共查询到20条相似文献，搜索用时 62 毫秒
1.
S. Yabushita 《Earth, Moon, and Planets》1982,26(2):135-141
The equation of state of the terrestrial material obtained from seismic data is adopted to construct three zone earth models under hypothesis of variable constant of gravityG as proposed by Dirac. Three hypotheses are investigated: variableG without creation, creation such thatm (mass) G
–1, and multiplicative creation,mG
–2. It is shown that, with the currently accepted value of the Hubble constant,
,
and
for each hypothesis. On the multiplicative creation, the Earth radius would have been 5100 km, which is in agreement with estimate by some geophysicists. 相似文献
2.
Multi-colourWBVR photoelectric observations of the eclipsing binary OX Cas were carried out. The photometric elements, absolute parameters and the angular rate of the apsidal motion (
= 9.1 deg yr–1 were obtained. The apsidal parameterk
2 derived for this system is by 15–25% smaller than the theoretical parameterk
2. 相似文献
3.
E. R. Lancaster 《Celestial Mechanics and Dynamical Astronomy》1970,2(1):60-63
Approximation formulas are found for
and
, wherex(t) satisfies
,x(0)=x
0,x(1)=x
1. The results are applied to an example of two-body motion. 相似文献
4.
If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations
and
where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example,
where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of
: the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral
indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations
and
for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of
with D. Next we calculate the turbulent viscosity coefficients defined by
whereC
ro
0
and C
o
0
are the velocity correlations for solid body rotation. In these calculations it was assumed that 2 was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v
ro
i
and v
0o
i
that allow for the calculation of C
ro
and C
0o
for any specified rotation law (with the proviso that 2 be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v
ro
1
and –v
0o
3
are the largest in each group, and v
0o
3
is negative.The equations for the meridional flow were first solved with
0 and
2 two linear functions of r (
0
1
= – 2 × 10 –12 cm –1) and (
2
1
= – 6 × 10 12 cm –1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s–1). Reasonable values for the meridional motions can only be obtained if
o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ. 相似文献
5.
V. V. Markellos 《Astrophysics and Space Science》1975,36(2):245-272
This paper reports on the numerical determination of families of periodic oscillations in the case =0.000 95 of the restricted problem. The families emanating out of the collinear Lagrangian pointsL
1,L
2,L
3 are examined as well as some asymmetric periodic oscillations related to them. An effort is made to complete the global picture of simple-periodic symmetric oscillations in the present case of the problem (the S-J case). This is done by examining the orbits with initial conditions such that the infinitesimal body starts from a position on the 1-axis (02 = 0) with a negative initial velocity
perpendicular to this axis
. In a previous article this investigation has been carried out for negative values of 01, where the position of the small primary defines 1=0. Now we proceed to consider orbits with 01>0. The phase portrait of asymmetric periodic orbits is also examined. 相似文献
6.
G. Bozis 《Celestial Mechanics and Dynamical Astronomy》1982,28(4):367-380
Conditions are found which are satisfied by the coefficients of the expression
being a second integral of the motion of an autonomous dynamical system with two degrees of freedom. The coefficientsA, B. , ,E are differentiable functions of the cartesian position coordinatesx, y. The velocity components are denoted by
. It is shown that must be constant andB must be of the formB =f(x+y) +g(x-y) wheref, g are arbitrary.Given andB one can always find the remaining coefficientsA, E and also the corresponding potential and second integral. Depending on the specifica case at hand a certain number of arbitrary constants (or arbitrary functions) enter into the potential and the second integral. To each potential (which may be of the separable or nonseparable type in the coordinatesx andy)there corresponds one integral of the above form. 相似文献
7.
John P. Vinti 《Celestial Mechanics and Dynamical Astronomy》1977,16(4):391-406
Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t)
–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then
. Here 0 is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH
0 be the present value of Hubble's constant
/R and 0c
the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of 0c
versusH
0 and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 1010 yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)–1, superposing it on the differential equation
. 相似文献
8.
J. E. Lancaster 《Celestial Mechanics and Dynamical Astronomy》1970,2(4):481-493
Analytical techniques are employed to demonstrate certain invariant properties of families of moon-to-earth trajectories. The analytical expressions which demonstrate these properties have been derived from an earlier analytical solution of the restricted three-body problem which was developed by the method of matched asymptotic expansions. These expressions are given explicitly to orderµ
1/2 where is the dimensionless mass of the moon. It is also shown that the inclusion of higher order corrections does not affect the nature of the invariant properties but only increases the accuracy of the analytic expressions.The results are compared with the work of Hoelker, Braud, and Herring who first discovered invariant properties of earth-to-moon trajectories by exact numerical integration of the equations of motion. (Similar properties for moon-to-earth trajectories follow from the principle of reflection). In each instance the analytical expressions result in properties which are equivalent, to orderµ
1/2, with those found by numerical integration. Some quantitative comparisons are presented which show the analytical expressions to be quite accurate for calculating particular geometrical characteristics.
Nomenclature
Orbital Elements near the Moon energy - angular momentum - semi-major axis - eccentricity - inclination - argument of node - argument of pericynthion Orbital Elements near the Earth h e energy - l e angular momentum - i inclination - argument of node - argument of perigee - t f time of flight Other symbols parameters used in matehing - U a function of the energy near the earth - a function of the angular momentum near the earth - r p perigee radius - perincynthion radius - radius at node near moon - true anomaly of node near moon - initial angle between node near moon and earth-moon line - a function ofU, , andi - earth phase angle - dimensionless mass of the moon - U 0, U1 U=U 0+U 1 - i 0, i1/2, i1 i=i 0+µ 1/2 i 1/2+µ i 1 - 0, 1/2, 1 = 0+µ 1/2 i 1/2+µ i 1 - p longitude of vertex line - n latitude of vertex line - R o ,S o ,N o functions ofU 0 and - a function ofU 0, and 相似文献9.
We study some simple periodic orbits and their bifurcations in the Hamiltonian
. We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (). In the regionsS andU there are lines of equal rotation numberm/n. Along these lines we have bifurcations of families of periodic orbits of multiplicityn. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region there are linesm/n, along which the orbits 1a, describedn-times, are doubly unstable; however, along these lines there are no bifurcations ofn-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (, ). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams. 相似文献
10.
A theoretical model for3He enrichments in solar energetic particles is developed. First, current-driven, electrostatic instabilities that have frequencies
(
is the cyclotron frequency of3He) are investigated for a plasma consisting of H,4He,3He, and electrons with the density of3He much lower than those of H and4He. It is found that in many cases the oblique ion-acoustic waves can have positive growth rates at frequencies
and, at the same time, negative growth rates at
and at H. This can occur near the marginal state of the instability. The wave damping at these frequencies is caused by the cyclotron resonances of4He and H. The cyclotron damping at
is negligible, however, because the abundance of3He is very small. The H cyclotron waves can be unstable at
for a wide region of plasma parameters; the electron-to-ion temperature ratio must beT
e
/T
H
1.5. To destabilize the4He cyclotron waves with
, high4He density and high electron temperature are both required. Then,3He enrichments are studied on the basis of the theory of nonlinear magnetosonic waves, which can promptly accelerate ions. The current-driven electrostatic waves with
can enhance fluctuation velocities of3He. Thus, in the presence of these waves, magnetosonic waves can selectively accelerate3He particles to high energies. Finally, cyclotron resonances of heavy ions with the waves
or
are briefly discussed. 相似文献
11.
H. Rovithis-Livaniou 《Astrophysics and Space Science》1977,52(2):271-306
The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea
n
(l)
integrals for partial eclipses and give them in terms ofa
0
0
,a
0
0
(of the associated -functions) and
integrals; while Section 3 gives the eclipse perturbations
arising from the tidal and rotational distortion of the two components. The
are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases. 相似文献
12.
The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed
is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When eff1, the sound speeda
g
2
=P
g
/ and the propagating speed of radiative disturbancea
f
2
=fc
2 appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When eff1, the isentropic sound speeda
s
2
=(P
g
+P
r
/ appears in the equilibrium case, and the radiation acoustic speeda
A
2
appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P
g
/(P
g
+P
r
). When
, the speeda
S
anda
A
arise from the modified classical mode, and when
, they originate from the radiation-induced mode. 相似文献
13.
Bert W. Rust Stephen G. Nash Barry J. Geldzahler 《Astrophysics and Space Science》1989,152(1):141-170
Two models for superluminal radio sources predict sharp lower bounds for the apparent velocities of separation. The light echo model predicts a minimum velocityv
min=2c, and the dipole field model predictsv
min=4.446c. Yahil (1979) has suggested that, if either of these models is correct, thenv
min provides a standard velocity which can be used to determine the cosmological parametersH andq
0. This is accomplished by estimating a lower envelope for the proper motion vs redshift relation. Yahil also argued that the procedure could easily be generalized to include a nonzero cosmical constant . We derive the formulas relating the proper motion
to the redshiftz in a Friedmann universe with a nonzero . We show that the determination of a lower envelope for a given sample of measured points
yields an estimate of the angle of inclination
i
for each source in the sample. We formulate the estimation of the lower envelope as a constrained maximum likelihood problem with the constraints specified by the expected value of the largest order statistic for the estimated
i
. We solve this problem numerically using an off-the-shelf nonlinearly constrained nonlinear optimization program from the NAg library. Assuming =0, we apply the estimation procedure to a sample of 27 sources with measured values
, using both the light echo and the dipole field models. The fits giveH=103 km s–1 Mpc–1 for the light echo model andH=46 km s–1 Mpc–1 for the dipole field model. In both cases the fits giveq
0=0.4, but the uncertainty in this result is too large to rule out the possibility thatq
0>0.5. When is allowed to be a free parameter, we obtainH=105 km s–1 Mpc–1 for the light echo model andH=47 km s–1 Mpc–1 for the dipole field model. In both cases the fits giveq
0=–1 and /H
0
2
=6.7, but no significance can be attached to these results because of the paucity of measured data at hight redshifts. For all of the fits, we compute the corresponding estimates of the
i
and compare the cumulative distribution of these values with that expected from a sample of randomly oriented sources. In all cases we find a large excess of sources at low-inclination angles (high apparent velocities). The expected selection effect would produce such an excess, but the excess is large enough to suggest a strong contamination of the sample by relativistic beam sources which would only be seen at low inclination angles.Applied Research Corporation 相似文献
14.
George Bozis 《Celestial Mechanics and Dynamical Astronomy》1983,29(4):329-334
Szebehely's partial differential equation for the force functionU=U(x,y) which gives rise to a given family of planar orbitsf(x,y)=Constant is generalized to account for velocity-dependent potentials V*=V*(x,y,
). The new partial differential equation is quasi-linear and of the first order. An example is given and a comparison is made of the two equations. 相似文献
15.
An analysis of an eleven-year photometric study of the first magnetic nova V1500 Cyg from observations made at the Crimean Observatory is presented. The data indicate the existence of a beat period caused by rotational-orbital asynchronization as well as its increase with time. The current rotational period of the primary component — a magnetic white dwarf — was calculated for each year by using the current values of the beat period and a constant value for the orbital period. It is shown that rapid synchronization of the components has not occurred uniformly with time: the rate of increase of the rotational period of the white dwarf was
during 1977–1979 and
over the next ten years. This would lead to synchronization of the rotational and orbital periods over about 230 year if
remains constant at 2.7 · 10–8.Translated fromAstrofizika, Vol. 39, No. 2, pp. 193–199, April–June, 1996. 相似文献
16.
Osman M. Kamel 《Earth, Moon, and Planets》1983,28(3):221-245
In this part we determine the value ofS
1,
and
in terms of the canonical variables of H. Poincaré. A complete solution of the auxiliary system of equations generated by the Hamiltonian
is presented. 相似文献
17.
Carlo Denis 《Celestial Mechanics and Dynamical Astronomy》1983,31(1):81-94
For Jupiter, an overall density model of the form=
0(1–x
n
), withn1/3 and
, is consistent with information presently at hand; for Saturn, however, such a density law would lead to unacceptably high densities in the vicinity of the centre. The limiting cases of the previous law are shown to ben=+, corresponding to a homogeneous sphere, andn=–3, corresponding to a particular central particle model, investigated by a number of astronomers over the last hundred years. Forn0, the central density becomes +. Another possible representation, valid both for Jupiter and Saturn, is the density law=
0(1–x)
m
), with
in the case of Jupiter, and
in the case of Saturn. Graber's density law based on a maximum entropy principle leads to unacceptably high surface densities, both for Jupiter and Saturn. Finally, the paper investigates the problems involved in fitting two-layered parametrically simple density laws to theoretically derived much more elaborate models of the Jovian planets. 相似文献
18.
Line-forming regions around close binaries with strong winds (
/4r
*
v
10–4 g cm–2) are large in extent compared with the stars, large enough to screen them. Their orbitally-modulated Doppler shifts can overestimate the mass function, because of a larger rotational lever arm. In particular, most of the black-hole candidates need not involve companions more massive than a neutron star.The solar-wind problem is reconsidered. An extrapolation to Wolf-Rayet stars suggests that their winds are centrifugally driven. Their mass-loss rates tend to have been overestimated.Seemingly single (massive) stars can hide a (compact) companion. 相似文献
19.
20.
J. J. Aly 《Solar physics》1987,111(2):287-296
We consider a simple model in which the coronal magnetic field B is assumed to be potential in the region between the solar surface
o
and an exterior source-surface 1 of arbitrary shape. We prove that the boundary value problem that determines B from the value B
lof its component on
0 along either
(orthoradial direction) or
(fixed direction) has at most one solution. On the other hand, we show that a solution can exist only if B
lsatisfies some solubility conditions. 相似文献