Imaging Borrelly

The nucleus, coma, and dust jets of short-period Comet 19P/Borrelly were imaged from the Deep Space 1 spacecraft during its close flyby in September 2001. A prominent jet dominated the near-nucleus coma and emanated roughly normal to the long axis of nucleus from a broad central cavity. We show it to have remained fixed in position for more than 34 hr, much longer than the 26-hr rotation period. This confirms earlier suggestions that it is co-aligned with the rotation axis. From a combination of fitting the nucleus light curve from approach images and the nucleus' orientation from stereo images at encounter, we conclude that the sense of rotation is right-handed around the main jet vector. The inferred rotation pole is approximately perpendicular to the long axis of the nucleus, consistent with a simple rotational state. Lacking an existing IAU comet-specific convention but applying a convention provisionally adopted for asteroids, we label this the north pole. This places the sub-solar latitude at ∼60° N at the time of the perihelion with the north pole in constant sunlight and thus receiving maximum average insolation.     

Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

Reorientation of planets with lithospheres: The effect of elastic energy

It is commonly assumed that internal energy dissipation will ultimately drive planets to principal axis rotation, i.e., where the rotation vector is aligned with the maximum principle axis, since this situation corresponds to the minimum rotational energy state. This assumption simplifies long-term true polar wander (TPW) studies since the rotation pole can then be found by diagonalizing the appropriate (non-equilibrium) inertia tensor. We show that for planets with elastic lithospheres the minimum energy state does not correspond to principal axis rotation. As the planet undergoes reorientation elastic energy is stored in the deforming lithosphere, and the state of minimum total energy is achieved before principal axis rotation. We find solutions for the TPW of planets that include this effect by calculating the elastic stresses associated with deformation, and then minimizing the total (rotational and elastic) energy. These expressions indicate that the stored elastic energy acts to reduce the effective size of the driving load (relative to predictions which do not include this energy term). Our derivation also yields expressions for the TPW-induced stress field that generalizes several earlier results. As an illustration of the new theory, we consider TPW driven by the development of the Tharsis volcanic province on Mars. Once the size of the Tharsis load and the Mars model is specified, the extended theory yields a more limited range on the possible TPW.     

Minor axis rotation and the intrinsic shape of the shell elliptical NGC 3923

We present kinematic observations of NGC 3923, one of the best-known examples of an elliptical galaxy with shells. Although NGC 3923 has no rotation on its major axis, it has minor axis rotation with an amplitude of some 20 km s⁻¹ out to 25 arcsec radius. This is possibily the result of a kinematically decoupled core, but we present arguments against this hypothesis, and if the core were formed by a merger, this must have been a different merger from that which gave rise to the shells. The minor axis rotation suggests that NGC 3923 is prolate or triaxial, at least in the inner region. A prolate geometry for the whole galaxy would favour the merger model over the interaction model for the shell formation mechanism. There is other evidence, however, that the shape of the underlying galaxy changes with radius, in which case it is possible that the minor axis rotation could be confined to the galaxy core. The kinematics could reflect a triaxial mass distribution, in which the long and short axes are aligned with the photometric major and minor axes, and the axial ratios change such that the galaxy is near-prolate in the inner regions and near-oblate at larger radii. Measuring the rotation curve to about double this radius along the minor axis, as well as offset from the nucleus along the major axis at the radius of the innermost shells, would enable the true extent of the minor axis rotation to be determined.     

Modeling of major martian magnetic anomalies: Further evidence for polar reorientations during the Noachian

Maps of the vector components of the Mars crustal magnetic field are constructed at the mapping altitude (360 to 410 km) using a selected set of data obtained with the Mars Global Surveyor magnetometer during 2780 orbits of the planet in 1999. Forward modeling calculations are then applied to six relatively strong and isolated, dominantly dipolar, magnetic anomalies for the primary purpose of estimating bulk directions of magnetization. Assuming that the magnetizing field was a (dipolar) core dynamo field centered in the planet, paleomagnetic pole positions are calculated for the six primary source bodies together with that for a seventh anomaly analyzed earlier. In agreement with several previous studies, it is found that six of the seven pole positions are clustered in what is now the northern lowlands in a region centered northwest of Olympus Mons (mean pole position: 34°±10° N, 202°±58° E). Assuming that the dynamo dipole moment vector was approximately parallel to the rotation axis, the modeling results therefore suggest a major reorientation of Mars relative to its rotation axis after magnetization was acquired. Such a reorientation may have been stimulated by internal mass redistributions associated with the formation of the northern lowlands and Tharsis, for example. A comparison of the mean paleo (magnetic) equator to the global distribution of crustal fields shows that magnetic anomalies tend to occur at low paleolatitudes. The same appears to be true for the Noachian-aged valley networks, which exhibit a broad spatial correlation with the magnetic anomalies. A possible interpretation is that the formation of magnetic anomalies and the valley networks was favored in the tropics where melting of water ice and snow was a stronger source of both surface valley erosion and groundwater recharge during the earliest history of the planet. This would be consistent with models in which hydrothermal alteration of crustal rocks played a role in producing the unusually strong martian magnetic anomalies.     

Empiric models of the Earth’s free core nutation

Free core nutation (FCN) is the main factor that limits the accuracy of the modeling of the motion of Earth’s rotational axis in the celestial coordinate system. Several FCN models have been proposed. A comparative analysis is made of the known models including the model proposed by the author. The use of the FCN model is shown to substantially increase the accuracy of the modeling of Earth’s rotation. Furthermore, the FCN component extracted from the observed motion of Earth’s rotational axis is an important source for the study of the shape and rotation of the Earth’s core. A comparison of different FCN models has shown that the proposed model is better than other models if used to extract the geophysical signal (the amplitude and phase of FCN) from observational data.     

Models of magnetic field generation in partly stable planetary cores: Applications to Mercury and Saturn

A substantial part of Mercury's iron core may be stably stratified because the temperature gradient is subadiabatic. A dynamo would operate only in a deep sublayer. We show that such a situation arises for a wide range of values for the heat flow and the sulfur content in the core. In Saturn the upper part of the metallic hydrogen core could be stably stratified because of helium depletion. The magnetic field is unusually weak in the case of Mercury and unusually axisymmetric at Saturn. We study numerical dynamo models in rotating spherical shells with a stable outer region. The control parameters are chosen such that the magnetic Reynolds number is in the range of expected Mercury values. Because of its slow rotation, Mercury may be in a regime where the dipole contribution to the internal magnetic field is weak. Most of our models are in this regime, where the dynamo field consists mainly of rapidly varying higher multipole components. They can hardly pass the stable conducting layer because of the skin effect. The weak low-degree components vary more slowly and control the structure of the field outside the core, whose strength matches the observed field strength at Mercury. In some models the axial dipole dominates at the planet's surface and in others the axial quadrupole is dominant. Differential rotation in the stable layer, representing a thermal wind, is important for attenuating non-axisymmetric components in the exterior field. In some models that we relate to Saturn the axial dipole is intrinsically strong inside the dynamo. The surface field strength is much larger than in the other cases, but the stable layer eliminates non-axisymmetric modes. The Messenger and Bepi Colombo space missions can test our predictions that Mercury's field is large-scaled, fairly axisymmetric, and shows no secular variations on the decadal time scale.     

Distribution of spin axes and senses of rotation for 20 large asteroids

Pole determinations for 20 large asteroids are presented. This is the first determination of the sense of rotation for 11 of the objects, and a sense of rotation opposite to previous results is obtained for two of the remaining nine asteroids. The spin axes are fairly isotropically distributed, with a statistically uncertain preference for prograde rotation. The mean of the component of the spin angular velocity vectors toward the north ecliptic pole is 〈ω_z〉 = (0.8 ± 0.5) rev/day. This suggests that for large asteroids an original predominance of prograde rotators has not completely been randomized by collisions (the median diameter in the present sample is approximately 200 km). Two fundamentally different pole determination methods were combined in order to get as reliable results as possible. The first is an Amplitude-Magnitude method based on triaxial ellipsoidal models. The celestial sphere is scanned with trial poles and the one is chosen for which the best fit is obtained with semiempirical amplitude-aspect-phase and magnitude-aspect-phase relationships. Triaxial approximations to the true asteroidal shapes are also obtained with this method. The second method uses the variation of the observed synodic period of rotation to derive the axis and sense of rotation. A well-defined “standard feature” in the lightcurves is selected and is assumed to remain at a fixed rotational phase. An efficient algorithm for finding the correct number of rotational cycles between observations during different apparitions is used. This makes it possible to identify extrema observed during different apparitions with each other (it is not safe to assume that, e.g., the primary maximum at one opposition remains primary at other aspect angles). Discrimination between ambiguous rotation periods can also be made with this method. 4 Vesta is shown to have one maximum and one minimum per rotational cycle. The secular variations of the period of rotation for 7 Iris and 15 Eunomia are less than 3 × 10⁻⁴ and 2 × 10⁻⁴ sec/year, respectively.     

Kinematical modeling of the Earth rotation,focusing on the Oppolzer terms in a rigid Earth and the Oppolzer-like terms in an elastic Earth

Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation (in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the motion of the outer bodies is taken into account.     

Peering over the Sun's pole: behavior of its rotational vortex

A new method for measuring spectroscopically the rotation at the Sun's poles is described. Using solar CO lines at 4.666 µm, infrared spectra are recorded at a fixed limb distance of 4.8 arc sec while progressing along an arc ±5.7 deg from the Sun's rotational pole. Since the poles dip twice a year to about 7 arc sec from the limb, our observations can range either side of and through the vortex axis. Advantages to this technique are: (1) a low disturbing signal from supergranules owing to their superposition at the limb, (2) no ‘limb shift’ error since limb distance is constant and the CO lines have no known limb shift, (3) emphasis is on the quiet Sun since the CO molecule is confined there, (4) negligible scattered light in the IR (<1%), and (5) the improved seeing afforded by the IR. Although any definitive determination of solar rotation requires observations over an extended time span, our preliminary results suggest two features peculiar to the extreme pole: (1) the occasional apparent cessation of rotation, (2) some sort of singularity, again occasional, producing a sharp velocity signal (a vortex?) within 1 deg of the pole.     

The study of excitation of the earthquake to Earth's rotation

The earthquake produces a global static displacement field due to the dislocation in the epicenter. This displacement field in turn changes the Earth's inertia tensor, hence exciting the variation of both polar motion and length of day. In general, large earthquake produces greater displacement field, which has greater effects upon the earth rotational properties. In spite of scientists efforts in the last decades, it is found that the polar motion and the length of day excited by earthquake are at least two orders of magnitude less than those derived from observation. In the future with high observational accuracy the effect of earthquake on polar motion and length of day would be observable.Using the fault plane parameters, the location of epicenter and the expression given by Dahlen as well as the step function, the accumulative change of the axial and equatorial moments of inertia of the Earth earthquake occurring in period of 1977–1994 is estimated in this paper. Results have shown that change of pole axis direction induced by single earthquake is independent of the magnitude of the earthquake, which is random, but large earthquake contributes most to the accumulative change of direction of polar drift. The earthquake tends to make the drift of rotational pole towards the direction of 130–150 E. This direction is roughly different to that inferred from observations. Accumulative changes of both the two equatorial principal moments and the axial moment of inertia of the Earth present the strongest non-randomness and secular behaviour. The change depends upon the slip angle of the fault movement in a large extent.     

脉冲星射电轮廓中高斯成分在主脉冲和中间脉冲的不同分布

研究了高斯辐射成分在可视点所画出轨迹上的分布,这个可视点因脉冲星的转动而作非匀速度运动.通过假设辐射区域围绕磁轴均匀分布,一个高斯辐射成分便对应于可视轨迹划过的一个辐射区域.因为演示辐射区域在可视轨迹上是不均匀的分布,因此高斯成分沿轨迹也是不均匀的,而高斯成分的密度在磁轴与视线距离最近时为最大.高斯成分的分布取决于脉冲星的两个角度:旋转轴和视线之间的夹角,以及磁轴和旋转轴之间的倾角.基于此模型,一个脉冲星平均轮廓中观察到的多个高斯成分便对应于可视轨迹在特定的转动相位范围内的辐射区域.演示了脉冲星旋转的近侧和远侧的相位,分别对应的主脉冲和中间脉冲,两者高斯成分的数量和分布是不同的.而且还发现,沿可视轨迹上的辐射区域总数与围绕磁轴的辐射区域的总数是不同,并且预测的辐射区域数目会因忽略可见点的运动而明显不同.拟合表明脉冲星轮廓的高斯成分的形状和数量可能与实际构成轮廓的成分的形状和数量不同.以PSR B0826–34的辐射为例,并假设辐射来自单一磁极.     

Rotation of close binary system components

The rotation of close binary system components is investigated. The principal physical characteristics as well as the equatorial rotational velocities and the axial and orbital inclinations for 46 close binary systems were determined. It is found that the rotation axes of the individual stars in a pair cross the orbital plane under different angles. As a rule, the rotation and orbital periods of a vast majority of the systems investigated here do not coincide.     

Determining a tilt in Titan’s north-south albedo asymmetry from Cassini images

Analysis of Titan’s hemispheric brightness asymmetry from mapped Cassini images reveals an axis of symmetry that is tilted with respect to the rotational axis of the solid body. Twenty images taken from 2004 through 2007 show a mean axial offset of 3.8 ± 0.9° relative to the solid body’s pole, directed 79 ± 24° to the west of the sub-solar longitude. These values are consistent with recent measurements of an implied atmospheric spin axis determined from isothermal mapping by [Achterberg, R.K., Conrath, B.J., Gierasch, P.J., Flasar, F.M., Nixon, C.A., 2008. Icarus 197, 549-555].     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Rotation effects in classical T Tauri stars

Surface temperature inhomogeneities in classical T Tauri stars (CTTS) induced by magnetic activity andmass accretion lead to rotationalmodulation of both photometric and spectroscopic parameters of these stars. Using the extended photometric catalogue byGrankin et al., we have derived the periods and amplitudes of the rotational modulation of brightness and color for 31 CTTS; for six of them, the periods have been revealed for the first time. The inclinations of the rotation axis and equatorial rotational velocities of CTTS have been determined. We show that the known periods of brightness variations for some of the CTTS are not the axial rotation periods but are the Keplerian periods near the inner boundary of the dusty disk. We have found that the angular velocity of CTTS with a mass of 0.3?3M _?? in the Taurus-Auriga complex remains constant in the age range 1?C10 Myr. CTTS on radiative evolutionary tracks rotate faster than completely convective CTTS. The specific angular momentum of CTTS depends on the absolute luminosity in the H?? line.     

The kinematical mechanism for the perturbation of the rotational axis in the rotation of the elastic Earth

Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation. First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation, A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation of the figure axis.     

Spin Axis Direction of Comet 19p/Borrelly Based on Observations from 2000 and 2001

We calculate the direction of the rotational angular momentum vector,M, of comet 19P/Borrelly based on rotational lightcurve data from 2000, groundbased imaging of the coma during the Deep Space 1encounter, and the basic near-nucleus coma morphology as revealed by the Deep Space 1 spacecraft. For the most likely direction, we derivea family of solutions (with center at RA = 221°, Dec = -7°) if the direction of M is towards the sunward hemisphere during the Deep Space 1 encounter, whereas if the rotation is of opposite sense, the diametrically opposite family of solutions (with center at RA = 41°, Dec = 7°) would result. We argue that the coma morphology in September 2001 is consistent with the nucleus being a principal axis rotator or one observationally indistinguishable from it. Therefore, for all practical purposes, the direction of the rotational angular momentum vector coincides with the spin axis. We also discuss why the determination of the spin axis direction based on observations from the last apparition is in disagreement with the current result.     

Equilibrium rotational stability and figure of Mars

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90° from the location of the massive Tharsis volcanic province. We demonstrate, using general physical arguments supported by a fluid Love number analysis, that the so-called non-hydrostatic theory is an inaccurate framework for analyzing the rotational stability of planets, such as Mars, that are characterized by long-term elastic strength within the lithosphere. In this case, the appropriate correction to the gravitational figure is the equilibrium rotating form achieved when the elastic lithospheric shell (of some thickness LT) is accounted for. Moreover, the current rotation vector of Mars is shown to be stable when the correct non-equilibrium theory is adopted using values consistent with recent, independent estimates of LT. Finally, we compare observational constraints on the figure of Mars with non-equilibrium predictions based on a large suite of possible Tharsis-driven true polar wander (TPW) scenarios. We conclude, in contrast to recent comparisons of this type based on a non-hydrostatic theory, that the reorientation of the pole associated with the development of Tharsis was likely less than 15° and that the thickness of the elastic lithosphere at the time of Tharsis formation was at least ∼50 km. Larger Tharsis-driven TPW is possible if the present-day gravitational form of the planet at degree 2 has significant contributions from non-Tharsis loads; in this case, the most plausible source would be internal heterogeneities linked to convection.     

利用光变曲线估计猎鹰九号火箭末级的旋转状态研究

光度观测是地基观测空间目标的主要手段之一,利用光度信息能够估计空间目标的相关特征信息.为了更好地了解空间目标的旋转状态,选取具有代表性的猎鹰九号火箭末级作为研究对象,由其光变信息研究旋转状态.首先利用云南天文台1.2 m光学望远镜获取猎鹰九号火箭末级的光度数据,再对目标星等进行斜距归一化,得到目标光变信息并分析目标星等...