Precession Of Equinoxes Research Articles

On a dynamo driven by topographic precession

More than half a century ago, Bullard suggested that the Earth's dynamo might be driven by the motions created in the Earth's core by the luni-solar precession. The precessionally forced motion of the mantle drives core flow through viscous forces and also, because of the electrical conductivity of the deep mantle, through magnetic forces. Both these couplings are thought to be insignificant in comparison with the topographical coupling created by the oblateness of the core-mantle interface. Because of technical difficulties in studying dynamo action in non-spherical bodies of electrically conducting fluid, this is the first serious attempt to study dynamo action by topographically forced flows. It describes the novel numerical methods that were employed, the tests that were devised to validate these methods, and the successful outcome of those tests. Some preliminary results for these dynamos are presented. It is shown that, in some parameter ranges, the magnetic field produced by the dynamos enhances the vigor of the precessional motions.

Stability Analysis of a Flexible Spinning and Precessing Rotor with Non-symmetric Shaft

The present work deals with stability analysis of a spinning non-symmetric shaft with a non-central disk mounted on a rotating (precessing) base, where the spin axis and the precession axis intersect at right angles. The nutation speed is zero and the spin and precession speeds are considered to be uniform. The motion of the rotor is such that it undergoes small elastic deformation superposed on rigid body rotation. The shaft-disk system is assumed to be axially and torsionally stiff. A four-degree- of-freedom model is considered for the stability analysis. A non-symmetric shaft (e.g., shaft with rectangular or elliptic cross-section, shaft with a keyway, cracked shaft etc.) of a rotor has dissimilar stiffness in two perpendicular transverse planes. The governing equations for such a rotor are expressed in the precessing but non-spinning frame. Since the governing equations of motion are found to have periodic stiffness terms, a variant of Hill’s method is adopted for stability analysis. The stability borderlines are constructed with respect to the spin speed and precession speed.

Super-rotation flow in a precessing sphere

The super rotation here means that the majority of fluid inside a precessing sphere rotates around the precession axis with angular velocity larger than that of the precession rotation itself. This phenomenon observed experimentally and numerically is explained to be driven by a cooperative interplay between the Coriolis force, the pressure gradient and the spherical geometry in the boundary layer.

Semianalytical Study of Geosynchronous Orbits About a Precessing Oblate Earth Under Lunisolar Gravitation and Tesseral Resonance

Previous studies of geosynchronous orbits indicated that the equinoctial precession (EP) of the Earth affects the long-term behavior of geosynchronous satellites for missions exceeding ten years. However, these studies did not include the lunisolar gravitation and tesseral resonance. In the present study, a model that includes the latter effects is developed. In particular, it is shown that the EP affects motion in the vicinity of the stable and unstable geostationary points. This effect is pronounced in the vicinity of the unstable points, shifting the satellite away from the geosynchronous altitude. Moreover, it is shown that secular inclination growth on time scales of 10–20 years is induced by the EP. This requires additional stationkeeping maneuvers that may increase the overall fuel usage by about 1%. An additional contribution of the present study is an analysis of EP-perturbed orbits with free inclination drift. An optimal initial node location, minimizing the inclination drift, is calculated while taking into account the effect of the EP. It is shown that the classical optimal initial node locations are changed due to the effect of the EP. A maneuvering program in the presence of EP is developed. It is shown that the timing and number of stationkeeping maneuvers is affected by the EP. The models developed herein utilize non-singular orbital elements.

The Effect of Lunisolar Precession on Pulsar Observations

In the measurements of pulsars’ periods and their rates of change there exists the effect of lunisolar precession. Via the analysis of this effect, we find that it can affect the accurate measurements of the periods of certain pulsars. An investigation of the periods of 1771 pulsars reveals that the measured periods of 81 pulsars suffer the influence of lunisolar precession in the range of the accuracy of measurements. With the improvement of the precision of measurements of pulsars’ periods and their change rates, this effect should get the corresponding corrections.

Les gravures rupestres des Pléiades de la montagne sacrée du Bego, Tende, Alpes-Maritimes, France

The stellar cluster of the Pleiads is depicted on two carved rocks in the Merveilles valley, in the mont Bego region, by six main zones, surrounded by several scattered cupmarks. On one of these rocks, referred to as “the Dancer”, the stellar cluster of the Pleiads is depicted above a carved halberd in a westerly direction, suggesting the heliac setting. On the other, the rock referred to as “the Pleiads”, the stellar cluster is depicted in the south, suggesting its zenith. Taking the precession of the equinoxes into account, it is possible to determine the date in the year of the heliac setting of the Pleiads in the west if the millennium is known. The latter is estimated between 3300 and 1800 years BC by comparing the types of arms carved into the rocks with those discovered in archaeological sites. Although today it is difficult to reach the Merveilles valley during the month of March because of snow, it was probably possible between 3000 and 2000 years before our era, at the end of the Atlantic period, during the Chalcolithic climatic optimum, when the climate was slightly warmer than at present.

Accurate Analytical and Statistical Approaches to Reduce O-C Discrepancies in the Precessional Parameters

ABSTRACTThe Hipparcos catalog provides a reference frame at optical wavelengths for the new International Celestial Reference System (ICRS). This new reference system was adopted following the resolution agreed at the 23rd IAU General Assembly held in Kyoto in 1997. Differences in the Hipparcos system of proper motions and the previous materialization of the reference frame, the FK5, are expected to be caused only by the combined effects of the motion of the equinox of the FK5 and the precession of the equator and the ecliptic. Several authors have pointed out an inconsistency between the differences in proper motion of the Hipparcos-FK5 and the correction of the precessional values derived from VLBI and lunar laser ranging (LLR) observations. Most of them have claimed that these discrepancies are due to slightly biased proper motions in the FK5 catalog. The different mathematical models that have been employed to explain these errors have not fully accounted for the discrepancies in the correction of the precessional parameters. Our goal here is to offer an explanation for this fact. We propose the use of independent parametric and nonparametric models. The introduction of a nonparametric model, combined with the inner product in the square integrable functions over the unitary sphere, would give us values which do not depend on the possible interdependencies existing in the data set. The evidence shows that zonal studies are needed. This would lead us to introduce a local nonparametric model. All these models will provide independent corrections to the precessional values, which could then be compared in order to study the reliability in each case. Finally, we obtain values for the precession corrections that are very consistent with those that are currently adopted.

On steady rotations of a rigid body bearing a single-axis powered gyroscope whose precession axis is parallel to a principal plane of inertia

The set of steady motions of the system named in the title is represented parametrically via the gyro gimbal rotation angle for an arbitrary position of the gimbal axis.

GIORDANO BRUNO AND NICOLAUS COPERNICUS

Abstract<title> ABSTRACT </title>Explaining the Copernican doctrine in a concise passage of THE ASH Wednesday Supper (La cena de le Ceneri, London, 1584), Giordano Bruno ascribed four motions to the earth, although Copernicus limited their number to three. This discrepancy may seem a mere misunderstanding, but a detailed and contextual reading of the passage reveals that Bruno, although accepting the Copernican 'idea' of explaining the motions of the sun and of the fixed stars through the displacement of our planet, Bruno probably drew these motions from Peuerbach's Theoricae novae planetarum rather than from Copernicus' De revolutionibus orbium coelestium. Thus, he 'transferred' to the earth the annual revolution and the three motions traditionally ascribed to the fixed stars (daily rotation, precession of the equinoxes and 'trepidation') to the earth: which makes four motions altogether.

Variation of the Equator due to a Highly Inclined and Eccentric Disturber

The New Horizons project is currently in progress, but until recently years ago, a mission to Neptune‐Triton System predicted in the mid term 2008–2013 was one of the priorities of NASA′s Solar System Exploration theme. Any way, it is important to increase our knowledge on the dynamics of the inner satellites of Neptune, since according to some authors, this was a key question in the mission to Neptune‐Triton system. In a previous work, we presented the expansion of the disturbing function for the dynamics of this system. Here we derive the averaged classical equations of the precession of the equator for this problem. The highly inclined and retrograde orbit of Triton makes this problem very unusual. Therefore, the classical truncations in the inclinations are not acceptable, so that the precession equations must be obtained in closed form for the inclination. With a significant mass and due to its distance from Neptune, which is continuously decreasing, Triton should exert in the future, important precession on Neptune′s equator. The effects of this precession on the inner satellites are shown, including some resonant cases predicted in the future. Although Triton′s orbit is almost circular, no expansion in the eccentricity is needed.

Streamline tori in a precessing sphere at small Reynolds numbers

The flow structure in a precessing sphere is investigated analytically and numerically at small Reynolds numbers. The spin angular velocity Ωs and the precession angular velocity Ωp are constant in magnitude and perpendicular to each other. The Navier–Stokes equation for an incompressible viscous fluid written in the precession frame is solved analytically in a power series of the Reynolds number Re(=a2Ωs/ν), where a is the sphere radius and ν is the kinematic viscosity of fluid. Steady solutions are obtained up to O(Re3) for arbitrary fixed values of the Poincaré number Γ(=Ωp/Ωs). By calculating the orbit of passive particles advected in these steady flows, we find that the individual particles move along circles centred on and perpendicular to the spin axis with small deviation of O(Re3Γ2) over one revolution and that in a long time span of O(1/(ΩsRe3Γ2)) (or O(a6Ωs2Ωp2/ν3) all the particles densely cover the whole tori, of thickness of O(Re), expressed as (x(y2+z2) in the Cartesian coordinate (x, y, z) system with x for the spin axis and z for the precession axis. There is a separatrix sphere of radius and of thickness O(Re), the fluid particles just above (or below) which can come close to the surface (or the centre) of the sphere.)

SPIN AXIS VARIATIONS OF MARS: NUMERICAL LIMITATIONS AND MODEL DEPENDENCES

Celestial mechanical integrations for the whole solar system are carried out over four billion years before and after the present. The orbital solution of the solar system is stable during this whole time period. An instantaneous spin axis model including triaxiality is developed. In particular, spin axis precession, the Martian obliquity, solar torques, and the orbital eccentricity/inclination of Mars are studied. Model dependences from general relativity, solar oblateness, the Martian moons, solar mass loss, etc. are tested. Although the obliquity of Mars sometimes shows dramatic variations, some structures are robust and seem insensitive to the initial spin precession rate. A full integration is carried out during a total of 8000 Myr resulting in a Martian obliquity that is restricted between 10 and 60°. The problems with numerical noise due to limited machine precision, integration step sizes, and the chaotic sensitivity of the solutions are studied and discussed. The limited machine precision (15-16 figures) alone is found to limit the duration of exact obliquity solutions to about 80 Myr.

Precession axis modification to a semianalytical Landau–Lifshitz solution technique

A recent article [Van de Wiele et al., IEEE Trans. Magn. 43, 2917 (2007)] presents a semianalytical method to solve the Landau–Lifshitz (LL) equation. Spin motion is computed analytically as precession about the effective field H, where H is assumed fixed over the time step. However, the exchange field dominates at short range and varies at the time scale of neighbor spin precessions, undermining the fixed field assumption. We present an axis corrected version of this algorithm. We add a scalar multiple of m to H (preserving torque and hence the LL solution) to produce a more stable precession axis parallel to the cross product of the torques m×H at two closely spaced time steps. We build a predictor-corrector solver on this foundation. The second order convergence of the solver enables calculation of adjustable time steps to meet a desired error magnitude.

Insights into homonuclear decoupling from efficient numerical simulation: Techniques and examples

A combination of techniques, including rational number synchronisation and pre-diagonalisation of the time-dependent periodic Hamiltonian, are described which allow the efficient simulation of NMR experiments involving both magic-angle spinning (MAS) and RF irradiation, particularly in the important special case of phase-modulated decoupling sequences. Chebyshev and conventional diagonalisation approaches to calculating propagators under MAS are also compared, with Chebyshev methods offering significant advantages in cases where the Hamiltonian is large and time-dependent but not block-diagonal (as is the case for problems involving combined MAS and RF). The ability to simulate extended coupled spin systems efficiently allows 1H spectra under homonuclear decoupling to be calculated directly and compared to experimental results. Reasonable agreement is found for the conditions under which homonuclear decoupling is typically applied for rigid solids (although the increasing deviation of experimental results from the predictions of theory and simulation at higher RF powers is still unexplained). Numerical simulations are used to explore three features of these experiments: the interaction between the magic-angle spinning and RF decoupling, the effects of tilt pulses in acquisition windows and the effects of “phase propagation delays” on tilted axis precession. In each case, the results reveal features that are not readily anticipated by previous analytical studies and shed light on previous empirical observations.

Long-term evolution of orbits about a precessing oblate planet: 3. A semianalytical and a purely numerical approach

Construction of an accurate theory of orbits about a precessing and nutating oblate planet, in terms of osculating elements defined in a frame associated with the equator of date, was started in Efroimsky and Goldreich (2004) and Efroimsky (2004, 2005, 2006a, b) .H ere we continue this line of research by combining that analytical machinery with numerical tools. Our model includes three factors: the J2 of the planet, its nonuniform equinoctial pre- cession described by the Colombo formalism, and the gravitational pull of the Sun. This semianalytical and seminumerical theory, based on the Lagrange planetary equations for the Keplerian elements, is then applied to Deimos on very long time scales (up to 1 billion years). In parallel with the said semianalytical theory for the Keplerian elements defined in the co-precessing equatorial frame, we have also carried out a completely independent, purely numerical, integration in a quasi-inertial Cartesian frame. The results agree to within fractions of a percent, thus demonstrating the applicability of our semianalytical model over long timescales. Another goal of this work was to make an independent check of whether the equinoctial-precession variations predicted for a rigid Mars by the Colombo model could We use the term "precession" in its general meaning, which includes any change of the instantaneous spin axis. So generally defined precession embraces the entire spectrum of spin-axis variations—from the polar wander and nutations through the Chandler wobble through the equinoctial precession.

Radiative torque alignment: essential physical processes

We study the physical processes that affect the alignment of grains subject to radiative torques (RATs). To describe the action of RATs, we use the analytical model (AMO) of RATs introduced in our previous paper. We focus our discussion on the alignment by anisotropic radiation flux with respect to the magnetic field, which defines the axis of grain Larmor precession. Such an alignment does not invoke paramagnetic dissipation (i.e. the Davis–Greenstein mechanism), but, nevertheless, grains tend to be aligned with long axes perpendicular to the magnetic field. When we account for thermal fluctuations within grains, we show that for grains that are characterized by a triaxial ellipsoid of inertia, the zero-J attractor point obtained in our earlier study develops into a low-J attractor point. The value of angular momentum at the low-J attractor point is of the order of the thermal angular momentum corresponding to the grain temperature. We show that, for situations when the direction of radiative flux is nearly perpendicular to a magnetic field, the alignment of grains with long axes parallel to the magnetic field (i.e. ‘wrong alignment’) reported in our previous paper, disappears in the presence of thermal fluctuations. Thus, all grains are aligned with their long axes perpendicular to the magnetic field. We study the effects of stochastic gaseous bombardment and show that gaseous bombardment can drive grains from low-J to high-J attractor points in cases when high-J attractor points are present. As the alignment of grain axes with respect to angular momentum is higher for higher values of J, counter-intuitively, gaseous bombardment can increase the degree of grain alignment with respect to the magnetic field. We also study the effects of torques induced by H2 formation and show that they can change the value of angular momentum at high-J attractor points, but marginally affect the value of angular momentum at low-J attractor points. We compare the AMO results with those obtained using the direct numerical calculations of RATs acting upon irregular grains and we validate the use of the AMO for realistic situations of RAT alignment.

Finding Spring on Planet X

For a given orbital period and eccentricity, we determine the maximum time lapse between the winter solstice and the spring equinox on a planet. In addition, given an axial precession path, we determine the effects on the seasons. This material can be used at various levels to illustrate ideas such as periodicity, eccentricity, polar coordinates, and vectors, in courses as diverse as precalculus, calculus, linear algebra, differential equations, and geometry.

Phase transition and molecular motion of cyclohexane confined in metal-organic framework, IRMOF-1, as studied by 2H NMR

Molecular motion and thermal properties of cyclohexane confined in [Zn 4O(O 2CC 6H 4CO 2) 3] n (IRMOF-1) were examined using 2H NMR and differential thermal analysis (DTA) measurements. DTA measurement revealed that cyclohexane confined in IRMOF-1 exhibits thermal anomaly at 121 K, 213 K and 306 K. Subsequent 2H NMR elucidated that cyclohexane undergoes precession of the C 3-axis at temperatures below 120 K and shows a tumbling motion with the large amplitude fluctuation of the precession axis from 120 K to 200 K; then isotropic reorientation is excited at temperatures above 200 K, revealing that cyclohexane in IRMOF-1 melts at 213 K.

Turbulence generator using a precessing sphere

We propose a precessing sphere as a tabletop turbulence generator, which has less uncertainty in the setting of control parameters and the resulting high flow-reproducibility. The precession is realized by rotating the spin axis of a sphere around another axis (the precession axis). In our experiments, the two axes are fixed at right angles. The flow inside the sphere is governed only by two nondimensional parameters, one being Re (the Reynolds number defined by the maximum peripheral velocity around the spin axis) and the other being Γ (the rate of precession). The range of parameters for sustaining turbulence is revealed by the time-series analysis of velocity fields measured by particle image velocimetry. Well-developed turbulence can be sustained even for Γ of the order of a few percent when Re is beyond a few thousands.

Effect of Equinoctial Precession on Geosynchronous Earth Satellites

The long-periodic effects of the equinoctial precession on geosynchronous Earth orbit satellites are investigated. The equations of motion in a reference frame that coprecesses with the Earth are developed, and the resulting variational equations are derived using mean classical orbital elements. The Earth gravitational model includes the J 2 and J 3 zonal harmonics, which induce the equinoctial precession due to the lunisolar gravitational torque. It is shown that the ever-growing lifetime and mass of geosynchronous Earth orbit satellites render the equinoctial precession a significant factor, which should be taken into account during mission design, as it affects north-south stationkeeping maneuvers. The equilibria of the variational equations including the zonal harmonics and the equinoctial precession are investigated and a class of stable frozen orbits which are equinoctial precession invariant is derived.