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1.
Solar-wind data obtained by the OGO-5 and IMP-6-8 Earth satellites show a positive correlation between the ratio of helium to hydrogen temperatures, T /T p, and the velocity difference between the two ions, v - v p . Although this result disagrees with the Prognoz-1 results reported earlier in this journal, it is consistent with the expected control by Coulomb collisions when the solar-wind density is high.  相似文献   

2.
An algorithm is given for normalizing conservative linear Hamiltonian systems. This one generalizes Siegel's method to the cases where the eigenvalues are multiple. We obtain by a canonical transformation a normal form of two blocks, one of which is the upper Jordan form, and the other, the lower Jordan form. We select real solutions from the solutions of these equations, and we apply the result to the restricted three body problem in the vicinity of the triangular points for Routh's critical mass ratio.

n est la matrice unité d'ordren,O n est la matrice nulle d'ordren.  相似文献   

3.
J. J. Aly 《Solar physics》1989,120(1):19-48
Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .  相似文献   

4.
We solve the first order non-linear differential equation and we calculate the two quadratures to which are reduced the canonical differential equations resulting from the elimination of the short period terms in a second order planetary theory carried out through Hori's method and slow Delaunay canonical variables when powers of eccentricities and the sines of semi-inclinations which are >3 are neglected and the eccentricity of the disturbing planet is identically equal to zero. The procedure can be extended to the case when the eccentricity of the disturbing planet is not identically equal to zero. In this latter general case, we calculatedthe two quadratures expressing angular slow Delaunay canonical variable 1 of the disturbed planet and angular slow Delaunay canonical variable 2 of the disturbing planet in terms of timet.  相似文献   

5.
Taking advantage of the radial intermediaries and the regularization and linearization methods, the zonal Earth satellite theory is studied in the polar nodal canonical set of variables (, , ,R, ¡,N).The variable is eliminated in the first order of the Hamiltonian by applying Deprit's method. Then, the elimination of the perigee is carried out by another canonical transformation. As a consequence, a new radial intermediary, which contains all theJ 2n(n1) harmonics, is given. A comparison with the previous radial intermediaries of Cid and Lahulla, Deprit and Alfriend and Coffey is made.Finally, a regularizing transformation which allows us to linearize part of the radial intermediary is proposed, and an analytical study of this process is presented.  相似文献   

6.
We derive upper limits to the radiation temperaturesT t(k) for emission near the fundamental and second harmonic of the electron plasma frequency in terms of the effective temperature for plasma wavesT l(k). We findT t(k)(c/(3)1/2 V e)3 T l(k) for emission near the fundamental which differs from the result of Melrose (1970b) by the factor in parentheses. This factor can exceed 4×104 in some plasmas. The conditions under which this limit could be reached are delinated. For emission near the second harmonicT t(k)T l(k) since the absorption coefficient in this case can only be positive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

7.
Knowledge of the perturbations of zero-rank is essential for the understanding of the behavior of a planetary or cometary orbit over a long interval of time. Recent investigations show that these zero-rank perturbations can cause large oscillations in both the shape and position of the orbit. At present we lack a complete analytical theory of these perturbations that can be applied to cases where either the eccentricity or inclination is large or has large oscillations. For this reason we here develop formulas for the numerical integration of the zero-rank effects, using a modified Hill's theory and suitable vectorial elements. The scalar elements of our theory are the two components of Hamilton's vector in a moving ideal reference frame and the three components of Gibb's rotation vector in an inertial system. The integration step can be taken to be several hundred years in the planetary or cometary case, and a few days in the case of a near-Earth space probe. We re-discuss Hill's method in modern symbolism and by applying the vectorial analysis in a pseudo-euclidean spaceM 3, we obtain a symmetrical computational scheme in terms of traces of dyadics inM 3. The method is inapplicable for two orbits too close together. In Hill's method the numerical difficulty caused by such proximity appears in the form of a small divisor, whereas in Halphen's method it appears as a slow convergence of a hypergeometric series. Thus, in Hill's method the difficulty can be watched more directly than in Halphen's method. The methods of numerical averaging have, at the present time, certain advantages over purely analytical methods. They can treat a large range of eccentricities and orbital inclinations. They can also treat the free secular oscillations as well as the forced ones, and together with their mutual cross-effects. At the present time, no analytical theory can do this to the full extent.Basic Notations m the mass of the disturbed body - M the mass of the Sun - f the gravitational constant - f(M+m) - r the heliocentric position vector of the disturbed body - r |r| - r 0 the unit vector alongr - n 0 the unit vector normal tor and lying in the orbital plane of the disturbed body - a the semi-major axis of the orbit of the disturbed body - e the eccentricity of the orbit of the disturbed body - g the mean anomaly of the disturbed body - the eccentric anomaly of the disturbed body - p a(1–e 2) - P 1 the unit vector directed from the Sun toward the perihelion of the disturbed body - P 2 the unit vector normal toP 1 and lying in the orbital plane of the disturbed body - s - the true orbital longitude of the disturbed body, reckoned from the departure point of the ideal system of coordinates - X the true orbital longitude of the perihelion of the disturbed body in the ideal system of coordinates reckoned from the departure point - the angular distance of the ascending node from the departure point - R 1,R 2,R 3 the unit vectors along the axes of the ideal system of coordinates,R 1 andR 2 are in the osculating orbital plane of the disturbed body,R 3 is normal to this plane. The intersection ofR 1 with the celestial sphere is the departure point - R 3 P 1×P 2 - S 1,S 2,S 3 the initial values ofR 1,R 2,R 3, respectively - q the Gibb's vector. This vector defines the rotation of the orbital plane of the disturbed body from its initial position to the position at the given timet - m the mass of the disturbing body - r the heliocentric position vector of the disturbing body - a the semi-major axis of the orbit of the disturbing body - e the eccentricity of the orbit of the disturbing body - g the mean anomaly of the disturbing body - the eccentric anomaly of the disturbing body - P1 the unit vector directed from the Sun toward the perihelion of the disturbing body - P2 the unit vector normal toP1 and lying in the orbital plane of the disturbing body - A1 a P1 - A2 - |r–r|  相似文献   

8.
It is found that charged particles of positive energiesE, when constrained on axisymmetric isoflux surfaces , execute sinusoidal motions with typical frequencies =(2E/m)1/2). In general, it was found that under equilibrium condition p=J ^B/cthe particles develop a non-ambipolar drift velocityv d =(cµ/eb)[1+q 2 +2(q/)2]p.  相似文献   

9.
The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C jk n (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin2t - i inclination of the orbit - J n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S jk n (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M++m) (gravitational constant times the sum of the masses of Earth and satellite) - n,k coefficients ofR component of disturbing acceleration (funtions off) - n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X 0 n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node  相似文献   

10.
Motion equations for the gravitationally coupled orbit-attitude motion of a spacecraft are presented. The gravitational force and torque are expanded in a Taylor series in the small ratio (spacecraft size/orbital radius). A recursive definition for higher moments of inertia is introduced which permits terms up tofourth order to be retained. The expressions are fully nonlinear in the attitude variables. A quasi-sunpointing (QSP) passive attitude-control mode is used to assess the effects of higher moments of inertia and gravitational coupling. The attitude motion is detectably coupled to the orbital motion. However, the higher moments of inertia influence only the attitude motion.Nomenclature f G ,g G ,f Gi ,g Gi total gravitational force and torque and their components of orderi in =/r 0 - angular momentum of spacecraft about 0 and the spacecraft mass center - J i ,I i general moment of inertia about 0 and the spacecraft mass center - second (dyadic), third (triadic), and fourth (tetradic) moment of inertia about 0 and the spacecraft mass center - A andB (and related components) of the second, third and fourth moments of inertia about 0, see Equation (9) - M, m Earth's mass, spacecraft mass - Q ba rotation matrix taking a into b - position vector from attracting body's mass center to a general mass element, to 0 and to the spacecraft mass center - 1, 2, 3 basis vectors of reference frame - , , N misalignment angle betweenb 3 and the (projected) true position of the Sun, its oscillatory component and nominal value - unit dyadic (-identity matrix) - ratio of characteristic spacecraft dimension to orbital radius - pitch angle (aboutb 2 axis) - Earth's gravitational parameter - , position vector from 0 to a general mass element and the spacecraft mass center - , the (projected) true longitude of the Sun and the true longitude of the spacecraft - / angular velocity of reference frame with respect to - (·), (*), (o) d()/dt with respect to inertial space I , and orbiting frame O and a body-fixed spacecraft frame b Presented at AAS/AIAA Astrodynamics Conference, Aug. 9–11, 1982.  相似文献   

11.
It is proved that (1) electromagnetic fields with electric and magnetic components parallel to one another are solutions of Maxwell's equations; (2) the equationB(B)=0 (B is the magnetic field) is gauge and relativistically-invariant for systems of reference moving with velocityv/c=EB(1+v 2/c 2)/(E 2+B 2).  相似文献   

12.
Keenan  F. P.  Foster  V. J.  Aggarwal  K. M.  Widing  K. G. 《Solar physics》1996,168(1):47-63
A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, ) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the B z component specified at the boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator 2 u + 2 u. Specifying two scalar functions, B x and B y on the intersection of the lateral part of the boundary with one selected plane z = constant, and using B z inside the , we have found B x and B y throughout .The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B does not exceed 1.0%. Boundary conditions for the B calculation were taken as given by the analytic LFFF solution B. Comparison of B with B, which was calculated by the potential non-photospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume.The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.  相似文献   

13.
A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.  相似文献   

14.
New families of three-dimensional double-symmetric periodic orbits are determined numerically in the Sun-Jupiter case of the restricted three-body problem. These families bifurcate from the vertical-critical orbits ( v = –1,c v ),c v=0) of the basic plane familiesi,g 1,g 2,h,a,m andl. Further the numerical procedure employed in the determination of these families has been described and interesting results have been pointed out. Also, computer plots of the orbits of these families have been shown in conical projections.  相似文献   

15.
A Monte Carlo approach to solving a stochastic-jump transition model for active-region energy (Wheatland and Glukhov: Astrophys. J. 494, 858, 1998; Wheatland: Astrophys. J. 679, 1621, 2008) is described. The new method numerically solves the stochastic differential equation describing the model, rather than the equivalent master equation. This has the advantages of allowing more efficient numerical solution, the modeling of time-dependent situations, and investigation of details of event statistics. The Monte Carlo approach is illustrated by application to a Gaussian test case and to the class of flare-like models presented in Wheatland (Astrophys. J. 679, 1621, 2008), which are steady-state models with constant rates of energy supply, and power-law distributed jump transition rates. These models have two free parameters: an index (δ), which defines the dependence of the jump transition rates on active-region energy, and a nondimensional ratio ( ) of total flaring rate to rate of energy supply. For the nondimensional mean energy of the active-region satisfies , resulting in a power-law distribution of flare events over many decades of energy. The Monte Carlo method is used to explore the behavior of the waiting-time distributions for the flare-like models. The models with δ≠0 are found to have waiting times that depart significantly from simple Poisson behavior when . The original model from Wheatland and Glukhov (Astrophys. J. 494, 858, 1998), with δ=0 (i.e., no dependence of transition rates on active-region energy), is identified as being most consistent with observed flare statistics.  相似文献   

16.
Will (1971) has discussed a possible anisotropy in the gravitational constantG. Suppose that the attractive gravitational force between two particles of massesm 1 andm 2 is given by the usual expressionF=–Gm 1 m 2 r/r 3, wherer is the separation vector. Ifc is the velocity of light in vacuo and if 1 r r/r, he expresses the anisotropy byG=G [1+(v·1 r/c)2], whereG is a constant,v is identified practically as the velocity of the Sun around the galaxy, and 1. Will's suggestion is to look for such an effect in the laboratory.The purpose of the present paper is to look for such an effect in the solar system, wherem 1 andm 2 become the masses of the Sun and a planet or of the Earth and the Moon. For simplicity I consider only those planets whose orbits are close to the ecliptic, so that the angle betweenv and the plane of the ecliptic is about 59°.With the above force, the resulting two-body problem is completely solvable. The results are these. If =1, there is an increase in mean motion of 7 parts in 108, a periodic fluctuation in true longitude with period half that of the orbit and amplitude ranging possibly from 0.01 to 0.02, and periodic fluctuations in the radius vector, with period also one half that for the orbit. The amplitudes are: 2.7 km for Mercury, 5.1 km for Venus, 7.0 km for Mars, 18 m for the Moon about the Earth, and 28 cm for a close artificial satellite with inclination 23°. The more conservative estimate <0.0115 would reduce these values by the factor 70.  相似文献   

17.
The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in =(l/a 0)2,l anda 0 being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.List of Symbols A ij, Bij coefficients in the eigenfunction expansion ofv i andw i respectively, Equation (10) - C k, Dk constants, Equation (21) - EI i flexural rigidity of theith appendage - E(u0) 2(1+e 0 cosu 0)2 h 0 3 - F(u0) perturbation function, Equation (17b) - F ,F ,F functions of librational angles and flexural displacements, Equation (11i) - F ,F ,F F ,F ,F with change of independent variable fromt tou 0 - I xx, Iyy, Izz principal moments of inertia of the undeformed satellite - [J i] inertia dyadic of the deformedith appendage - [J d] inertia dyadic of the deformed satellite - M mass of the satellite - P R, Pu functions of librational angles and flexural displacements, Equation (15d) and (15e), respectively - R c magnitude ofR c - R c0, R1 unperturbed value and first order perturbation ofR c, respectively - R c ,R 0 position vectors of the c.m. of the deformed and undeformed satellite, respectively - T kinetic energy of the satellite - U potential energy of the satellite - U e, Ug elastic and gravitational potential energy, respectively - X, Y, Z orbital co-ordinate axes, located at the c.m. of the deformed satellite - Y 1(u0), Y2(u0) functions ofu 0, Equation (18b) and (18c), respectively - a semi-major axis - a 0 unperturbed value ofa - e eccentricity - e 0 unperturbed value ofe - h 0 unperturbed angular momentum per unit mass of the satellite - i inclination of the orbital plane to the ecliptic - i, j, k unit vectors alongx (or ),y (or ) andz (or ) axes, respectively - l characteristic length of the satellite - l i length of theith appendage - [l i] matrix of direction cosines ofx i, vi andw i - l ,l ,l direction cosines ofR c - m 0, mi mass of the main body andith appendage, respectively - p i 2 - q m, Qm generalized co-ordinate and force, respectively - r 1 R 1/Rc0 - r position vector of an element of the body referred toxyz axes - r u position vector of an element after deformation, referred to axes - r c x c i+y c j+z c k, position vector of the c.m. of the deformed body referred toxyz axes - s x i/li - t time - u true anomaly - u 0, u1 unperturbed value and the first order perturbation ofu, respectively - u elastic displacement vector - u c u–r c - velocity of an element relative to axes - v i, wi flexural deformations - x, y, z body co-ordinate axes with origin at the c.m. of the undeformed satellite - x i distance of an element of theith appendage from the root - j jth eigenfunction (normalized) of a cantilever - angle between the line of nodes and vernal equinox - , , components of nondimensionalized angular velocity of the satellite - , , pitch (spin), yaw and roll, respectively - i nominal inclination of theith appendage in the orbital plane - - small parameter, (l/a 0)2 - j jth eigenvalue of a cantilever - gravitational constant - jk constant, Equation (11j) - , , body co-ordinate axes with origin at the c.m. of the deformed satellite - ( i + j + k), angular velocity of the satellite  相似文献   

18.
Previous global models of coronal magnetic fields have used a geometrical construction based on a spherical source surface because of requirements for computational speed. As a result they have had difficulty accounting for (a) the tendency of full magnetohydrodynamic (MHD) models to predict non-radial plasma flow out to r 10r and (b) the appreciable magnitude, 3, of B r , (the radial component of B) consistently observed at r 1 AU. We present a new modelling technique based on a non-spherical source surface, which is taken to be an isogauss of the underlying potential field generated by currents in or below the photosphere. This modification of the source surface significantly improves the agreement between the geometrical construction and the MHD solution while retaining most of the computational ease provided by a spherical source surface. A detailed comparison between the present source-surface model and the MHD solution is made for the internal dipole case. The resulting B field agrees well in magnitude and direction with the coronal B field derived from the full MHD equations. It shows evidence of the slightly equatorward meridional plasma flow that is characteristic of the MHD solution. Moreover, the B field obtained by using our non-spherical source surface agrees well with that observed by spacecraft in the vicinity of the Earth's orbit. Applied to a solar dipole field with a moment of 1 G-r 3 , the present model predicts that B r at r 1 AU lies in the range of 1–2 and is remarkably insensitive to heliomagnetic latitude. Our method should be applicable also to more general (i.e., more realistic) configurations of the solar magnetic field. Isogauss surfaces for two representative solar rotations, as calculated from expansions of observed photospheric magnetic-field data, are found to show large and significant deviations from sphericity.  相似文献   

19.
An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H 0 applied magnetic field - H magnetic field intensity - (j x , j y , j z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n e electron number density - P Prandtl number - q velocity vector - (T, T w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U 0 uniform velocity - v 0 suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - e charge density - electrical conductivity - e electron collision time  相似文献   

20.
The Kustaanheimo-Stiefel (KS) transformation is shown to follow naturally from the general solution of the two-body motion if half-arguments are introduced. Application to collision orbits and to the exact triangular solutions of Lagrange (vide E. Stiefel and G. Scheifele: 1971,Linear and Regular Celestial Mechanics, Springer, Berlin-Heidelberg-New York, p. 23–35).Notations x Position vector (x, y, z) - r=|x| Distance from the origin - 1/2h Energy constant or Kepler motion - c Angular momentum vector of Kepler motion - t physical time ()·=d/dt () - new independent variable ()=d/d () Note by editor: This is the well-known Three-dimensional regularization, published in 1965 by P. Kustaanheimo and E. Stiefel, Perturbation Theory of Kepler Motion Based on Spinor Regularization,J. reine angewandte Mathematik 218, 204. The present article was written during Professor Volk's stay at the Zurich Technische Hochschule in 1972, when he also celebrated his 80th birthday.  相似文献   

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