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1.
The aim of the present investigation will be to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axisA, eccentricitye, and longitude of the periastron ), arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between 0e<1; and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.In Section 2 following brief introductory remarks the variational equations of the problem of plane motion will be set up in terms of the rectangular componentsR, S, W of disturbing accelerations with respect to a revolving system of coordinates. The explicit form of these coefficients will be established in Section 3 to the degree of accuracy to which squares and higher powers of quantities of the order of superficial distortion can be ignored. Section 4 will be devoted to a derivation of the explicit form of the variational equations for the case of a perturbing function arising from axial rotation; and in Section 5 we shall derive variational equations which govern the perturbation of orbital elements caused by lagging dynamical tides.Numerical integrations of these equations, which govern the tidal evolution of close binary systems prompted by viscous friction at constant mass, are being postponed for subsequent investigations.Prepared at the Lunar Science Institute, Houston, Texas, under the joint support of the Universities Space Research Association, Charlottesville, Virginia, and the National Aeronautics and Space Administration Manned Spacecraft Center, Houston, Texas, under Contract No. NSR 09-051-001. This paper constitutes Lunar Science Institute Contribution no. 100.Normally at the Department of Astronomy, University of Manchester, England.  相似文献   

2.
Our aim is to investigate tidal interaction in High‐Mass X‐ray Binary stars in order to determine in which objects the rotation of the mass donors is synchronized or pseudosynchronized with the orbital motion of the compact companion. We calculate the pseudosynchronization period (Pps) and compare it with the rotational period of the mass donors (Prot). We find that (1) the Be/X‐ray binaries are not synchronized, the mass donors rotate faster than the orbital period and the ratio Pps/Prot is 2–300; (2) the giant and supergiant systems are close to synchronization and for them the ratio Pps/Prot is 0.3–2 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant, the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational) on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained by Rambaux and Bois [Astron. Astrophys. 413, 381–393]. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

4.
The IAU Working Group on Precession and the Equinox looked at several solutions for replacing the precession part of the IAU 2000A precession–nutation model, which is not consistent with dynamical theory. These comparisons show that the (Capitaine et al., Astron. Astrophys., 412, 2003a) precession theory, P03, is both consistent with dynamical theory and the solution most compatible with the IAU 2000A nutation model. Thus, the working group recommends the adoption of the P03 precession theory for use with the IAU 2000A nutation. The two greatest sources of uncertainty in the precession theory are the rate of change of the Earth’s dynamical flattening, ΔJ2, and the precession rates (i.e. the constants of integration used in deriving the precession). The combined uncertainties limit the accuracy in the precession theory to approximately 2 mas cent−2. Given that there are difficulties with the traditional angles used to parameterize the precession, zA, ζA, and θA, the working group has decided that the choice of parameters should be left to the user. We provide a consistent set of parameters that may be used with either the traditional rotation matrix, or those rotation matrices described in (Capitaine et al., Astron. Astrophys., 412, 2003a) and (Fukushima Astron. J., 126, 2003). We recommend that the ecliptic pole be explicitly defined by the mean orbital angular momentum vector of the Earth–Moon barycenter in the Barycentric Celestial Reference System (BCRS), and explicitly state that this definition is being used to avoid confusion with previous definitions of the ecliptic. Finally, we recommend that the terms precession of the equator and precession of the ecliptic replace the terms lunisolar precession and planetary precession, respectively.  相似文献   

5.
The dynamics of the spin-orbit interaction of a sphereM 8 and a rotating asymmetrical rigid bodyM a are examined. No restrictions are imposed on the masses, on the orientation of the rotation axis to the orbit plane, or on the orbit eccentricity. The zonal potential harmonics ofM a induce a precession of the spin axis as well as a precession of the orbit plane, the net effect being a uniform precession of the node on an invariant plane normal to the constant total angular momentum of the system. In general, the effect of the tesseral harmonics is to induce short-period perturbations of small amplitude in both the orbital and spin motions. Resonances are shown to exist whenever the orbital and rotational periods are commensurable. In any resonant state a single coordinate is found to represent both orbital and spin perturbations; and the system may be described as trapped in a localized potential well. The resultant spin and orbit librations are in phase with a common period. The relative amplitudes of the spin/orbit modes are determined by the characteristic parameter =M a M s a 2 /3(M a +M s )C, wherea is the semimajor axis of the orbit, andC is the moment of inertia ofM a about the rotation axis. When ga1, the solutions reduce to those for pureorbital resonance, in whichM s librates in an appropriate reference frame while the rotation rate of the asymmetrical body remains constant. In the opposite extreme of 1, the solutions are appropriate to purerotational resonance, in which the orbital motion is unperturbed but the spin ofM a librates. In each of these special cases the equations developed herein on the basis of a single theory are in agreement with those previously determined from separate theories of spin and orbital resonances.  相似文献   

6.
The light outside the eclipses of the totally eclipsing RS CVn binary SV Camelopardalis (SV Cam) is Fourier analysed and the amplitudes of the distortion waves have been derived. The distribution of the percentage contributions of these amplitudes inV, B andU colours with respect to the luminosities of the binary components indicates that the hotter component is the source of the distortion waves. These distortion waves, attributed to star spots, are modelled according to Budding (1977) and spot parameters like longitude, latitude, temperature and size are obtained. From this study it is noticed that while symmetric waves with two minima could be fitted satisfactorily, asymmetric waves with more than two minima could not be fitted well. From the longitudes of the minima of the best fitted curves, migration periods of four spot groups are determined. Assuming synchronism between rotation and orbital periods, the rotation periods of the four spot groups are derived from their migration periods. The period of rotation of one of the spot groups having direct motion is found to be 0d.5934209 while the periods of the other three spot groups having retrograde motion are 0d.5926588, 0d.592607 and 0d.5924688. As the latitudes of these spots are known from modelling parameters, the latitude having a rotation period equal to that of the orbital period (co-rotating latitude) is found to be about 30°  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.
The subject of the paper is the problem of stellar differntial rotation in close binaries (CB) ofRS CV n type. The differential-rotation parameters we find on the basis of the migration of the depression in the light curves caused by the spot effect over the orbital phase. For that purpose, a simple model (Bussoet al., 1985) and inverse-problem procedure, based on the Marquardt (1963) algorithm, are used. To verify the obtained solutions, the SIMPLEX algorithm (Torczon, 1991) is applied, suitable for the nonlinear parameter optimisation. This algorithm enables a correct solution of the nonlinear equation system describing the differential rotation. The procedure is applied in the determination of the parameters of differential rotation forCV Cam, VV Mon andSS Boo binaries.  相似文献   

9.
We present the results of 10 years of photometric CCD observations of the intermediate polar V709 Cas obtained by using different instruments during 2003–2013. We detected a new variability with a period of Pnew = 0.d016449979(5) which seems to be real. The spin variability is not clearly seen in all our data, so we are unable to study any evolution of the white dwarf rotation. From the best night (in 2010) we obtained a spin period of Pspin = 311.s8(5). We analyzed the orbital variability using (O – C) analysis. We found no variations of the orbital period on a timescale of 10 years, but the linear fit to the (O – C) diagram shows that the value of the orbital period is Porb = 0.d2222123(6), which is close to the earlier published values. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
A detector sharing the orbital rate of Venus has a unique perspective on solar periodicities. Fourier analysis of the 8.6 year record of solar EUV output gathered by the Langmuir probe on Pioneer Venus Orbiter shows the influences of global oscillation modes located in the convective envelope and in the radiative interior. Seven of the eight lowest angular harmonic r-mode families are detected by their rotation rates which differ almost unmeasurably from ideal theoretical values. This determines a mean sidereal rotation rate for the envelope of 457.9 ± 2.0 nHz which corresponds to a period of 25.3 days. Many frequencies are aliased at ± 106 nHz by modulation from the lowest angular harmonic r-mode in the envelope. The rotation of this mode seems slightly retrograde, -1.5 ± 2.0 nHz, but small positive values are not excluded. We confirm that the rotation of the radiative interior, 381 nHz, is slower than the envelope by detecting g-mode frequencies for angular harmonics, 2 l 6, and a possible first detection of the rotation rate for the l = 1 case. Solar EUV lacks the sudden darkenings (dips) shown by visible irradiance; vortex cores in the photosphere and below are again suggested as a possible explanation.  相似文献   

11.
The orientations of the albedo lineaments, bands, and lineations on Europa's surface have been compared in previous studies with the global stress fields set up by orbital eccentricity, orbital recession, and nonsynchronous rotation. Of these orbital and rotational effects, nonsynchronous rotation, combined with an offsetting of the tidal bulge, comes closest to providing agreement between the stress field generated and the lineation orientations, if the lineations trace tension or extension fractures (McEwen 1986.Nature321, 49–51). However, inferred minimum principal stress directions for a broad region of wedge-shaped bands near the anti-Jove point cannot satisfactorily be accounted for by any of the stress fields above, but are consistent with the stresses resulting from a rotation of Europa's ice shell about an axis through the sub- and anti-Jove points, clockwise as seen from the anti-Jove hemisphere (P. M. Schenk and W. B. McKinnon 1989.Icarus79, 75–100). Calculations by Ojakangas and Stevenson (1989.Icarus81, 220–241) of the thermal state of Europa's ice shell indicate that spatial variations in the thickness of the shell may cause it to undergo such a reorientation. We have investigated whether any reorientation of the shell about an axis through the sub- and anti-Jove points produces a stress field consistent with the full, global set of prominent lineations on Europa's surface. We find that no such reorientation provides a good fit between the lineations and plausible fracture orientations derived from the principal stress trajectories. Topographic ridges, identified in a limited zone south of the anti-Jove point, are roughly consistent with compression due to clockwise polar wander, but the orientations of these ridges may be strongly biased by illumination direction. Within the limitations of the presently available imagery, nonsynchronous rotation is still the most likely cause of the prominant fractures on Europa's surface, and the best specific, albeit regionally limited, tectonic evidence consistent with recent polar wander remains the wedge-shaped bands.  相似文献   

12.
V1162 is a δ-Scuti type variable star for which a rotational velocity of V  sini=46±4 km s−1 has been observed. The star has been modelled according to its observed parameters and oscillation frequencies. The results obtained by approximating rotation to the first order have been compared with the ones provided by new calculations that include rotation up to the second order. We found that second order rotation term should be included in frequency calculations for comparatively high rotation speeds.  相似文献   

13.
The optical light of the symbiotic binary BF Cyg during its last eruption after 2006 shows orbital variations because of an eclipse of the outbursting compact object. The first orbital minimum is deeper than the following ones. Moreover, the Balmer profiles of this system acquired additional satellite components indicating a bipolar collimated outflow at one time between the first and second orbital minima. This behaviour is interpreted in the framework of the model of a collimated stellar wind from the outbursting object. It is supposed that one extended disc‐like envelope covering the accretion disc of the compact object and collimating its stellar wind forms in the period between the first and second minima. The uneclipsed part of this envelope is responsible for the decrease of the depth of the orbital minimum. The calculated UBVRCIC fluxes of this uneclipsed part are in agreement with the observed residual of the depths of the first and second orbital minima. The parameters of the envelope require that it is the main emitting region of the line Hα but the Hα profile is less determined from its rotation and mostly from other mechanisms. It is concluded that the envelope is a transient nebular region and its destruction determines the increase of the depth of the orbital minimum with fading of the optical light. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
MulticolourWBVR photoelectric observations of the eclipsing binary V 451 Oph were carried out, and a highly accurate light curve was obtained. The angular velocity of the orbital rotation, =2.1 deg yr–1, and the apsidal motion constantk 2=0.0045 are given.  相似文献   

15.
Owing to its extremely slow rotation, Venus must be regarded as a triaxial body with differences of all three principal moments of inertia comparable in magnitude, thus rendering it a body essentially different from a rapidly rotating planet. The dynamical problem then arises of how such a body, with a rotation-period comparable with its orbital period, would be affected by couples exerted upon it by the gravitational action of the Sun. Equations for the rotatory motion are set up in a form suitable for numerical solution by machine-calculations, but the problem so presented can be adequately investigated only for a hypothetical planet with far larger differences of principal moments than could hold for Venus. Results obtained on this limited basis nevertheless suggest that for the actual planet the direction of the rotation axis may move almost randomly between the two hemispheres defined by the orbital plane and thus that the present direction near the south celestial pole of the orbit may be only a temporary situation. Order-of-magnitude considerations based on the equations of motion suggest that a time-scale of order 107 to 108 yr may on average be required for large changes in direction of the rotation axis to take place.  相似文献   

16.
HD 115781 and HD 116204 (BL CVn and BM CVn) are shown to be RS CVn binaries with periods near 20 days. HD 115781 is double-lined; the primary type is about K1III, while the secondary is probably a late-type subgiant. The masses of the two components are equal within observational error. There is substantial photometric variability with a period half the orbital period; it is attributed to ellipsoidal variation. HD 116204 is also of type K1III. It shows exceptionally strong Ca II H and K emission, together with an emission-line spectrum typical of RS CVn stars in theIUE ultraviolet region, but Hα is an absorption line. The secondary star in the HD 116204 system has not been detected. The primary shows photometric variations, presumably due to starspots, with a period 5 per cent longer than the orbital period.  相似文献   

17.
E. Bois  N. Rambaux   《Icarus》2007,192(2):308-317
Mercury's capture into the 3:2 spin–orbit resonance can be explained as a result of its chaotic orbital dynamics. One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Analytical approaches at the first-order level using the Cassini state assumptions give the obliquity constant or quasi-constant. Which is the obliquity's dynamical behavior deriving from a complete spin–orbit motion of Mercury simultaneously integrated with planetary interactions? We have used our SONYR model (acronym of Spin–Orbit N-bodY Relativistic model) integrating the spin–orbit N-body problem applied to the Solar System (Sun and planets). For lack of current accurate observations or ephemerides of Mercury's rotation, and therefore for lack of valid initial conditions for a numerical integration, we have built an original method for finding the libration center of the spin–orbit system and, as a consequence, for avoiding arbitrary amplitudes in librations of the spin–orbit motion as well as in Mercury's obliquity. The method has been carried out in two cases: (1) the spin–orbit motion of Mercury in the 2-body problem case (Sun–Mercury) where an uniform precession of the Keplerian orbital plane is kinematically added at a fixed inclination (S2K case), (2) the spin–orbit motion of Mercury in the N-body problem case (Sun and planets) (Sn case). We find that the remaining amplitude of the oscillations in the Sn case is one order of magnitude larger than in the S2K case, namely 4 versus 0.4 arcseconds (peak-to-peak). The mean obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference of 10.8 arcseconds. These theoretical results are in a good agreement with recent radar observations but it is not excluded that it should be possible to push farther the convergence process by drawing nearer still more precisely to the libration center. We note that the dynamically driven spin precession, which occurs when the planetary interactions are included, is more complex than the purely kinematic case. Nevertheless, in such a N-body problem, we find that the 3:2 spin–orbit resonance is really combined to a synchronism where the spin and orbit poles on average precess at the same rate while the orbit inclination and the spin axis orientation on average decrease at the same rate. As a consequence and whether it would turn out that there exists an irreducible minimum of the oscillation amplitude, quasi-periodic oscillations found in Mercury's obliquity should be to geometrically understood as librations related to these synchronisms that both follow a Cassini state. Whatever the open question on the minimal amplitude in the obliquity's oscillations and in spite of the planetary interactions indirectly acting by the solar torque on Mercury's rotation, Mercury remains therefore in a stable equilibrium state that proceeds from a 2-body Cassini state.  相似文献   

18.
Sedimentation of particles in a fluid has long been used to characterize particle size distribution. Stokes’ law is used to determine an unknown distribution of spherical particle sizes by measuring the time required for the particles to settle a known distance in a fluid of known viscosity and density. In this paper, we study the effects of gravity on sedimentation by examining the resulting particle concentration distributed in an equilibrium profile of concentration C m,n above the bottom of a container. This is for an experiment on the surface of the Earth and therefore the acceleration of gravity had been corrected for the oblateness of the Earth and its rotation. Next, at the orbital altitude of the spacecraft in orbit around Earth the acceleration due to the central field is corrected for the oblateness of the Earth. Our results show that for experiments taking place in circular or elliptical orbits of various inclinations around the Earth the concentration ratio C m,n /C m,ave , the inclination seems to be the most ineffective in affecting the concentration among all the orbital elements. For orbital experiment that use particles of diameter d p =0.001 μm the concentration ratios for circular and slightly elliptical orbits in the range e=0–0.1 exhibit a 0.009 % difference. The concentration ratio increases with the increase of eccentricity, which increases more for particles of larger diameters. Finally, for particles of the same diameter concentration ratios between Earth and Mars surface experiments are related in the following way .  相似文献   

19.
Based on two high-dispersion spectra of the close binary BW Boo, we have detected lines of the secondary component whose contribution to the combined spectrum does not exceed 2%. We have determined the rotation velocities of the components and spectroscopic orbital elements. Numerous lines of neutral and ionized iron have been used to determine the effective temperature and surface gravity for the primary component. The photometric light curves for this binary have been solved for the first time. Its primary component is an A2Vm star with a mass of 2 ± 0.1M ⊙ and a radius of 1.9 ± 0.4R ⊙. Its rotation velocity is 2 km s−1, which is a factor of 18 lower than the pseudo-synchronous velocity for this component. The G6 secondary component, a T Tau star, has a rotation velocity of 17 km s−1, amass of 1.1M ⊙, and a radius of 1 R ⊙. The age of the binary has been estimated to be 107 yr.  相似文献   

20.
A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J. 646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h−1. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.  相似文献   

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