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1.
R. A. Lyttleton 《Earth, Moon, and Planets》1980,22(1):13-23
The standard discussion of tidal friction in the Earth-Moon system has been that given by Jeffreys in successive editions ofThe Earth over the past several decades. It is herein shown to contain several erros vitiating its results. The dynamical equation utilised for finding the rate of change of angular velocity of the Earth fails to take account of the fact that the moment of inertia of the Earth may be changing with time, and all subsequent equations which depend on this are incorrect as a result. Simple equations have been left unsolved that ought to have been solved, and the alleged numerical conclusions in no way follow from the values set down initially for the observed apparent secular accelerations of the Moon and Sun.The revised dynamical equations are shown to enable the lunar and solar tidal couples to conform to theory, and may imply that the moment of inertia of the Earth is decreasing at a non-negligible rate. Recognition of this is the key to the whole problem. The only available hypothesis providing adequate contraction is that following from the phase-change theory of the nature of the terrestrial core, and the value of the rate of decrease of moment of inertia calculated from this is in close agreement with that implied by modern improved values of the secular accelerations.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy. 相似文献
2.
James B. Hartle 《Astrophysics and Space Science》1973,24(2):385-405
Equations are given which determine the moment of inertia of a rotating relativistic fluid star to second order in the angular
velocity with no other approximation being made. The equations also determine the moment of inertia of matter located between
surfaces of constant density in a rotationally distorted star; for example, the moments of inertia of the crust and core of
a rotationally distorted neutron star can be calculated in this way. The method is applied ton=3/2 relativistic polytropes and to neutron star models constructed from the Baym-Bethe-Pethick-Sutherland-Pandharipande equation
of state.
Supported in part by the National Science Foundation.
Alfred P. Sloan Research Fellow. 相似文献
3.
Christopher McCord 《Celestial Mechanics and Dynamical Astronomy》2004,89(2):99-118
In the N-body problem, it is a simple observation that relative equilibria (planar solutions for which the mutual distances between
the particles remain constant) have constant moment of inertia. In 1970, Don Saari conjectured that the converse was true:
if a solution to the N-body problem has constant moment of inertia, then it must be a relative equilibrium. In this note, we confirm the conjecture
for the planar three-body problem with equal masses.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
Julian I. Palmore 《Celestial Mechanics and Dynamical Astronomy》1979,19(2):167-171
A solution of the Newtoniann-body problem for which the moment of inertia (with respect to the centre of mass) is constant is a solution of relative equilibrium.Research supported in part by NSF grant MCS-77-01716. 相似文献
5.
For the many-body problem in the field of general attraction, the evolution of the moment of inertia is studied, we obtain the bifurcation curves between the attainable domain and the forbidden domain in the plane (,t), where is the mean quadratic distance (proportional to the square root of the moment of inertia). That is an extension of the conclusion in [1]. Moreover, the dependence of the bifurcation curves on the generalized potential is obtained.This project is supported by the National Science Foundation of China. 相似文献
6.
The moment of inertia of a giant planet reveals important information about the planet’s internal density structure and this information is not identical to that contained in the gravitational moments. The forthcoming Juno mission to Jupiter might determine Jupiter’s normalized moment of inertia NMoI = C/MR2 by measuring Jupiter’s pole precession and the Lense–Thirring acceleration of the spacecraft (C is the axial moment of inertia, and M and R are Jupiter’s mass and mean radius, respectively). We investigate the possible range of NMoI values for Jupiter based on its measured gravitational field using a simple core/envelope model of the planet assuming that J2 and J4 are perfectly known and are equal to their measured values. The model suggests that for fixed values of J2 and J4 a range of NMoI values between 0.2629 and 0.2645 can be found. The Radau–Darwin relation gives a NMoI value that is larger than the model values by less than 1%. A low NMoI of ∼0.236, inferred from a dynamical model (Ward, W.R., Canup, R.M. [2006]. Astrophys. J. 640, L91–L94) is inconsistent with this range, but the range is model dependent. Although we conclude that the NMoI is tightly constrained by the gravity coefficients, a measurement of Jupiter’s NMoI to a few tenths of percent by Juno could provide an important constraint on Jupiter’s internal structure. We carry out a simplified assessment of the error involved in Juno’s possible determination of Jupiter’s NMoI. 相似文献
7.
Yu. A. Fadeyev 《Astrophysics and Space Science》1993,210(1-2):261-267
The pulsation motions of the limit-cycle model can be described as a superposition of the Fourier harmonics, in the adiabatic layers each harmonics being identified with the corresponding standing wave. Near the resonance II
o
/II
l
=k the harmonics of orderk is also identified with the overtone of orderl. The spectra of the oscillatory moment of inertia obey to the power dependence on the Fourier harmonics orderk. In cepheids with periods shorter than 9 days the bump is due to the wave packet generated by the second overtone, whereas at periods longer than 10 days the bump feature is due to the traveling pulse reflected off the stellar core. 相似文献
8.
The optical pulsations in DQ Her are universally believed to be due to emission from the magnetic poles of the white dwarf.
However, there is no way for a pulsation to be seen if the magnetic axis and the spin axis are aligned; whether the optical
pulsation is seen directly from the magnetic poles or as a result of re-processing this beam from sides in an accretion disc,
the magnetic and spin axes must be offset. This fact explains why the `oblique rotator' model has been adopted as a standard
model for the DQ Her primary. In a recent paper, we have computed several axisymmetric models simulating the DQ Her white
dwarf before its `turn-over' (where the term `turn-over' describes the process by which the magnetic axis gets inclining relative
to the spin axis at a gradually increasing angle, the so-called `turn-over angle'). For such models, we have found that the
moment of inertia along the rotation axis, I
33, is less than the moment(s) of inertia along the two other principal axes, I
11=I
22. The situation I
11>I
33 is known as `dynamical asymmetry', and can cause a spontaneous turn-over of the magnetic axis with respect to the rotation
axis . Consequently, the DQ Her white dwarf is either an oblique rotator undergoing its turn-over phase, or it is already
qalmostequal a `perpendicular rotator', i.e., its turn-over angle is almost equal to 90°. Assuming the first case, we study numerically the so-called `turn-over scenario', that is, a scenario on rotational evolution
in which the turn-over phase is taken into account. We give emphasis on computations concerning the spin-down time rate of
the DQ Her white dwarf due to turn-over (not to be confused with its spin-uptime rate due to accretion) for several possible
values of the magnetic field.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
A brief review on the history of constructing Earth-like models of the Venusian interior is presented. Available observational data are analyzed. An explanation for the anomalously large ratio of the quadrupole gravitational moment J2 to the small parameter of Venus q is proposed. Thus, estimates were obtained for the precession constant and principal moments of inertia for the Earth-like model of Venus.
相似文献10.
It is well-known that the optical pulsations in DQ Her are due to emission from the magnetic poles of the white dwarf. As
the white dwarf spins on its axis, the magnetic poles sweep into and out of the line of sight due to the fact that the magnetic
axis and the spin axis are not aligned, that is, the DQ Her white dwarf is an `oblique rotator'. So, a central question is
if an initially axisymmetric model simulating the DQ Her white dwarf before its `turn-over' (where the term `turn-over' describes
the process by which the magnetic axis gets inclining relative to the spin axis at a progressively increasing angle, the so-called
`turn-over angle') is indeed susceptible to turn-over. For the puprose of resolving this problem, we compute several axisymmetric
models of the DQ Her white dwarf. Our results show that, for both the rotation periods proposed on the basis of the observational
evidence regarding the optical pulsations of DQ Her (i.e.,71 s or 142 s), the moment of inertia along the rotation axis is
less than the corresponding moment of inertia along the remaining two principal axes of the axisymmetric configuration, I
33 > I
11(=I
22). This is because toroidal magnetic field (tending to derive prolate equidensity surfaces) dominates over rotation (tending,
in turn, to derive oblate equidensity surfaces), mainly in the interior of the star. The situation I
11 < I
33 is known as `dynamical asymmetry', and can cause a turn-over of the magnetic symmetry axis with respect to the rotation axis,
eventually deriving a nonaxisymmetric configuration corresponding to the so-called `perpendicular rotator' with turn-over
angle almost equal to 90°. In this view, our results explain why the DQ Her white dwarf is now an oblique rotator.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
P. B. Jones 《Astrophysics and Space Science》1976,45(2):369-381
The time dependences of the inertia tensor and of a dissipative torque caused by the nonleptonic weak interaction have been investigated for a certain class of pulsars with no solid core. Early in the life of the pulsar, the angular velocity vector is predicted to move with respect to fixed body axes in such a way that it becomes perpendicular to the magnetic dipole moment. During this motion, the solid outer shell suffers plastic deformation so that the dipole moment becomes approximately collinear with a principal axis. After 104 or 105 yr, the dissipative torque is negligibly small compared with the electromagnetic torque, the Euler equations are those for a simple rigid body, and alignment of spin and dipole moment occurs. If the dipole moment discussed by Lyneet al. (1975) is interpreted as being equal to the component perpendicular to the spin, its secular decay is a natural property of this model and is not a consequence of field decay through electrical resistivity. 相似文献
12.
Han-Shou Liu 《Celestial Mechanics and Dynamical Astronomy》1972,6(4):421-424
In order to achieve the maximum strength of higher resonance locks for satellites in the elliptic orbit, the condition of satellite orientation during the process of deployment is established. It is shown that for maximum strength locks the axis of the minimum moment of inertia of satellites should point toward the attracting body at ±(5/8) and 0 values of the true anomalyf. This condition of deployment is applicable to all cases of resonance rotation regardless of the value of lock numberk and orbit eccentricitye. 相似文献
13.
A relativistic, first-order differential equation is derived for the accumulated moment of inertia of a spherically symmetric
celestial body. An approximate equation is proposed to describe the contribution of relativistic effects to the moment of
inertia of a superdense star. For configurations of an incompressible fluid, this approximation describes the results of the
numerical calculations of Chandrasekhar and Miller to within 5% in the entire range of central pressures from 0 to ∞.
Translated from Astrofizika, Vol. 40, No. 1, pp. 87–96, January–March, 1997. 相似文献
14.
A. G. Lyne S. L. Shemar F. Graham Smith 《Monthly notices of the Royal Astronomical Society》2000,315(3):534-542
Shemar & Lyne have previously presented observations and an analysis of 32 glitches and their subsequent relaxations observed in a total of 15 pulsars. These data are brought together in this paper with those published by other authors. We show quantitatively how glitch activity decreases linearly with decreasing rate of slow-down. As indicated previously from studies of the Vela pulsar, the analysis suggests that 1.7 per cent of the moment of inertia of a typical neutron star is normally contained in pinned superfluid which releases its excess angular momentum at the time of a glitch. There is a broad range of glitch amplitude and there is a strong indication that pulsars with large magnetic fields suffer many small glitches while others show a smaller number of large glitches. Transient effects following glitches are very marked in young pulsars and decrease linearly with decreasing rate of slow-down, suggesting that the amount of loosely pinned superfluid decreases with age. We suggest that the low braking index of the Vela and Crab pulsars cannot be caused by a decreasing moment of inertia and should be attributed to step increases in the effective magnetic moment of the neutron star at the glitches. 相似文献
15.
Veronique Dehant William Folkner Etienne Renotte Daniel Orban Sami Asmar Georges Balmino Jean-Pierre Barriot Jeremy Benoist Richard Biancale Jens Biele Frank Budnik Stefaan Burger Olivier de Viron Bernd Häusler Özgur Karatekin Sébastien Le Maistre Philippe Lognonné Michel Menvielle Michel Mitrovic Martin Pätzold Marie Yseboodt 《Planetary and Space Science》2009,57(8-9):1050-1067
The paper presents the concept, the objectives, the approach used, and the expected performances and accuracies of a radioscience experiment based on a radio link between the Earth and the surface of Mars. This experiment involves radioscience equipment installed on a lander at the surface of Mars. The experiment with the generic name lander radioscience (LaRa) consists of an X-band transponder that has been designed to obtain, over at least one Martian year, two-way Doppler measurements from the radio link between the ExoMars lander and the Earth (ExoMars is an ESA mission to Mars due to launch in 2013). These Doppler measurements will be used to obtain Mars’ orientation in space and rotation (precession and nutations, and length-of-day variations). More specifically, the relative position of the lander on the surface of Mars with respect to the Earth ground stations allows reconstructing Mars’ time varying orientation and rotation in space.Precession will be determined with an accuracy better by a factor of 4 (better than the 0.1% level) with respect to the present-day accuracy after only a few months at the Martian surface. This precession determination will, in turn, improve the determination of the moment of inertia of the whole planet (mantle plus core) and the radius of the core: for a specific interior composition or even for a range of possible compositions, the core radius is expected to be determined with a precision decreasing to a few tens of kilometers.A fairly precise measurement of variations in the orientation of Mars’ spin axis will enable, in addition to the determination of the moment of inertia of the core, an even better determination of the size of the core via the core resonance in the nutation amplitudes. When the core is liquid, the free core nutation (FCN) resonance induces a change in the nutation amplitudes, with respect to their values for a solid planet, at the percent level in the large semi-annual prograde nutation amplitude and even more (a few percent, a few tens of percent or more, depending on the FCN period) for the retrograde ter-annual nutation amplitude. The resonance amplification depends on the size, moment of inertia, and flattening of the core. For a large core, the amplification can be very large, ensuring the detection of the FCN, and determination of the core moment of inertia.The measurement of variations in Mars’ rotation also determines variations of the angular momentum due to seasonal mass transfer between the atmosphere and ice caps. Observations even for a short period of 180 days at the surface of Mars will decrease the uncertainty by a factor of two with respect to the present knowledge of these quantities (at the 10% level).The ultimate objectives of the proposed experiment are to obtain information on Mars’ interior and on the sublimation/condensation of CO2 in Mars’ atmosphere. Improved knowledge of the interior will help us to better understand the formation and evolution of Mars. Improved knowledge of the CO2 sublimation/condensation cycle will enable better understanding of the circulation and dynamics of Mars’ atmosphere. 相似文献
16.
We present a variety of well behaved classes of Charge Analogues of Tolman’s iv (1939). These solutions describe charged fluid
balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality
condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound
is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. These solutions give us
wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling
of super dense stars. keeping in view of well behaved nature of these solutions, one new class of solutions is being studied
extensively. Moreover, this class of solutions gives us wide range of constant K (0.3≤K≤0.91) for which the solution is well behaved hence, suitable for modeling of super dense stars like Strange Quark stars,
Neutron stars and Pulsars. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible
with Quark stars, Neutron stars and Pulsars. By assuming the surface density ρ
b
=2×1014 g/cm3 (like, Brecher and Caporaso in Nature 259:377, 1976), corresponding to K=0.30 with X=0.39, the resulting well behaved model has the mass M=2.12M
Θ, radius r
b
≈15.27 km and moment of inertia I=4.482×1045 g cm2; for K=0.4 with X=0.31, the resulting well behaved model has the mass M=1.80M
Θ, radius r
b
≈14.65 km and moment of inertia I=3.454×1045 g cm2; and corresponding to K=0.91 with X=0.135, the resulting well behaved model has the mass M=0.83M
Θ, radius r
b
≈11.84 km and moment of inertia I=0.991×1045 g cm2. For n=0 we rediscovered Pant et al. (in Astrophys. Space Sci. 333:161, 2011b) well behaved solution. These values of masses and moment of inertia are found to be consistent with other models of Neutron
stars and Pulsars available in the literature and are applicable for the Crab and the Vela Pulsars. 相似文献
17.
Dual-spin or gyrostat satellites subject to gravitational torques can adopt an infinite number of possible equilibria obtained by adjusting the magnitude and direction of the rotor angular momentum within the satellite. This paper seeks to answer the question, which of these equilibria is best — and best is chosen here to mean most stable in the sense that the energy required to perturb the orientation by any prescribed amount is maximized, i.e. the smallest eigenvalue of the Hessian matrix of the dynamic potential energy is maximized. Using this criterion, it is shown that the conventional configuration for dual-spin satellites with the angular momentum of the rotor, the spacecraft principal axis of maximum moment of inertia, and the perpendicular to the orbital plane coincident is not always the best orientation. The optimal configuration is shown to have the minimum moment of inertia always aligned with the local vertical, but the principal axis of maximum moment of inertia, shifts from the perpendicular to the orbital plane to lying in-plane as the angular momentum of the rotor is increased from zero (corresponding to a rigid gravity gradient satellite) to some sufficiently large value which is determined as a function of parameters. For angular momentum greater than this value, global optimality is established analytically, and otherwise local optimality is proved analytically with global optimality demonstrated numerically. 相似文献
18.
Mass, radius and moment of inertia are direct probes of compositions and Equation of State (EoS) of dense matter in neutron star interior. These are computed for novel phases of dense matter involving hyperons and antikaon condensate and their observable consequences are discussed in this article. Furthermore, the relationship between moment of inertia and quadrupole moment is also explored. 相似文献
19.
The rate of inelastic relaxation of asteroid 1620 Geographos in the vicinity of the poles, corresponding to rotation about the axes of minimal and maximal principal moment of inertia, was considered on the basis of the theory stated by Efroimsky and Lazaryan. The low bound of the total relaxation time is estimated as 4 × 106 years. 相似文献
20.
Riccardo Brunino Ignacio Trujillo Frazer R. Pearce Peter A. Thomas 《Monthly notices of the Royal Astronomical Society》2007,375(1):184-190
Using the Millennium N -body Simulation we explore how the shape and angular momentum of galaxy dark matter haloes surrounding the largest cosmological voids are oriented. We find that the major and intermediate axes of the haloes tend to lie parallel to the surface of the voids, whereas the minor axis points preferentially in the radial direction. We have quantified the strength of these alignments at different radial distances from the void centres. The effect of these orientations is still detected at distances as large as 2.2 R void from the void centre. Taking a subsample of haloes expected to contain disc-dominated galaxies at their centres we detect, at the 99.9 per cent confidence level, a signal that the angular momentum of those haloes tends to lie parallel to the surface of the voids. Contrary to the alignments of the inertia axes, this signal is only detected in shells at the void surface (1 < R < 1.07 R void ) and disappears at larger distances. This signal, together with the similar alignment observed using real spiral galaxies, strongly supports the prediction of the Tidal Torque theory that both dark matter haloes and baryonic matter have acquired, conjointly, their angular momentum before the moment of turnaround. 相似文献