New methods of studying the figure of the earth

Molodensky, M. S.

doi:10.1007/bf02537957

Cited by 6 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the Newtonian approximation the trace of the energy-momentum tensor is reduced to the negative value of the matter density of the perturbation, T ≃ −µ, while T ≃ ∆ N T . Hence, equation (60) matches its Newtonian counterpart (11). Outside the mass distribution the master equation for the anomalous gravity potential is reduced to the covariant Laplace equation…”

Section: The Master Equation For the Anomalous Gravity Potentialmentioning

confidence: 78%

See 1 more Smart Citation

Towards an exact relativistic theory of Earth's geoid undulation

2015

View full text Add to dashboard Cite

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulate differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. (Sergei M. Kopeikin), e_mazurova@mail.ru (Elena M. Mazurova), rector@ssga.ru (Alexander P. Karpik) 1 It is the same J. B. Listing who introduced in 1847 the term topology in mathematics.

show abstract

Section: The Master Equation For the Anomalous Gravity Potentialmentioning

confidence: 78%

“…Equations ( 60), (61) extend similar equations (11), (12) of classic geodesy to the realm of general relativity. The main difference is that the covariant Laplace operator in (60), (61) is taken in curved space with the metric ḡαβ .…”

Section: The Master Equation For the Anomalous Gravity Potentialmentioning

confidence: 87%

Towards an exact relativistic theory of Earth's geoid undulation

2015

View full text Add to dashboard Cite

show abstract

“…A anomalia de altura, proposta por Molodensky (1958), é um elemento importante, pois permite a integração entre as superfícies de referências nas técnicas de maregrafia e ALTSAT. A maregrafia mede as variações do nível do mar em relação à uma superfície de referência local (nível médio do mar local), já a altimetria por satélite realiza as mensurações em relação a um elipsoide e modelo geoidal global.…”

Section: � ℎ �� unclassified

Comparação das Variações do Nível Médio do Mar a partir de Dados de Altimetria por Satélites e Maregrafia em Fortaleza – CE

2021

View full text Add to dashboard Cite

Historicamente as variações do nível médio do mar têm sido estimadas a partir de dados provenientes de marégrafos instalados na costa. No entanto, diante da dificuldade de obtenção de longas séries de dados maregráficos, vê-se como alternativa a utilização de dados de sensoriamento remoto por satélites altimétricos (ALTSAT). Neste sentido, o presente estudo tem como objetivo avaliar as variações relativamente do Nível Médio do Mar (NMM) a partir de dados ALTSAT e de maregrafia. Para este propósito, obtevese dados da missão CryoSat-2 e da estação maregráfica EMFOR (Fortaleza-CE), pertencente a Rede Maregráfica Permanente para Geodésia (RMPG), referentes ao período entre fevereiro de 2011 e maio de 2019. A análise relativa procedeu-se pela estimativa mensal do NMM obtido a partir de ambas as técnicas. Os resultados demostraram que a metodologia proposta é viável e pode ser empregada alternativamente ao uso de estações maregráficas, reduzindo sobretudo, os custos de levantamentos de campo. A técnica ALTSAT também permite estimativas para locais em que dados maregráficos são inexistentes ou de baixa acurácia. Comparativamente ao emprego de dados maregráficos coletados in loco, ALTSAT mostrou-se bastante eficiente neste estudo, apresentando uma discrepância média, mínima e máxima de, respectivamente, 4 mm, -4 cm e 3,9 cm. Além disso, ambas as técnicas concordaram indicando uma elevação média do nível do mar no período analisado.

show abstract

“…There are two methods for studying the figure of the geoid [4]: 1) geometric (or astronomical-geodetic), is carried out by measuring the mutual position of points on the Earth's surface and the direction of the plumb line (triangulation and astronomical definitions); 2) physical (or gravimetric), is performed by measuring the acceleration the force of gravity. These methods differ significantly from each other: the first allows the study and determination of the figure of the geoid only on the basis of measurements carried out on a limited area of the earth's surface, and studies the figure corresponding to this area, and the second is applicable only when known the values of the acceleration the force of gravity at all points on the earth's surface, thus obtaining the whole figure of the geoid [2,3,6].…”

Section: Introductionmentioning

confidence: 99%

Gravimetric Measurments in Extremely Mountainous Region of the Territory of South-Western Bulgariarila Mountain

Kirilova¹

2020

JSAR

View full text Add to dashboard Cite

The subject of the research is to perform gravimetric measurements in local extreme areas of the territory of South-western Bulgaria (S / W), and more precisely the north-western end of the Rila - Rhodope mountain massif - Rila mountain in order to analysis and evaluation the optimal option for practical modelling of the local geoid (quasi-geoid) in the area limited within the boundaries 41052'06"N<ϕ<42º21'22"N and 23001'11"E<λ<24º01'05"E. The measured force of gravity in 287 gravimetric points an evenly distributed on the study area provides reliable gravimetric information that helps to deduce the surface of the local geoid for the Rila Mountains, where topographic effects completely dominate the local variations of the gravitational field.

show abstract

New methods of studying the figure of the earth

Cited by 6 publications

References 0 publications

Towards an exact relativistic theory of Earth's geoid undulation

Towards an exact relativistic theory of Earth's geoid undulation

Comparação das Variações do Nível Médio do Mar a partir de Dados de Altimetria por Satélites e Maregrafia em Fortaleza – CE

Gravimetric Measurments in Extremely Mountainous Region of the Territory of South-Western Bulgariarila Mountain

Contact Info

Product

Resources

About