) resulting in photospheric Hall current systems. The corresponding Joule dissipation is associated with the surrounding plage area. For critical values of the driving or convective winds (speeds 1 km/s), two stream instability results. The computed energy is of the order of that found in solar flares.  相似文献   

12.
The problem of stability of the equilibrium points in the problem of motion of a mass point in the neighbourhood of a rotating triaxial ellipsoid in a degenerate case (the Gaussian of the Hamiltonian is equal to zero) is investigated.It is proved that the equilibrium points in the degenerate case are stable in the strict sence.
Résumé On étudie le problème de la stabilité des positions d'équilibre relatif dans le problème du mouvement du point matériel au voisinage de l'ellipsoid à trois axes tournant dans un cas dégénéré (le gaussian du Hamiltonian égal zéro).On a démontré que des positions d'équilibre relatif dans le dégénéré sont stables dans le sens rigoureux.
( )., .
  相似文献   

13.
Measurements of the Nimbus-7 and Solar Maximum Mission satellites reported temporary large decreases of the solar constant of the order of a few tenths of a percent on a time-scale from days to weeks. Our investigations show that these decreases were caused by active sunspot groups with fast development and complex structure. This connection between the solar constant variation and the appearance of the active groups seems to be more clear in the maximum of the solar activity. At the time of the solar minimum, mainly in the second part of 1984, there were not any active sunspot groups practically on the solar disk, the value of the solar constant only fluctuated around its mean without large variation. The results of time series analyses show that the periodicity of the solar constant values, of young and active spot areas was nearly 23.5 days in 1980, which increases to 28 days towards the minimum of the solar cycle till 1983. During this time interval the main periodicity of the old, passive spot areas was around 28 days. In 1984, at the time of the solar minimum, there were not any obvious periodicities practically in the projected areas of the different types of the sunspot groups.  相似文献   

14.
Solar wind and interplanetary magnetic field data were obtained by the PROGNOZ 1 and PROGNOZ 2 satellites during the period following the August 4, 1972 (0621 UT) solar flare. A thermalized plasma was recorded one hour after the shock followed two hours later by the plasma piston with a bulk velocity higher than 1700 km s-1. The comparison between the PROGNOZ and PIONEER 9 solar wind data shows an attenuation of the plasma properties with the deflection from the flare's meridian.  相似文献   

15.
Nova Delphini 1967 has been observed in the red and photographic infrared at the Haute-Provence Observatory from September 7 to November 12, 1968. Dispersions range from 230 Å/mm to 4 Å/mm. The slope of the continuous spectrum in the region 1.3–1.7 –1 leads to a gradient of 3.06, which did not appear to vary during the observing period. This gradient is, however, very different from the value 1.71 measured on plates secured in August 1968. Lines ofHi, Hei, Heii, Feii,Oi,Cii and forbidden transitions due toOi,Oii, Fevii, Fex, Fexi,Siii,Aiii,Av,Axi and Nixv have been identified. Their intensities at various dates are given in Table II. Line profiles could be measured for a few lines taken on a 39 Å/mm spectrogram on October 3. Hei 6678 and 7065 are displayed on Figures 2 and 3. Figure 4 gives the [Oii] doublet at 7319–7330, while the H profile, obtained on October 4 can be seen on Figure 5. The line extends over more than 45 Å and narrow absorptions are seen at 6551.05; 6555.75; 6563.15; 6571.49; 6574.45. Due to the absence of published data on radial velocities of absorption lines in the visible spectrum at that time, it is not possible to give a clear identification for these features. Some of them may belong to H, while others are probably due to metals.  相似文献   

16.
The three-dimensional structure of the solar magnetic field in the interplanetary space is inferred from a theoretical point of view. We use the magnetic field produced by a magnetic dipole rotating obliquely in vacuum. The correction for the presence of a plasma surrounding the Sun is taken into account in terms of a phenomenological approximation.Our method well reproduces the basic features of the polarity-reversal-surface (the neutral sheet in the two-hemisphere model by Saito (1975)) obtained on the basis of observational data, i.e. the snail-shell like structure and variation of its precise shape in accordance with the solar cycle, except for the folding of the surface.  相似文献   

17.
To obtain improved maps of the coronal electron density distribution we have devised an iterative technique in which an approximation of the unknown distribution is successively modified to reduce discrepancies with the original data. With this technique we can now map the corona to a much finer resolution than shown in our previous papers, without greatly increasing the computational cost. The series representation of density may now contain more than 23 000 terms compared with previous limit of 128. This results in a fourfold increase in linear resolution, so that features about a tenth of a solar radius in width are now separated. The iteration algorithm can be adjusted to apply a mathematically optimal correction to a given approximation of the density. Although this correction minimizes noise levels, a cheaper version of the algorithm yields a better result.  相似文献   

18.
A Lie transformation technique proposed by the author (1977) utilizing an approach due to Kolmogorov and Arnol'd is modified to eliminate the calculation of unproductive terms. Special features of the original method — the ability to eliminate simultaneously both short- and long-period terms, and [formal] quadratic convergence for non-degenerate system sand nearly quadratic convergence for degenerate systems—are retained in an even more efficient technique. Comparisons of the new method with other available Lie transform techniques is made.  相似文献   

19.
The technique of the general planetary theory has been proposed for constructing a theory of motion of the Moon. This method enables us to elaborate the consistent theory of motion of the principal planets and the Moon, which is of particular importance for determining planetary perturbations in lunar motion. As an initial approximation for lunar motion, an intermediate orbit generalizing the Hill's variational curve has been built. This orbit includes all solar and planetary inequalities independent of eccentricities and inclinations of the Moon, Sun and planets. In calculating this orbit, the motion of the principal planets in quasi-periodic intermediate orbits has been taken into account. This solution was produced with the aid of the Universal Poissonian Processor (UPP) elaborated in the Institute for Theoretical Astronomy (Leningrad).Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980.  相似文献   

20.
A nonlinear theory of secular resonances is developed. Both terms corresponding to secular resonances 5 and 6 are taken into account in the Hamiltonian. The simple overlap criterion is applied and the condition for the overlap of these resonances is found. It is shown that in given approximation the value p = (1 - e2)1/2(1 - cosI) is an integral of motion, where the mean eccentricity e and mean inclination I are obtained by eliminating short-period perturbations as well as the nonresonant terms from the planets. The overlap criterion yields a critical value of parameter p depending on the semi-major axis a of the asteroid. For p greater than the critical value, resonance overlap occurs and chaotic motion has to be expected. A mapping is presented for fast calculation of the trajectories. The results are illustrated by level curves in surfaces of section method.  相似文献   

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