The Variation in J2 and in the Moments of Inertia: Satellite Results and Consequences for the Angular Momentum Budget of the Earth-Moon-Sun System

1990 ◽  
pp. 52-57 ◽  
Author(s):  
M. Burša
Keyword(s):  
Angular Momentum ◽  
Moments Of Inertia ◽  
The Earth ◽  
Momentum Budget

scholarly journals Isentropic Pressure and Mountain Torques

2009 ◽  
Vol 137 (9) ◽  
pp. 3047-3054 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Potential Temperature ◽  
Polar Caps ◽  
The Earth ◽  
Momentum Budget

Abstract The relation of pressure torques and mountain torques is investigated on the basis of observations for the polar caps, two midlatitude and two subtropical belts, and a tropical belt by evaluating the lagged covariances of these torques for various isentropic surfaces. It is only in the polar domains and the northern midlatitude belts that the transfer of angular momentum to and from the earth at the mountains is associated with pressure torques acting in the same sense. The situation is more complicated in all other belts. The covariances decline with increasing potential temperature (height). The role of both torques in the angular momentum budget of a belt is discussed.

Axial Atmospheric Angular Momentum Budget at Diurnal and Subdiurnal Periodicities

2008 ◽  
Vol 65 (1) ◽  
pp. 156-171 ◽  
Author(s):  
François Lott ◽  
Olivier de Viron ◽  
Pedro Viterbo ◽  
François Vial
Keyword(s):  
Boundary Layer ◽  
Angular Momentum ◽  
Surface Pressure ◽  
Vertical Direction ◽  
Zonal Flow ◽  
Atmospheric Angular Momentum ◽  
Model Driven ◽  
The Earth ◽  
Momentum Budget ◽  
Diurnal Period

Abstract The diurnal and subdiurnal variations of the mass and wind terms of the axial atmospheric angular momentum (AAM) are explored using a 1-yr integration of the Laboratoire de Météorologie Dynamique (LMDz) GCM, twelve 10-day ECMWF forecasts, and some ECMWF analysis products. In these datasets, the wind and mass AAMs present diurnal and semidiurnal oscillations for which tendencies far exceed the total torque. In the LMDz GCM, these diurnal and semidiurnal oscillations are associated with axisymmetric (s = 0) and barotropic circulation modes that resemble the second gravest (n = 2) eigensolution of Laplace’s tidal equations. This mode induces a Coriolis conversion from the wind AAM toward the mass AAM that far exceeds the total torque. At the semidiurnal period, this mode dominates the axisymmetric and barotropic circulation. At the diurnal period, this n = 2 mode is also present, but the barotropic circulation also presents a mode resembling the first gravest n = 1 eigensolution of the tidal equations. This last mode does not produce anomalies in the mass and wind AAMs. A shallow-water axisymmetric model driven by zonal mean zonal forces, for which the vertical integral equals the zonal mean zonal stresses issued from the GCM, is then used to interpret these results. This model reproduces well the semidiurnal oscillations in mass and wind AAM, and the semidiurnal mode resembling the n = 2 eigensolution that produces them, when the forcing is distributed barotropically in the vertical direction. This model also reproduces diurnal modes resembling the n = 1 and n = 2 eigensolutions when the forcings are distributed more baroclinically. Among the dynamical forcings that produce these modes of motion, it is found that the mountain forcing and the divergence of the AAM flux are equally important and are more efficient than the boundary layer friction. In geodesy, the large but opposite signals in the mass and wind AAM due to the n = 2 modes can lead to large errors in the evaluation of the AAM budget. The n = 2 responses in surface pressure can affect the earth ellipcity, and the n = 1 diurnal response can affect the geocenter position. For the surface pressure tide, the results suggest that the dynamical forcings of the zonal-mean zonal flow are a potential cause for its s = 0 component.

Discrepancies in the Earth-atmosphere angular momentum budget

1990 ◽  
Vol 95 (B1) ◽  
pp. 265 ◽  
Author(s):  
Richard D. Rosen ◽  
David A. Salstein ◽  
Tamara M. Wood
Keyword(s):  
Angular Momentum ◽  
Earth Atmosphere ◽  
The Earth ◽  
Momentum Budget

Addendum 2020 to ‘Measurement of the Earth’s rotation: 720 BC to AD 2015’

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200776
Author(s):  
L. V. Morrison ◽  
F. R. Stephenson ◽  
C. Y. Hohenkerk ◽  
M. Zawilski
Keyword(s):  
Angular Momentum ◽  
Earth’S Rotation ◽  
The Sun ◽  
Earth's Rotation ◽  
Moon System ◽  
Link Type ◽  
The Earth ◽  
Solar Eclipses ◽  
Rotation Of The Earth

Historical reports of solar eclipses are added to our previous dataset (Stephenson et al. 2016 Proc. R. Soc. A 472 , 20160404 ( doi:10.1098/rspa.2016.0404 )) in order to refine our determination of centennial and longer-term changes since 720 BC in the rate of rotation of the Earth. The revised observed deceleration is −4.59 ± 0.08 × 10 −22  rad s −2 . By comparison the predicted tidal deceleration based on the conservation of angular momentum in the Sun–Earth–Moon system is −6.39 ± 0.03 × 10 −22  rad s −2 . These signify a mean accelerative component of +1.8 ± 0.1 × 10 −22  rad s −2 . There is also evidence of an oscillatory variation in the rate with a period of about 14 centuries.

scholarly journals Accretion of the Moon from non-canonical discs

2014 ◽  
Vol 372 (2024) ◽  
pp. 20130256 ◽  
Author(s):  
J. Salmon ◽  
R. M Canup
Keyword(s):  
Angular Momentum ◽  
Rotation Period ◽  
Major Axis ◽  
The Moon ◽  
Large Excess ◽  
Semi Major Axis ◽  
Earth’S Mantle ◽  
The Earth ◽  
Post Impact ◽  
Impact Simulations

Impacts that leave the Earth–Moon system with a large excess in angular momentum have recently been advocated as a means of generating a protolunar disc with a composition that is nearly identical to that of the Earth's mantle. We here investigate the accretion of the Moon from discs generated by such ‘non-canonical’ impacts, which are typically more compact than discs produced by canonical impacts and have a higher fraction of their mass initially located inside the Roche limit. Our model predicts a similar overall accretional history for both canonical and non-canonical discs, with the Moon forming in three consecutive steps over hundreds of years. However, we find that, to yield a lunar-mass Moon, the more compact non-canonical discs must initially be more massive than implied by prior estimates, and only a few of the discs produced by impact simulations to date appear to meet this condition. Non-canonical impacts require that capture of the Moon into the evection resonance with the Sun reduced the Earth–Moon angular momentum by a factor of 2 or more. We find that the Moon's semi-major axis at the end of its accretion is approximately 7 R ⊕ , which is comparable to the location of the evection resonance for a post-impact Earth with a 2.5 h rotation period in the absence of a disc. Thus, the dynamics of the Moon's assembly may directly affect its ability to be captured into the resonance.

scholarly journals Boundary conditions for the formation of the Moon

2015 ◽  
Vol 95 (2) ◽  
pp. 131-139 ◽  
Author(s):  
M. Reuver ◽  
R.J. de Meijer ◽  
I.L. ten Kate ◽  
W. van Westrenen
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Total Angular Momentum ◽  
Nuclear Explosion ◽  
Moment Of Inertia ◽  
The Moon ◽  
Moon System ◽  
Giant Impact ◽  
The Earth ◽  
The Impact

AbstractRecent measurements of the chemical and isotopic composition of lunar samples indicate that the Moon's bulk composition shows great similarities with the composition of the silicate Earth. Moon formation models that attempt to explain these similarities make a wide variety of assumptions about the properties of the Earth prior to the formation of the Moon (the proto-Earth), and about the necessity and properties of an impactor colliding with the proto-Earth. This paper investigates the effects of the proto-Earth's mass, oblateness and internal core-mantle differentiation on its moment of inertia. The ratio of angular momentum and moment of inertia determines the stability of the proto-Earth and the binding energy, i.e. the energy needed to make the transition from an initial state in which the system is a rotating single body with a certain angular momentum to a final state with two bodies (Earth and Moon) with the same total angular momentum, redistributed between Earth and Moon. For the initial state two scenarios are being investigated: a homogeneous (undifferentiated) proto-Earth and a proto-Earth differentiated in a central metallic and an outer silicate shell; for both scenarios a range of oblateness values is investigated. Calculations indicate that a differentiated proto-Earth would become unstable at an angular momentum L that exceeds the total angular momentum of the present-day Earth–Moon system (L0) by factors of 2.5–2.9, with the precise maximum dependent on the proto-Earth's oblateness. Further limitations are imposed by the Roche limit and the logical condition that the separated Earth–Moon system should be formed outside the proto-Earth. This further limits the L values of the Earth–Moon system to a maximum of about L/L0 = 1.5, at a minimum oblateness (a/c ratio) of 1.2. These calculations provide boundary conditions for the main classes of Moon-forming models. Our results show that at the high values of L used in recent giant impact models (1.8 < L/L0 < 3.1), the proposed proto-Earths are unstable before (Cuk & Stewart, 2012) or immediately after (Canup, 2012) the impact, even at a high oblateness (the most favourable condition for stability). We conclude that the recent attempts to improve the classic giant impact hypothesis by studying systems with very high values of L are not supported by the boundary condition calculations in this work. In contrast, this work indicates that the nuclear explosion model for Moon formation (De Meijer et al., 2013) fulfills the boundary conditions and requires approximately one order of magnitude less energy than originally estimated. Hence in our view the nuclear explosion model is presently the model that best explains the formation of the Moon from predominantly terrestrial silicate material.

scholarly journals Wave Forcing of Zonal Mean Angular Momentum in Various Coordinate Systems

2014 ◽  
Vol 71 (6) ◽  
pp. 2221-2229
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka
Keyword(s):  
Angular Momentum ◽  
Weighted Averaging ◽  
Coordinate Systems ◽  
Mean Flow ◽  
Flux Divergence ◽  
Standard Case ◽  
Wave Forcing ◽  
Momentum Budget ◽  
Flow Part ◽  
Isentropic Coordinates

Abstract The wave forcing of the atmospheric mean flow in isentropic coordinates has been investigated intensively in the past with the divergence of the Eliassen–Palm flux playing a dominating role. These concepts are reviewed briefly and it is pointed out that angular momentum is attractive in this context because the wave driving can be written in the form of a flux divergence. This helps to evaluate the wave forcing in other coordinate systems with a different separation of waves and mean flow. The following coordinates are chosen: (λ, φ, z), (λ, φ, θ), and (λ, θ, z). To be consistent, only one type of zonal averaging should be used. Mass-weighted averaging is applied in the isentropic standard case and simple averaging is applied in the others. The wave driving is presented for all three systems. It has to balance essentially the mean-flow part of the “Coriolis term” in the angular momentum budget in (φ, z) and (θ, z) coordinates but not in the (φ, θ) system where the form drag is a mean-flow term and, therefore, the forcing pattern differs from what has been published so far.

scholarly journals Division I Working Group on “Precession and the Ecliptic”

2005 ◽  
Vol 1 (T26A) ◽  
pp. 67-67
Author(s):  
James L. Hilton ◽  
N. Capitaine ◽  
J. Chapront ◽  
J.M. Ferrandiz ◽  
A. Fienga ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Division I ◽  
General Assembly ◽  
Angular Momentum Vector ◽  
Inertial Reference Frame ◽  
Matrix Representations ◽  
Momentum Vector ◽  
Polynomial Coefficients ◽  
The Earth ◽  
The Mean

AbstractThe WG has conferred via email on the topics of providing a precession theory dynamically consistent with the IAU 2000A nutation theory and updating the expressions defining the ecliptic. The consensus of the WG is to recommend:(a) The terms lunisolar precession and planetary precession be replaced by precession of the equator and precession of the ecliptic, respectively.(b) The IAU adopt the P03 precession theory, of Capitaine et al (2003a, A& A 412, 567–586) for the precession of the equator (Eqs. 37) and the precession of the ecliptic (Eqs. 38); the same paper provides the polynomial developments for the P03 primary angles and a number of derived quantities for use in both the equinox based and celestial intermediate origin based paradigms.(c) The choice of precession parameters be left to the user.(d) The recommended polynomial coefficients for a number of precession angles are given in Table 1 of the WG report, including the P03 expressions set out in Tables 3–;5 of Capitaine et al (2005, A& A 432, 355–;367), and those of the alternative Fukushima (2003, AJ 126, 494–;534) parameterization; the corresponding matrix representations are given in equations 1, 6, 11, and 22 of the WG report.(e) The ecliptic pole should be explicitly defined by the mean orbital angular momentum vector of the Earth-Moon barycenter in an inertial reference frame, and this definition should be explicitly stated to avoid confusion with older definitions. The formal WG report will be submitted, shortly to Celest. Mech. for publication and their recommendations will be submitted at the next General Assembly for adoption by the IAU.

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