Earth's Angular Momentum Research Articles

The Earth's rotational modes revisited

In the conventional treatment of the Earth's rotational dynamics using the Earth's angular momentum description (AMD), it is customary to assume that the velocity/displacement of a mass element in the liquid core (LC) has a displacement as well as an explicit rigid rotation component in addition to the uniform (solid-body) rotation. This makes for a very complex set of non-linear differential equations in the treatment of the dynamics of this body. In this work, I will use a simple three-layer Earth model with a rigid mantle (MT), a rigid inner core (IC), and an incompressible and homogeneous LC to show that in the alternative linearised dynamics of this body, it is redundant to assign a rigid rotation component to the motion. Next, I will use an approximation commonly used in dealing with the Earth's rotational dynamics, and further assume that the MT rotates uniformly, to show that the linearised equations yield identical analytical results to those in the literature for the periods of the inner-core wobble (ICW) and the free inner-core nutation (FICN).

Exchange interactions in two-state systems: rare earth pyrochlores

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.

The Little Ice Age was 1.0–1.5 °C cooler than current warm period according to LOD and NAO

We study the yearly values of the length of day (LOD, 1623-2016) and its link to the zonal index (ZI, 1873-2003), the Northern Atlantic oscillation index (NAO, 1659-2000) and the global sea surface temperature (SST, 1850-2016). LOD is herein assumed to be mostly the result of the overall circulations occurring within the ocean-atmospheric system. We find that LOD is negatively correlated with the global SST and with both the integral function of ZI and NAO, which are labeled as IZI and INAO. A first result is that LOD must be driven by a climatic change induced by an external (e.g. solar/astronomical) forcing since internal variability alone would have likely induced a positive correlation among the same variables because of the conservation of the Earth's angular momentum. A second result is that the high correlation among the variables implies that the LOD and INAO records can be adopted as global proxies to reconstruct past climate change. Tentative global SST reconstructions since the 17th century suggest that around 1700, that is during the coolest period of the Little Ice Age (LIA), SST could have been about 1.0-1.5 {\deg}C cooler than the 1950-1980 period. This estimated LIA cooling is greater than what some multiproxy global climate reconstructions suggested, but it is in good agreement with other more recent climate reconstructions including those based on borehole temperature data.

A demonstration of the conservation of the orbital angular momentum of Earth

We describe a simple but quantitative experiment to demonstrate the conservation of angular momentum. We measure the correlation of the apparent radius and angular velocity of the Sun with respect to the stars, due to the conservation of the angular momentum of Earth in its orbit. We also determine the direction of Earth's angular momentum vector and show that it is conserved. The experiment can be performed using a small telescope and a digital camera. It is conceptually simple, allowing students to get direct physical insight from the data. The observations are performed near the resolution limit imposed by the atmosphere, and in the presence of strong competing effects. These effects necessitate a careful experimental setup and allow students to improve their skills in experimentation.

Toughness Evaluation of LARES Satellite Tungsten Alloy

LARES (LAser RElativity Satellite) is a passive satellite, it was launched on February 13, 2012 using the new European Space Agency (ESA) launcher VEGA, to measure with high accuracy the effect of the Earth angular momentum on the spacetime geometry that in turn affect the orbital motion of a satellite. This effect is called frame-dragging or Lense-Thirring effect. The reduction of the surface-to-mass ratio is the most important parameter in this respect. A tungsten alloy has been chosen as the best cost effective solution. The LARES 2 mission has been recently proposed aiming at the construction and launch of a second LARES satellite which, in one possible configuration, has a larger diameter and mass. During the LARES manufacturing some issues related to the low fracture toughness of tungsten alloys were evident, the most critical parts being the screws used in the retroreflectors mounting system. The aim of this work, on the basis of all these considerations, is to measure the fracture toughness of this alloy in order to evaluate, in a second stage, feasible thermomechanical treatments that should be able to increase safety margins.

Spatial and temporal variations of atmospheric angular momentum and its relation to the earth length of day

The characteristics of atmospheric-angular-momentum (AAM) and length-of-day (LOD) on different timescales are investigated in this paper, on the basis of the NECP/NCAR reanalysis data and an LOD dataset for 1962–2010. The variation and overall trend of the AAM anomaly (AAMA) at different latitudes are presented, and the relationship between AAMA and LOD is discussed. The AAMAs in different latitude regions exhibit different patterns of variation, and the AAMA in the tropics makes a dominant contribution to the global AAMA. In the tropics, the AAMA propagates poleward to the extratropical regions. It is confirmed that a downward propagation of the AAMA occurs in the lower stratosphere. Correlation analysis shows that the relationship between AAMA and LOD varies significantly on different timescales. Specifically, the tropical AAMA is positively correlated with LOD on short timescales, but they are not obviously correlated on long timescales. This indicates that the interaction between AAM and the earth’s angular momentum follows the conservative restriction on short timescales, but the influence of the earth angular momentum on that of the atmosphere depends on the interaction process on long timescales.

Dense Plasma Focus: A question in search of answers, a technology in search of applications

Diagnostic information accumulated over four decades of research suggests a directionality of toroidal motion for energetic ions responsible for fusion neutron production in the Dense Plasma Focus (DPF) and existence of an axial component of magnetic field even under conditions of azimuthal symmetry. This is at variance with the traditional view of Dense Plasma Focus as a purely irrotational compressive flow. The difficulty in understanding the experimental situation from a theoretical standpoint arises from polarity of the observed solenoidal state: three independent experiments confirm existence of a fixed polarity of the axial magnetic field or related azimuthal current. Since the equations governing plasma dynamics do not have a built-in direction, the fixed polarity must be related with initial conditions: the plasma dynamics must interact with an external physical vector in order to generate a solenoidal state of fixed polarity. Only four such external physical vectors can be identified: the earth's magnetic field, earth's angular momentum, direction of current flow and the direction of the plasma accelerator. How interaction of plasma dynamics with these fields can generate observed solenoidal state is a question still in search of answers; this paper outlines one possible answer. The importance of this question goes beyond scientific curiosity into technological uses of the energetic ions and the high-power-density plasma environment. However, commercial utilization of such technologies faces reliability concerns, which can be met only by first-principles integrated design of globally-optimized industrial-quality DPF hardware. Issues involved in the emergence of the Dense Plasma Focus as a technology platform for commercial applications in the not-too-distant future are discussed.

Analysis of vertically propagating convectively coupled equatorial waves using observations and a non‐hydrostatic Boussinesq model on the equatorial beta‐plane

AbstractA non‐hydrostatic model on the equatorial beta‐plane is solved for the most basic solutions of vertically and zonally propagating internal plane waves. Solutions tilt in the vertical and propagate upward, with buoyancy as a principal restoring force. Results indicate that when frequency is of the same order of magnitude as a reduced buoyancy frequency, the shallow‐water model equivalent depth depends on frequency. One consequence of this dependence is that Kelvin waves become dispersive at high frequencies. In a complementary observational analysis, linear regression and a space‐time wavelet spectrum analysis of observed convectively coupled mixed Rossby gravity (MRG) waves are applied to estimate vertical wavelengths that are consistent with the strongest signals associated with observed convectively coupled waves at specific zonal wave numbers and frequencies. Substitution of these dispersion parameters into the model yields theoretical structures characterized by vertical and horizontal wavenumbers and frequencies similar to those observed in the lower and middle troposphere. These model solutions demonstrate that the Coriolis terms associated with the horizontal component of the earth's angular momentum explain substantial meridional tilts and phase shifts between quantities associated with observed convectively coupled waves, especially proximate to the surface of the Earth. Copyright © 2011 Royal Meteorological Society

The role of storm-relative advection of absolute angular momentum in strengthening of Atlantic tropical cyclones

[1] This study examined absolute angular momentum tendency in Atlantic tropical cyclones. Each advective and torque term in the storm-relative Eulerian absolute angular momentum tendency equation was calculated in a storm relative reference frame using modeled and observational data. 18 storms between 2004 and 2006 were simulated using the hurricane weather research and forecast model. In addition, the storm-relative advection of absolute angular momentum was calculated using reconnaissance aircraft wind data from 12 Atlantic hurricanes which occurred between 2003 and 2007. Through methods of statistical correlation, categorical composition and linear regression, it was found that mid-level horizontal advection of relative angular momentum was most relevant to 12 hour strength change in the modeled tropical cyclones. Mid-level horizontal advection of relative angular momentum was most relevant to intensity change in the observed hurricanes, while mid-level advection of Earth's angular momentum was found to be most closely related to strength change in observed hurricanes.

On the anomalous secular increase of the eccentricity of the orbit of the Moon

A recent analysis of a Lunar Laser Ranging (LLR) data record spanning 38.7 yr revealed an anomalous increase of the eccentricity of the lunar orbit amounting to de/dt_meas = (9 +/- 3) 10^-12 yr^-1. The present-day models of the dissipative phenomena occurring in the interiors of both the Earth and the Moon are not able to explain it. We examine several dynamical effects, not modeled in the data analysis, in the framework of long-range modified models of gravity and of the standard Newtonian/Einsteinian paradigm. It turns out that none of them can accommodate de/dt_meas. Many of them do not even induce long-term changes in e; other models do, instead, yield such an effect, but the resulting magnitudes are in disagreement with de/dt_meas. In particular, the general relativistic gravitomagnetic acceleration of the Moon due to the Earth's angular momentum has the right order of magnitude, but the resulting Lense-Thirring secular effect for the eccentricity vanishes. A potentially viable Newtonian candidate would be a trans-Plutonian massive object (Planet X/Nemesis/Tyche) since it, actually, would affect e with a non-vanishing long-term variation. On the other hand, the values for the physical and orbital parameters of such a hypothetical body required to obtain the right order of magnitude for de/dt are completely unrealistic. Moreover, they are in neat disagreement with both the most recent theoretical scenarios envisaging the existence of a distant, planetary-sized body and with the model-independent constraints on them dynamically inferred from planetary motions. Thus, the issue of finding a satisfactorily explanation for the anomalous behavior of the Moon's eccentricity remains open.

Engineering and scientific aspects of LARES satellite

LAser RElativity Satellite (LARES) is an Italian passive satellite designed for the accurate test of a phenomenon predicted by Einstein General Relativity called frame-dragging, or gravitomagnetism, i.e., the Earth angular momentum generates spacetime curvature that causes an additional perturbation of the satellite orbit, called the Lense–Thirring effect. LARES is a laser-ranged satellite of the type of the two LAGEOS satellites already orbiting the Earth. Data from these three satellites will also be used to improve the accuracy in the measurement of the Lense–Thirring effect.

Closure in the Earth's angular momentum budget observed from subseasonal periods down to four days: No core effects needed

Short period variations in the Earth's rotation rate, length‐of‐day (LOD), are driven mainly by the atmosphere with smaller contributions by the oceans. Previous studies have noted a lag of atmospheric angular momentum (AAM) with LOD that would imply another source. We examine AAM from the European Centre for Medium‐Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) reanalysis series, along with oceanic angular momentum (OAM) from the ECCO consortium; land hydrological effects made no discernible impact. The NCEP reanalysis together with OAM produces a significant lag with LOD, while the ECMWF reanalysis AAM with OAM shows no phase lag. We find significant coherence with LOD variations down to periods of 4 days; coherence losses at shorter periods likely arise from the inverted barometer assumption and unmodeled dynamical processes. Thus the inclusion of core effects is not needed to balance the axial angular momentum budget on sub‐seasonal time scales.

WILL IT BE POSSIBLE TO MEASURE INTRINSIC GRAVITOMAGNETISM WITH LUNAR LASER RANGING?

In this paper we mainly explore the possibility of measuring the action of the intrinsic gravitomagnetic field of the rotating Earth on the orbital motion of the Moon with the lunar laser ranging (LLR) technique. Expected improvements in it should push the precision in measuring the Earth–Moon range to the mm level; the present-day root mean square (RMS) accuracy in reconstructing the radial component of the lunar orbit is about 2 cm; its harmonic terms can be determined at the mm level. The current uncertainty in measuring the lunar precession rates is about 10-1 milliarcseconds per year. The Lense–Thirring secular — i.e. averaged over one orbital period — precessions of the node and the perigee of the Moon induced by the Earth's spin angular momentum amount to 10-3 milliarcseconds per year, yielding transverse and normal shifts of 10-1-10-2 cm yr-1. In the radial direction there is only a short-period — i.e. nonaveraged over one orbital revolution — oscillation with an amplitude of 10-5 m. Major limitations come also from some systematic errors induced by orbital perturbations of classical origin, such as the secular precessions induced by the Sun and the oblateness of the Moon, whose mismodeled parts are several times larger than the Lense–Thirring signal. The present analysis holds also for the Lue–Starkman perigee precession due to the multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP); indeed, it amounts to about 5 × 10-3 milliarcseconds per year.

The LAGEOS satellites orbital residuals determination and the Lense–Thirring effect measurement

The method applied since 1996 for the analysis of the orbital residuals of the LAGEOS satellites in order to measure the Lense–Thirring effect has been the subject of the present work. This method, based on the difference between the orbital elements of consecutive arcs, is explained and analysed also from the analytical point of view. It is proved that this “difference method” works well for the determination of the secular effects, as in the case of the relativistic precession induced by the Earth's angular momentum, but also very useful for the determination and study of the long-term periodic effects. Indeed, the only limitation in the determination of the periodic effects is the possibility of the reduction of their amplitude by a factor which depends from the periodicity of the given perturbation and from the orbital arc length chosen for the satellite during the data analysis. In the case of the Yarkovsky–Schach effect, the main non-gravitational perturbation seen in the LAGEOS satellites orbital residuals, in particular in its perigee rate and eccentricity vector excitation residuals, we show that the “difference method” is quite good also for the determination of the long-period perturbations induced by this subtle non-conservative force.

LAGEOS II perigee rate and eccentricity vector excitations residuals and the Yarkovsky–Schach effect

We have analysed LAGEOS II perigee rate and eccentricity vector excitation residuals over a period of about 7.8 years, adjusting and computing the satellite orbit with the full set of dynamical models included in the GEODYN II software code. The long-term behaviour of these orbital residuals appears to be characterised by several distinct frequencies which are a clear signature of the Yarkovsky–Schach perturbing effect. This non-gravitational perturbation is not included in the GEODYN II models for the orbit determination and analysis. Through an independent numerical analysis, and using the new LOSSAM model to represent the spin-axis behaviour of the satellite, we propagated the Yarkovsky–Schach effect on LAGEOS II perigee rate and compared the results obtained with the orbital residuals. We have thus been able to satisfactorily fit the amplitude of the Yarkovsky–Schach effect to the observed residuals. Our approach here has proven very successful with very positive results. We have been able to obtain a fractional reduction of about 40% of the post-fit rms with respect to the pre-fit value. When analysing the eccentricity vector residuals, we have been able to obtain a better result in the case of the real component, with a fractional reduction of the post-fit rms of about 49% of the initial value. The analysis of the effect's imaginary component in the eccentricity vector rate is more complicated and deserves additional scrutiny. In this case we need a deeper study which includes the analysis of other unmodelled and mismodelled effects acting on the imaginary component. The study performed in this paper will be of significant relevance not only for the geophysical applications involving LAGEOS II orbit analysis, but also for a refined re-analysis of the general relativistic precession produced by the Earth angular momentum, i.e., the Lense-Thirring effect.

Atmospheric torques on land and ocean and implications for Earth's angular momentum budget

The exchange of angular momentum between the atmosphere and the oceans and solid Earth is examined using 40 years of atmospheric angular momentum (AAM) and ocean and land torque data from the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis. Land torques are the dominant driving mechanism for AAM at submonthly periods. Ocean torques are as important as land torques at periods of 3 months and longer, however. With the exception of the annual and semiannual bands the ocean torque seems to mainly damp the AAM signals. The importance of the ocean torque implies a three‐way interaction among atmosphere, oceans, and solid Earth. For an ocean that simply transmits to the solid Earth the angular momentum exchanged with the atmosphere, with a delay of a few days at most, the analyzed torques imply that AAM should lead the length of day (LOD), which is contrary to the observations at monthly and longer periods. Sources of missing angular momentum variability, either from atmospheric or other origins, that can potentially explain the observed AAM and LOD phase relationship are discussed.

Wind contributions to the Earth's angular momentum budgets in seasonal variation

The atmospheric contributions to seasonal variations in length of day (LOD) and wobble are discussed for the period 1988–1997. The data sets used here are SPACE97 and EOP97C04 for LOD and wobble, respectively. Two atmospheric angular momentum (AAM) functions are calculated from the operational objective analysis data of the Japan Meteorological Agency (JMA) and the reanalysis data of the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR). Both the axial AAM functions agree well in annual variation and roughly in semiannual variation, with the function inferred from the observed LOD. The two equatorial AAM functions show the different wind contributions to the function inferred from the observed wobble, in both annual and semiannual variations, which are attributable in part to the different vertical wind integration methods between NCEP/NCAR and JMA. The equatorial tropospheric wind contributions, calculated by the same method, are found to show discrepancies arising from the different tropospheric regional winds associated with the Asian monsoon.

Some similarities of expansion phenomena in the vicinity of the earth and in the universe as a whole

Some expansion phenomena in the immediate vicinity of the Earth and their influence on the Earth's angular momentum are considered. It is noted that the tidal mechanism which is traditionally used to explain the lunar retreat is actually unfounded. These expansion effects are compared with the Hubble expansion of the universe and their similarity is shown. A way for the solution of the lunar retreat paradox is suggested combining the tidal effects and Hubble expansion. An increase of the Earth-Sun distance is predicted and the rate of this removal is estimated.

Angular momentum exchange among the solid Earth, atmosphere, and oceans: A case study of the 1982–1983 El Niño event

The 1982–1983 El Nino/Southern Oscillation (ENSO) event was accompanied by the largest interannual variation in the Earth's rotation rate on record. In this study we demonstrate that atmospheric forcing was the dominant cause for this rotational anomaly, with atmospheric angular momentum (AAM) integrated from 1000 to 1 mbar (troposphere plus stratosphere) accounting for up to 92% of the interannual variance in the length of day (LOD). Winds between 100 and 1 mbar contributed nearly 20% of the variance explained, indicating that the stratosphere can play a significant role in the Earth's angular momentum budget on interannual time scales. Examination of LOD, AAM, and Southern Oscillation Index (SOI) data for a 15‐year span surrounding the 1982–1983 event suggests that the strong rotational response resulted from constructive interference between the low‐frequency (∼4–6 year) and quasi‐biennial (∼2–3 year) components of the ENSO phenomenon, as well as the stratospheric Quasi‐Biennial Oscillation (QBO). Sources of the remaining LOD discrepancy (∼55 and 64 μs rms residual for the European Centre for Medium‐Range Forecasting (EC) and U.S. National Meteorological Center (NMC) analyses) are explored; noise and systematic errors in the AAM data are estimated to contribute 18 and 33 μs, respectively, leaving a residual (rms) of 40 (52) μs unaccounted for by the EC (NMC) analysis. Oceanic angular momentum contributions (both moment of inertia changes associated with baroclinic waves and motion terms) are shown to be candidates in closing the interannual axial angular momentum budget.

Comment on ″A seasonal budget of the Earth's axial angular momentum″by Naito and Kikuchi

Comment on ″A seasonal budget of the Earth's axial angular momentum″by Naito and Kikuchi