The Earth’s Global Density Distribution and Gravitational Potential Energy

Marchenko, A. N.

doi:10.1007/978-3-540-85426-5_58

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…In view of geophysics the energy E may also be applied as an estimate of a lower limit to the mantle viscosity obtained from the rate of timechanges of E [Rubincam, 1979]. The continuous Legendre-Laplace law, Roche's law, Bullard's model, Gaussian distribution of the Earth and the piecewise continuous Roche profile were applied in Marchenko (2009) for several estimations of E that led to the inequality with minimum limit corresponding to Gauss' continuous profile and very close to the piecewise PREM model [Marchenko, Zayats, 2011]. Therefore, the comparison of all the E-estimates gives GaussEarthHmin ££<-EEEW .…”

Section: Planets Gravitational Potential Energy Conclusion and Summerymentioning

confidence: 99%

“…( 25) into Eq. ( 24 3 were computed using the direct formula (29) [Marchenko, 2009] based on the expression (24):…”

Section: Planets Gravitational Potential Energy Conclusion and Summerymentioning

confidence: 99%

“…It should be noted that the case of the Earth the Gaussian distribution of density (or the normal law) agrees best of all with the PREM-model also based on the seismic data. On the other hand, the continues Gauss' model of radial density leads to the most reliable estimation Gauss E of the potential energy E [Marchenko, 2009] taken from the piecewise PREMmodel [Marchenko, & Zayatz, 2011]…”

Section: Introductionmentioning

confidence: 99%

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Geodynamics

Marchenko¹,

Perii²,

Pokotylo³

et al. 2021

JGD

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The basic goal of this study (as the first step) is to collect the appropriate set of the fundamental astronomic-geodetics parameters for their further use to obtain the components of the density distributions for the terrestrial and outer planets of the Solar system (in the time interval of more than 10 years). The initial data were adopted from several steps of the general way of the exploration of the Solar system by iterations through different spacecraft. The mechanical and geometrical parameters of the planets allow finding the solution of the inverse gravitational problem (as the second stage) in the case of the continued Gaussian density distribution for the Moon, terrestrial planets (Mercury, Venus, Earth, Mars) and outer planets (Jupiter, Saturn, Uranus, Neptune). This law of Gaussian density distribution or normal density was chosen as a partial solution of the Adams-Williamson equation and the best approximation of the piecewise radial profile of the Earth, including the PREM model based on independent seismic velocities. Such conclusion already obtained for the Earth’s was used as hypothetic in view of the approximation problem for other planets of the Solar system where we believing to get the density from the inverse gravitational problem in the case of the Gaussian density distribution for other planets because seismic information, in that case, is almost absent. Therefore, if we can find a stable solution for the inverse gravitational problem and corresponding continue Gaussian density distribution approximated with good quality of planet’s density distribution we come in this way to a stable determination of the gravitational potential energy of the terrestrial and giant planets. Moreover to the planet’s normal low, the gravitational potential energy, Dirichlet’s integral, and other planets’ parameters were derived. It should be noted that this study is considered time-independent to avoid possible time changes in the gravitational fields of the planets.

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Section: Planets Gravitational Potential Energy Conclusion and Summerymentioning

confidence: 99%

“…( 25) into Eq. ( 24 3 were computed using the direct formula (29) [Marchenko, 2009] based on the expression (24):…”

Section: Planets Gravitational Potential Energy Conclusion and Summerymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geodynamics

Marchenko¹,

Perii²,

Pokotylo³

et al. 2021

JGD

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“…Цей принцип розглянуто також у роботах [Maxwell J., 1981, Chandrasekhar S., 1969, Moritz H., 1990. Оригінальні результати отримано в роботах [Mescheryakov G., 1977, Marchenko A., 2009, Marchenko A. and Zayats A., 2011. Виконання цього принципу передбачає, що на початковій стадії еволюції планети її матеріальні складові були переважно в розплавленому і частково в газоподібному стані.…”

Section: історична ретроспектива досліджень геодинамічних процесів щunclassified

Geodynamics

Tserklevych¹,

Shylo²,

Shylo³

2018

ГЕОДИНАМІКА

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Estimation of the gravitational potential energy of the earth based on different density models

Marchenko

Zayats

2011

Stud Geophys Geod

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The estimation of the Earth's gravitational potential energy E was obtained for different density distributions and rests on the expression E =  (W min + W) derived from the conventional relationship for E. The first component W min expresses minimum amount of the work W and the second component W represents a deviation from W min interpreted in terms of Dirichlet's integral applied on the internal potential. Relationships between the internal potential and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error propagation rule) accuracy  E of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement between E = E Gauss derived from Gaussian distribution and other E, in particular for E = E PREM based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information about density jumps is absent or incomplete.

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The Earth’s Global Density Distribution and Gravitational Potential Energy

Cited by 4 publications

References 7 publications

Geodynamics

Geodynamics

Geodynamics

Estimation of the gravitational potential energy of the earth based on different density models

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