共查询到20条相似文献，搜索用时 93 毫秒
1.
A. W. Harris 《Earth, Moon, and Planets》1995,71(3):113-117
I derive an approximate criterion for the tidal disruption of a rubble pile body as it passes close to a planet (or the sun): % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdi3aaS% baaSqaaiaacogaaeqaaOGaeyisIS7aamWaaeaacaaIYaGaeqyWdihd% caWGWbGccaGGDbWaaeWaaeaadaWcaaqaaiaadkfamiaadchaaOqaai% aadkhaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIZaaaaOGaey4k% aSYaaeWaaeaadaWcaaqaaiabeM8a3bqaaiabeM8a3XGaaGimaaaaaO% GaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2fa% amaabmaabaWaaSaaaeaacaWGHbaabaGaamOyaaaaaiaawIcacaGLPa% aacaGGSaaaaa!5229!\[\rho _c \approx \left[ {2\rho p]\left( {\frac{{Rp}}{r}} \right)^3 + \left( {\frac{\omega }{{\omega 0}}} \right)^2 } \right]\left( {\frac{a}{b}} \right),\] where
c
is the critical density below which the body will be disrupted,
p
is the density of the planet (or sun), R
p
is the radius of the planet, r is the periapse distance, is the rotation frequency of the body, 0 is the surface orbit frequency about a body of unit density, and a/b is the axis ratio of the body, considered as a prolate ellipsoid. For P/Shoemaker Levy 9, in its passage close to Jupiter in 1992, this expression suggests that the critical density is ~1.2 for a spherical, non-spinning nucleus, but could be >2.5 for a 2:1 elongate body with a typical rotation period of ~10 hours. 相似文献
2.
We define a stretching number (or Lyapunov characteristic number for one period) (or stretching number) a = In % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaqWaaeaada% Wcaaqaaiabe67a4jaadshacqGHRaWkcaaIXaaabaGaeqOVdGNaamiD% aaaaaiaawEa7caGLiWoaaaa!3F1E!\[\left| {\frac{{\xi t + 1}}{{\xi t}}} \right|\]as the logarithm of the ratio of deviations from a given orbit at times t and t + 1. Similarly we define a helicity angle as the angle between the deviation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGNaam% iDaaaa!3793!\[\xi t\]and a fixed direction. The distributions of the stretching numbers and helicity angles (spectra) are invariant with respect to initial conditions in a connected chaotic domain. We study such spectra in conservative and dissipative mappings of 2 degrees of freedom and in conservative mappings of 3-degrees of freedom. In 2-D conservative systems we found that the lines of constant stretching number have a fractal form. 相似文献
3.
I. H. Urch 《Astrophysics and Space Science》1984,104(2):357-366
The diffusion of charged particles in a stochastic magnetic field (strengthB) which is superimposed on a uniform magnetic fieldB
0
k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements z in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average
was then used to find the parallel diffusion coefficient
. The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB/B
0. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field. 相似文献
4.
Shuichi Tamazawa Kiyotaka Toyama Noboru Kaneko Yôrô Ôno 《Astrophysics and Space Science》1975,32(2):403-421
Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of
is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn
0=108 cm–3 andT
0=104 K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×1033 erg s–1, which primarily arises from the optical surface (1) ofT104 K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10. 相似文献
5.
, — . , , . , , . 相似文献
6.
André Deprit Jesúus Palacián Etienne Deprit 《Celestial Mechanics and Dynamical Astronomy》2001,79(3):157-182
The relegation algorithm extends the method of normalization by Lie transformations. Given a Hamiltonian that is a power series = 0+ 1+ ... of a small parameter , normalization constructs a map which converts the principal part 0into an integral of the transformed system — relegation does the same for an arbitrary function [G]. If the Lie derivative induced by [G] is semi-simple, a double recursion produces the generator of the relegating transformation. The relegation algorithm is illustrated with an elementary example borrowed from galactic dynamics; the exercise serves as a standard against which to test software implementations. Relegation is also applied to the more substantial example of a Keplerian system perturbed by radiation pressure emanating from a rotating source.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
7.
В. В. Железняков 《Astrophysics and Space Science》1971,13(1):74-86
, v
0c (c — ). , , . 1919, . ( ) 0532. , . 相似文献
8.
In this paper we consider the low-frequency limit of the electromagnetic and gravitational radiation from a relativistic particle falling into a Kerr black hole. The radiation spectra are obtained with help of the solution of Teukolsky's equations in terms of the hypergeometric functions. It is shown that in the low-frequency limit the spectra are flat and the power radiated depends strongly on the radiation spin. Dependence of the power on the initial kinetic energy of the radiating particle has the same character as that obtained by the WKB technique for the band of frequencies
, where 0=(1–u
0
2
/c
2)–1/2 is the particle Lorentz factor at infinity. The full energy radiated is proportional to 0 in 0 for electromagnetic radiation and to
0
3
for gravitational radiation. 相似文献
9.
A physically based explanation is given for the distribution of flare energies N(E)E
– where 1.5. In contrast to previous approaches, the present treatment is based on a physical theory of the flare reconnection site. The central assumption is that topological flare energy, although released explosively, is slowly accumulated over several hundred Alfvén timescales. When coupled to the geometric properties of the reconnective flare source, this assumption is shown to lead naturally to a deduction of the flare energy distribution. Current sheet models yield the exponent
whereas more compact current structures imply steeper spectra
. 相似文献
10.
11.
A new modified Kramers Kronig Integral is derived and shown to produce excellent results when k data is only known over a limited range. By considering the effect of resonance features simulated using the Dirac-Delta function, the new integral is shown to be more rapidly converging than both the conventional Kramers Kronig integral and a modified (Subtractive Kramers Kronig – SKK) integral introduced by Ahrenkiel (1971). The new integral does not require extensive extrapolation of reflectance data outside the measured region in order to produce reliable results. By extending the above procedure to include n data points, it is shown that at wavelength 0, \[ n(_0)=\sum_{i=1}^{\rm n}(-1)^{\rm n+1}\prod_{\stackrel{j=1}{j \not=i}}^{\rm n} \frac{(_j^2-_0^2)}{(_i^2- _j^2)}n(_i)+\frac{2}{\pi}P\int_{0}^{\infty}(-1)^{\rm n+1} \frac{\prod_{i=1}^{\rm n}(_i^2-_0^2)}{\prod_{i=0}^{\rm n}(^2-_i^2)} k()d \] with relative error given by, \[ R_n(_0)=\prod_{i=1}^{\rm n}\frac{_i^2- _0^2}{_^2-_i^2} . \] This nth order expression should prove useful in establishing the internal self-consistency of data sets for which both optical coefficients have been theoretically derived. 相似文献
12.
13.
L. G. Lukjanov 《Celestial Mechanics and Dynamical Astronomy》1977,15(4):489-500
Some particular solutions of the restricted three-body problem which determine outgoing or incoming orbits near libration points are considered. The solutions are obtained in the form of absolutely convergent Liapounov series. It is proved that these asymptotic solutions are plane curves situated in the orbital plane of the primaries. Each family of asymptotic solutions for every collinear point consists of four solutions which are the separatrices of a saddle point. The angles of inclination of the separatrices are determined.
aaa a a aa , a. a a a. a, a . . aa, a a aaa. . a . a a , aaa a. . aa aa a .相似文献
14.
For a given family of orbits f(x,y) = c
* which can be traced by a material point of unit in an inertial frame it is known that all potentials V(x,y) giving rise to this family satisfy a homogeneous, linear in V(x,y), second order partial differential equation (Bozis,1984). The present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity . The new equation, which relates the synodic potential function (x,y), = –V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780!\[\tfrac{1}{2}\]2(x
2 + y
2) to the given family f(x,y) = c
*, is again of the second order in (x,y) but nonlinear.As an application, some simple compatible pairs of functions (x,y) and f(x, y) are found, for appropriate values of , by adequately determining coefficients both in and f. 相似文献
15.
K. D. Abhyankar 《Astrophysics and Space Science》1984,99(1-2):355-361
Pre-Main-Sequence contracting objects, post-Main-Sequence expanding stars and mass-losing components of semi-detached systems all occupy more or less the same region in the conventional H-R-diagram. We make a transformation to variables (logL) and (logT
e), where is the difference between the observed quantity, logL or logT
e, and the value of that quantity which a star of the same mass would have on the empirical Main Sequence. It is demonstrated that a plot between the new variables clearly separates the mass-losing stars from other objects which is essentially an effect of the increasing abundance of helium relative to hydrogen.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983. 相似文献
16.
А. М. Крымский Л. С. Марочник П. Д. НаселБский Н. В. Пелихов 《Astrophysics and Space Science》1978,55(2):299-324
=qr, I II (Marochniket al., 1975 a, b), . , II; , . , , ye , . . t
g. 相似文献
17.
A possibility of developing the analytical theory of perturbed motion for a balloon-satellite influenced by solar radiation pressure force is analysed here on the basis of the limit case modification of the two fixed centers problem whose force-field is a superposition of the Newtonian central field and a homogeneous one. Such an approach enables us in the intermediate orbit already to take into account the effect of a constant force, all coordinates of a satellite being expressed as functions of some monotonically increasing variable by means of inversion of elliptic quadratures. The relations between canonical constants of the intermediate orbit and a quasikeplerian elements coinciding in the absence of solar radiation pressure with keplerian ones are derived. The numerical results and illustrating the perturbations in the radius-vector of the intermediate orbit of a balloon-satellite of the Echo-I type are given.
-, , , . , , . , . , - - -I.相似文献
18.
Makhlouf Amar 《Celestial Mechanics and Dynamical Astronomy》1991,52(4):397-406
We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t). 相似文献
19.
, , . , . ( , , ), - qqi . - ; , - . , , . 相似文献
20.
An estimate of the period of the rotation of the line of apsides of the double-star system Phe is obtained by representing the density function as a product of a normal Gaussian distribution and an associated Legendre polynomial
.The asymptotic behaviour of this function coincides with the results obtained by Zeldovichet al. (1981).The period of motion of the line of apsides of Phe (about 63 years) obtained in this way comes close to the period determined by an empirical formula for
of Batten (1973). 相似文献