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1.
We consider the dynamics of a test particle co-orbital with a satellite of mass m
s which revolves around a planet of mass M
0 m
s with a mean motion n
s and semi-major axis a
s. We study the long term evolution of the particle motion under slow variations of (1) the mass of the primary, M
0, (2) the mass of the satellite, m
s and (3) the specific angular momentum of the satellite J
s. The particle is not restricted to small harmonic oscillations near L
4 or L
5, and may have any libration amplitude on tadpole or horseshoe orbits. In a first step, no torque is applied to the particle, so that its motion is described by a Hamiltonian with slowly varying parameters. We show that the torque applied to the satellite, as measured by s = js/(n
s
J
s) induces an distortion of the phase space which is entirely described by an asymmetry coefficient = s/, where = m
s/M. The adiabatic invariance of action implies furthermore that the long term evolution of the particle co-orbital motion depends only on the variation of m
s
a
s with time. Applying a constant torque to the particle, as measured by s = js/(n
s
J
p) is then merely equivalent to replacing = s/ by = (s – p)/. However, if the torque acting on the particle exhibits a radial gradient, then the action is no more conserved and the evolution of the particle orbit is no more controlled by m
s
a
s only. We show that even mild torque gradients can dominate the orbital evolution of the particle, and eventually decide whether the latter will be pulled towards the stable equilibrium points L
4 or L
5, or driven away from them. Finally, we show that when the co-orbital bodies are two satellites with comparable masses m
1 and m
2, we can reduce the problem to that of a test particle co-orbital with a satellite of mass m
1 + m
2. This new problem has then parameters varying at rates which are combinations, with appropriate coefficients, of the changes suffered by each satellite. 相似文献
2.
By solving the Euler hydrodynamical equations we have obtained closed form solutions for the angular velocities and pressures of a three stratified non-confocal heterogeneous oblate spheroid. Limiting and particular solutions cases, such as a spheroid with N layers, a stratified spheroid with the same eccentricities, as well as confocal layered spheroids are also explicitly written down. As an application, we have numerically estimated planet Earth's outer and inner cores' ellipticities to be o=1/413.318 and i=1/424.616, respectively. These Earth's ellipticities values are in good agreement with those found in the literature. 相似文献
3.
We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI
h is foliated by the invariant toriI
hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI
hc is conjugated to a linear flow of rotation number
h
(c).A well-known result asserts that if we require
h
(c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2)
h
(c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2. 相似文献
4.
A map of the Moon at 2 cm wavelength is presented. The angular ( 1arc) and temperature resolution (< 0.1 K) is sufficient to study systematic details of the brightness distribution. In particular, the centre-to-limb variation is considered. An estimate of the dielectric constant is possible (1.4 2.5). The existence of a temperature gradient in the lunar surface layers is used to derive the depth of penetration of electromagnetic waves (L
e
), which isL
e
8 m for 2 cm wavelength. The parameters derived from the 2 cm map are found to be compatible with those obtained from a former observation at 6 cm wavelength. 相似文献
5.
Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non-linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate = 0
n
T
nT
m
,are given in terms of Gauss' hypergeometric function. This model for the structure of the Sun gives the run of density, mass, pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun. 相似文献
6.
Vittorio Coti Zelati 《Celestial Mechanics and Dynamical Astronomy》1989,46(2):177-186
We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in
m
(any m 2) where one of the bodies has mass equal to 1 and the others have masses 2,...,
N
, small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass i moves close to one of the circular solutions of the two body problem of period T/k
i, where ki is any odd number. No relation has to be satisfied by k
2,...,k
N. 相似文献
7.
Jean Meffroy 《Earth, Moon, and Planets》1980,23(1):73-97
Using a method previously applied to the treatment of the Mathieu differential equation, we solve the Hill's differential equation of lunar theory through the way of operational calculus, which avoids the cumbersome infinite determinants of the classical procedure. The one-sided Laplace transformation changes it into a difference equation with an infinite number of terms and variable coefficients. When its first member is divided by a suitable factor, this difference equation is the image of an integral equation of the Volterra type which is equivalent to the initial Hill's differential equation. Solution of this Volterra integral equation is unique and it is the general solution of the Hill's differential equation. This solution is a series in the powers of a small dimensionless parameter
2 which appears as a factor in the second member of the Hill's differential equation. We reduce it to the sum of its terms of degree 12 with respect to which is the precision usually required in a lunar theory and we write down effectively the coefficients of the terms in
2, (
2)2 and the coefficient of the term in (
2)3 which depends upon the initial valuey(0) of the Hill's differential equation. 相似文献
8.
A numerical solution to the Fisk and Lee (1980) equations for the particle intensity upstream of a corotating interplanetary shock is considered for the November 1991 event observed at Ulysses. A numerically derived parallel diffusion coefficient is available for this region (Quenby et al., 1993), based upon in-situ magnetometer data. Fitting the transport equations solution to the upstream energetic particle distribution function, employing a radial diffusion coefficient = 0 r, where r and are, respectively, radial distance from the Sun and particle velocity, and with 0 fixed from the magnetometer derived coefficient yielded a range of statistically acceptable values of (, ). These ran from (0.5, 0.0) to (1.8, 1.6) along a thin strip of — space, hence demonstrating the improbability that the velocity and radial dependence of the particle diffusion can be fixed from such particle and magnetic field data alone. 相似文献
9.
M. Fracassini F. Manzolini L. E. Pasinetti M. Ruggenini 《Astrophysics and Space Science》1980,69(2):401-423
Apparent radius, visual brightness, effective temperature and absolute radius for 416 B5 v-F5 v stars of the catalogue of the Geneva Observatory (Rufener, 1976) have been determined.Twenty-eight stars, anomalous in log versus (m
v)0 diagrams, have been singled out. A good correlation for seven stars, in common with the list of Hanbury Brownet al. (1974), has been found. Similar parameters determined for 279 B5 v-F5 v stars of two preceding papers (Fracassiniet al., 1973, 1975) have allowed us to determine the averaged diagrams logq
v/q, logR/R
and logT
e versus (B-V)0 for 695 B5 v-F5 v stars.Moreover, in the present paper a good correlation logq
v/q versus logR/R
and careful relation M
v=–7.40logR/R
+3.31 for B5 v-F5 v stars have been determined. Plain correlations between logR/R
and blanketing parameterm
2 for some spectral types seem to point out that there arereal differences in the absolute radii of stars of thesame spectral type, in agreement with recent researches on the HR diagram (Houck and Fesen, 1978).Systematic differences between double (spectroscopic and visual) and single stars are found. In particular, the averaged relation m
2 versus logR/R
shows that A2 v-F5 v double stars may have a higher metallicity indexm
2 and smaller absolute radii than single stars. Finally, the diagram logv sini versus logR/R
confirms some properties of binary systems found by other researchers (Huang, 1966; Plavec, 1970; Levato, 1974; Kitamura and Kondo, 1978).Thesis for the degree in Applied Physics. 相似文献
10.
In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH
0-functionH
0() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases. 相似文献
11.
We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec2 at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C
min the H- 1.5 Å image (C
m 0.1 type I, C
m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C
m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C
m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C
min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C
m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C
m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C
m- A scatter diagram, in H and H wings, indicates a wide range of variability for C
m in correspondence with very narrow range of variability for A. 相似文献
12.
R. Caimmi 《Astrophysics and Space Science》1993,209(1):1-17
The present attempt aims to predict the dependence of the spin parameter, , the angular momentum,J, and the typical radius,a
vir, on the mass,M, which have been found inN-body simulations of expanding density perturbations in hierarchical clustering, when virialization is attained. We show that M
0 for systems with same adimensional density distribution and velocity distribution, and in particular for scale-free density perturbations in hierarchical clustering. In the special case of ellipsoidal perturbations, it is also found:J M
7/4,a
vir M
1/2. All these results turn out to be in close agreement withN-body simulations, despite the simple model adopted. Expanding and virialized perturbations are modelled, respectively, by homogeneous and heterogeneous, similar ellipsoids which allow flat rotation curves far from the centre. Both energy and angular momentum maintain from a given time on, lying between the beginning of strong decoupling from the Hubble flow and the occurrence of maximum volume. Then the whole set of virialized ellipsoidal configurations with same energy and angular momentum are derived, and the dependence of the spin parameter on the anisotropy parameter, pec is investigated. Turning our attention to the formation of galaxies, we derive the total mass as a function of the collapse factor, using the empirical anticorrelation between dark to visible mass ratio within the optical radius of disk galaxies and their luminous masses. Observational data related to a sample of elliptical galaxies provide evidence that the contraction in these bodies occurred in proportion to the square root of the ratio of total to luminous mass. On the contrary, it is deduced that dissipation of angular momentum in elliptical galaxies occurred more or less at the same rate. If both shape and anisotropy parameter are preserved during the collapse, typical axis rations 21 = 0.98, 31 = 0.69, are found to correspond to a moderate anisotropy, pec 0.27, with a small dependence on the spin parameter in the range allowed. 相似文献
13.
A model of a first generation intermediate star of 5M
, with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell.
=(log/log)
T
and
T
=(log/logT)
were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including
=(log/log)
T
and
=(log/logT)
of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode. 相似文献
14.
Jan-Cees Van Der Meer 《Celestial Mechanics and Dynamical Astronomy》1982,27(2):131-149
Consider a Hamiltonian system of two degrees of freedom at an equilibrium. Suppose that the linearized vectorfield has eigenvaluesi,i,–i,–i ( , >0) and is not semisimple. In this paper we discuss the real normalization of the Hamiltonian function of such a system. We normalize the Hamiltonian up to 4th order and show how to compute its coefficients. For the planar restricted three body problem atL
4 the coefficient that plays an important role in the investigation of the qualitative behaviour of periodic solutions near the equilibrium is explicitly calculated. 相似文献
15.
General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities 0, where 0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of –-hyperons at >
c
, where
c
40. The electric resistivities along and acrossB, and , and the Hall resistivity
H
are calculated and fitted by simple analytical formulae at
c
and >
c
for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If
c
, one has = [1 + (B/B
0)2] for the normal neutrons, and for the superfluid neutrons, while
H
=
B/B
e
for both cases. HereB
e
109
T
8
2
G,B
01011
T
8
2
G, andT
8 is temperature in units of 108 K. Accordingly for the normal neutrons atBB
0, the transverse resistivity suffers an enhancement, 1/4 1. When 50 andB varies from 0 toBB
p
1013
T
8
2
G, increases by a factor of about 103–104 and
H
changes sign. WhenBB
p
, remains constant for the superfluid neutrons, and
H
B
2 for the normal neutrons, while
H
B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB. 相似文献
16.
Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed
m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin
p
cos
q
which peaks near the equator (q p) will correspond to a cos
n
magnetic field at high latitudes only if p = 1 and
m = n /R. Recent measurements of n 8 and 600 km2 s–1 would then give
m 7 m s–1. 相似文献
17.
Jaume Llibre 《Celestial Mechanics and Dynamical Astronomy》1982,28(1-2):83-105
We study some aspects of the restricted three-body problem when the mass parameter is sufficiently small. First, we describe the global flow of the two-body rotating problem, =0, and we use it for the analysis of the collision and parabolic orbits when 0. Also we show that for any fixed value of the Jacobian constant and for any >0, there exists a 0>0 such that if the mass parameter [0,0], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than .Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics. 相似文献
18.
The electrical conductivity of the lunar interior has been determined from magnetic field step transients measured on the lunar dark side. The simplest model which best fits the data is a spherically symmetric three layer model having a nonconducting outer crust of radial thickness 0.03R
moon; an intermediate layer of thicknessR0.37R
moon, with electrical conductivity
1 3.5 × 10–4 mhos/m; and an inner core of radiusR
2 0.6R
m
with conductivity
2 10–2 mhos/m. Temperatures calculated from these conductivities in the three regions for an example of an olivine Moon are as follows: crust, < 440 K; intermediate layer, 890 K; and core, 1240 K. The whole-moon relative permeability has been calculated from the measurements to be/
0 = 1.03 ± 0.13. Remanent magnetic fields at the landing sites are 38 ± 3 at Apollo 12, 43 ± 6 and 103 ± 5 at two Apollo 14 sites separated by 1.1 km, and 6 ± 4 at the Apollo 15 site. Measurements show that the 38 remanent field at the Apollo 12 site is compressed to 54 by a solar wind pressure increase of 7 × 10–8 dynes/cm2.National Research Council Postdoctoral Associate. 相似文献
19.
A. M. I. Osman 《Astrophysics and Space Science》1985,116(2):299-311
Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB
T
=13.57 with maximum diameters 1.57×1.34 (at threshold
m
=27.7 mag.//) andV
T
=12.91 with maximum diameters 1.54×1.32 (at threshold
m
=27.7 mag./). The integrated colour index(B–V)
T
=0.66 and the effective surface brightness
e
(B=19.0 mag./) and
e
(V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr
*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×107 yr. 相似文献
20.
The exact geometry of the Roche curvilinear coordinates (, , ) in which corresponds to the zero-velocity surfaces is investigated numerically in the plane, as well as in the spatial, case for various values of the mass-ratio between the two point-masses (m
1,m
2) constituting a binary system.The geometry of zero-velocity surfaces specified by -values at the Lagrangian points are first discussed by taking their intersections with various planes parallel to thexy-, xz- andyz-planes. The intersection of the zero-velocity surface specified by the -value at the Lagrangian equilateral-triangle pointsL
4,5 with the planex=1/2 discloses two invariable curves passing through the pointsL
4,5 and situated symmetrically with respect to thexy-plane whose form is independent of the mass-ratio.The geometry of the remaining two coordinates (, ) orthogonal to the zero-velocity surfaces is investigated in thexy- andxz-planes from extensive numerical integrations of differential equations generated from the orthogonality relations among the coordinates. The curves (x, y)=constant in thexy-plane are found to be separated into three families by definite envelopes acting as boundaries whose forms depend upon the mass-ratio only: the inner -constant curves associated with the masspointm
1, the inner -constant curves associated with the mass-pointm
2 and the outer -constant curves. All the -constant curves in thexy-plane coalesce at either of the Lagrangian equilateraltriangle pointsL
4,5, except for a limiting case coincident with thex-axis. The curves (x, z)=constant in thexz-plane are also separated by definite envelopes depending upon the mass-ratio into different families: the inner -constant curves associated with the mass-pointm
1, the inner -constant curves associated with the mass-pointm
2 and the outer -constant curves on both sides out of the envelopes. For larger values ofz, the curves =constant tend asymptotically to the line perpendicular to thex-axis and passing through the centre of mass of the system, except for a limiting case coincident with thex-axis. The geometrical aspects of the envelopes for the curves (x, y)=constant in thexy-plane and the curves (x, z)=constant in thexz-plane are also discussed independently.In the three-dimensional space, the Roche coordinates can be conveniently defined in such a way as to correspond to the polar coordinates in the immediate neighbourhood of the origin, and to the cylindrical coordinates at great distances. From numerical integrations of simultaneous differential equations generating spatial curves orthogonal to the zero-velocity surfaces, the surfaces (x, y, z)=constant and the surfaces (x, y, z)=constant are constructed as groups of such spatial curves with common values of some parameters specifying the respective surfaces.On leave of absence from the University of Tokyo as an Honorary Fellow of the Victoria University of Manchester. 相似文献