共查询到20条相似文献，搜索用时 906 毫秒
1.
André Duijveman 《Solar physics》1983,84(1-2):189-203
Shortly after the occurrence of the impulsive spikes of the two-ribbon flare of May 21, 1980, a temperature analysis of the X-ray emitting flare plasma showed the presence of a low-temperature component [n = 15 × 1010 cm#X2212;3; T = 20 × 106 K] and a high-temperature component [n = 2 × 1010 cm#X2212;3; T = 40 × 106 K]. The mean free path of an electron in the hot component is comparable to the size of the source (≈ 104 km). Heat losses from the hot source can therefore not be described with classical formulae. Theoretical arguments show that most likely the electron to ion temperature ratio T e/Ti in the hot plasma is close to unity. This implies the presence of a hot ion component (T i ≈ 40 × 106 K) as well. Under these conditions (T e ≈ T i) heat flux limitation by electrostatic turbulence is ineffective. However, reduction of the heat flux is still possible due to the breakdown of classical theory. It is demonstrated that only non-classical current dissipation processes can sustain a hot source against cooling by a saturated heat flux. Investigation of the collisionality as a function of position along a magnetic loop shows that the breakdown of classical theory should be expected to occur first near the base of the loop. We conclude that the newly discovered hot source is important for the energy budget of the flare, even if the heat losses are considerably reduced. It is estimated that for the May 21, 1980 flare a total of about 1031 ergs were necessary to maintain the hot source against heat losses over the time period that it was observed (≈ 10 min). 相似文献
2.
We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S
1 action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J
2-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J
2-Hamiltonian is a collective Hamiltonian of the T3 momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J
2 effect as geometric phases. 相似文献
3.
J. Baumgarte 《Celestial Mechanics and Dynamical Astronomy》1972,5(4):490-501
A stabilization of the classical equations of two-body motion is offered. It is characterized by the use of the regularizing independent variable (eccentric anomaly) and by the addition of a control-term to the differential equations. This method is related to the KS-theory (Stiefel, 1970) which performed for the first time a stabilization of the Kepler motion. But in contrast to the KS-theory our method does not transform the coordinates of the particle. As far as the theory of stability and the numerical experiments are concerned we restrict ourselves to thepure Kepler motion. But, of course, the stabilizing devices will also improve the accuracy of the computation of perturbed orbits. We list, therefore, also the equations of the perturbed motion. 相似文献
4.
Myron Lecar 《Celestial Mechanics and Dynamical Astronomy》1996,64(1-2):163-166
We have accumulated thousands of orbits of test particles in the Solar System from the asteroid belt to beyond the orbit of Neptune. We find that the time for an orbit to make a close encounter with a perturbing planet, T
c
,is a function of the Lyapunov time, T
ty
.The relation is log (T
c
/T
o
)= a + b log (T
ly
T
o
)where T
o
is a fiducial period which we have taken as the period of the principal perturber or the period of the asteroid. There are exceptions to this rule interior to the 2/3 resonance with Jupiter. There, at least in the restricted problem, for sufficiently small Jupiter mass, orbits may have a positive Lyapunov exponent and still be blocked from having a close approach to Jupiter by a zero velocity curve. Of more serious concern is whether the relation holds for purely secular resonances, and if it does, how to choose T
o
.This is the case of interest for the planets in the solar system. 相似文献
5.
6.
Paule Kustaanheimo 《Celestial Mechanics and Dynamical Astronomy》1972,6(1):52-59
The ordinary spinor differential Equation (20) of the unperturbed Kepler motion is obtained from the classical equation of motion (19) if one uses the spinor regularization (9) and postulates an essential subsidiary condition (10). A natural generalization for the Kepler motion follows by dropping this subsidiary conditions; it is the 8-parameter set of solutions of the spinor equation of motion (20). The sixteen natural extensive integrals (30)–(35) for this generalized Kepler motion are here deduced by means of the relativistic motors (2), (7) of the Spinor Ring Algebra. These integrals form, with respect to the Poisson bracket operation, a 15-dimensional Lie algebra (40)–(44), closely related to the Lie algebras in quantum mechanics.Dedicated to Professor G. Järnefelt on his 70th anniversary. 相似文献
7.
Maria Dina Vivarelli 《Celestial Mechanics and Dynamical Astronomy》1987,41(1-4):359-370
As an outcome of our previous notes [13, 14] on the quaternion regularization of the classical Kepler problem and pre-quantization of the Kepler manifold we show, first, that both the cross product of two quaternions and the cross product of their anti-involutes are susceptible of a simple geometrical representation in the ordinary 3-dimensional euclidean spaceR
3 and, secondly, that they satisfy anSO(4)-invariant relation that implies projection of curves from the quaternion space onto the spaceR
3. ThisSO(4)-invariance allows—in the particular case of orthogonal quaternions of equal norm—a straight derivation: (i) of the correspondence between the free motion on the surface of a sphereS
3 and the physical elliptical Kepler motion (collisions included) on a plane denoted by
w
; (ii) of the celebrated Kepler equation and (iii) of the Levi-Civita regularizing time transformation. With (i) and (ii) we recover some of Györgyi's [3] results. The aforesaid orbital plane
w
and the orbital plane *, arrived at independently by exploiting the Kustaanheimo-Stiefel regularizing transformation, are shown to be inclined exactly at an angle characterizing the ratio of the semi-axes of the elliptical orbits and intimately related to the cross product representation. Thus the eventual superimposition of the two planes confirms the intimate connection between the various regularization procedures—transforming the classical Kepler problem into the geodesic flow onS
3—and the Fock's procedure for the quantum theoretical Kepler problem of the hydrogen atom (accidental degeneracy).This research was supported by the Consiglio Nazionale delle Ricerche of Italy (C.N.R.-G.N.F.M.). 相似文献
8.
9.
In this paper, an efficient algorithm is established for computing the maximum (minimum) angular separation ρ max(ρ min), the corresponding apparent position angles ( $\theta|_{\rho_{\rm max}}$ , $\theta|_{\rho_{\rm min}}$ ) and the individual masses of visual binary systems. The algorithm uses Reed’s formulae (1984) for the masses, and a technique of one-dimensional unconstrained minimization, together with the solution of Kepler’s equation for $(\rho_{\rm max}, \theta|_{\rho_{\rm max}})$ and $(\rho_{\rm min}, \theta|_{\rho_{\rm min}})$ . Iterative schemes of quadratic coverage up to any positive integer order are developed for the solution of Kepler’s equation. A sample of 110 systems is selected from the Sixth Catalog of Orbits (Hartkopf et al. 2001). Numerical studies are included and some important results are as follows: (1) there is no dependence between ρ max and the spectral type and (2) a minor modification of Giannuzzi’s (1989) formula for the upper limits of ρ max functions of spectral type of the primary. 相似文献
10.
Jörg Waldvogel 《Celestial Mechanics and Dynamical Astronomy》1980,21(2):171-175
Letx
0
(t),x
0
4 be a homothetic solution of the planar three-body problem with total energyh, described in relative coordinates with respect to one body. It is shown that the variational equation of the problem atx
0
(t) can be solved explicitly in terms of hypergeometric functions. This is done by using the scaled true anomaly of the one-dimensional Kepler motion as the independent variable.The classical theorems about hypergeometric functions allow a simple calculation of all the values needed in applications. By means of this theory the past of a homothetic triple close encounter may be described in a linearized approximation.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978. 相似文献
11.
V. B. Magalinsky Tapan K. Chatterjee 《Celestial Mechanics and Dynamical Astronomy》1996,65(4):399-405
The classical Kepler Problem consists in the determination of the relative orbital motion of a secondary body (planet) with respect to the primary body (Sun), for a given time. However, any natural system tends to have minimum energy and is subjected to differential gravitational or tidal forces (called into play mainly due to the finite size and deformability of the secondary body). We formulate the Kepler Problem taking into account the finite size of the secondary body and consider an approximation which tends towards minimum energy orbits, by increasing the dimensionality of the problem. This formulation leads to a conceivable natural explanation of the fact that the planetary orbits are characterized by small eccentricities. 相似文献
12.
13.
Action-angle variables for the Levi-Civita regularized planar Kepler problem were introduced independently first by Chenciner and then by Deprit and Williams. The latter used explicitly the so-called Lissajous variables. When applied to the transformed Keplerian Hamiltonian, the Lissajous transformation encounters the difficulty of being defined in terms of the constant frequency parameter, whereas the Kepler problem transformed into a harmonic oscillator involves the frequency as a function of an energy-related canonical variable. A simple canonical transformation is proposed as a remedy for this inconvenience. The problem is circumvented by adding to the physical time a correcting term, which occurs to be a generalized Kepler’s equation. Unlike previous versions, the transformation is symplectic in the extended phase space and allows the treatment of time-dependent perturbations. The relation of the extended Lissajous–Levi-Civita variables to the classical Delaunay angles and actions is given, and it turns out to be a straightforward generalization of the results published by Deprit and Williams. 相似文献
14.
The Kepler problem for the resistive force r/r
2 is known to have a conserved vector which is the analogue to Hamilton's vector for the standar Kepler problem. In this note it is shown in a very elementary way that many similar force laws display the same property. The orbit equation can be obtained easily in such cases. 相似文献
15.
16.
Short-term satellite onboard orbit propagation is required when GPS position measurements are unavailable due to an obstruction or a malfunction. In this paper, it is shown that natural intermediary orbits of the main problem provide a useful alternative for the implementation of short-term onboard orbit propagators instead of direct numerical integration. Among these intermediaries, Deprit’s radial intermediary (DRI), obtained by the elimination of the parallax transformation, shows clear merits in terms of computational efficiency and accuracy. Indeed, this proposed analytical solution is free from elliptic integrals, as opposed to other intermediaries, thus speeding the evaluation of corresponding expressions. The only remaining equation to be solved by iterations is the Kepler equation, which in most of cases does not impact the total computation time. A comprehensive performance evaluation using Monte-Carlo simulations is performed for various orbital inclinations, showing that the analytical solution based on DRI outperforms a Dormand–Prince fixed-step Runge–Kutta integrator as the inclination grows. 相似文献
17.
The effect of resonant planetary perturbations on the evolution of the orbit of a satellite driven by tidal forces is studied in this paper. The basic equations that govern it are similar to the equations found in orbit-orbit and in spin-orbit couplings. The general form of these equations is:
A general treatment of such equations, proposed earlier (J. Kovalevsky, in Dynamical Trapping and Evolution of the Solar system, IAU Colloquium no74, V. V. Markellos and Y. Kozai, eds., 1983) is sketched.In particular, the effects of the large long periodic variations of the excentricity e' of the planet are analysed on an example taken from the lunar theory and the Earth's general theory due to Bretagnon.The argument of the well known planetary term =18 V-16T due to the tidal friction and quasi-periodic variations due to the presence of e' in the expression of the mean motion of the Moon. Their joint effect, has been to produce in the past resonant situations for this argument that repeated more than 100 times. Every such situation can be treated by equation (1).Numerical integration, using conditions that might have occurred while or similar other arguments were quasi resonant, have produced the following results: (a) In some cases, the argument becomes temporarily resonant. Between the capture to and the escape from the resonance, the semi-major axis undergoes oscillations, but the tidal secular evolution is stopped. (b) In other cases, the argument is not trapped into a resonant conditions, but the semi-major axis undergoes a quick change while d/dt is close to zero.A number of arguments that have been quasi resonant in the past history of the Earth-Moon system has been identified from the Chapront and Chapront-Touzé Lunar Theory. It appears that the phenomena described are frequent features in the evolution of the Lunar orbit. 相似文献
18.
J. Hamel 《Astronomische Nachrichten》2009,330(6):526-535
In the beginning Copernicus' system of the world did not have empirical confirmation. In this situation, Kepler's research, as well as the astronomical observations with the telescope, invented in 1608, played a decisive role. Under the assumption of the central position of the Sun, Kepler discovered the elliptical orbital motion of the planets as a base of the computation of noticeably improved ephemerides. The first telescopic observations – Jupiter's moons, phases of Venus, sunspots, surface features of the moon, gave important arguments for Copernicus' system. Galilei was one of the first who used the telescope for astronomical research (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
The bulk flow of the solar wind plasma in the flank-side of the magnetospheric boundary layer, where the magnetic field lines are closed, has a component transverse to the ambient field. There is quite a strong velocity shear. The theoretical model ignores inhomogeneities in the ambient field and the mass density which occur at the magnetopause on about the same length scale as that of the velocity shear.Consideration is restricted to hydromagnetic waves which have a k-vector nearly normal to the Bo-Vo plane, i.e., approximately the magnetopause surface (kx >kz ～ ky′kxLB > 1 and LB = 0.1 ～ 1.0 RE where LB is a characteristic length of the boundary layer). It is found that a long-period (T ? 40 sec) hydromagnetic wave [the Alfvén-like wave ()] driven by velocity shear instability can be excited in the shear plasma. It is also found that the group velocity of the HM-wave is directed almost along the magnetic field line and that the magnetic variance in the shear plasma tends to be parallel to the Bo-Vo plane. The velocity shear instability in the magnetospheric boundary layer is judged to be a likely source of long-period magnetic pulsations. 相似文献
20.
Photoelectric observations of the WR binary CQ Cephei (WN6+O9) are presented. the depths of the eclipses in the light curves are best represented by an inclination of the orbit i = (68°.8±0.6) and the width of the very asymmetric eclipse curves can be represented by only an overcontact configuration (Ω1 = Ω2 = 3.65 ± 0.05, and f = 27%). Simultaneous solution of the light and radial velocity curves strongly supports CQ Cep's membership of the Cep OB1 association. By considering this membership we obtained absolute dimensions of the system, which lead to a consistent physical model for CQ Cephei. The more luminous WR primary turns out to be the hotter but slightly less massive component: MWR = 20.8 M⊙, RWR = 8.2R⊙, Teff(WR) = 43600 K, and Mo = 21.4 M⊙, Ro = 8.3 R⊙, Teff(O) = 37000 K. 相似文献