The Assesment Of The Celestial Body Influence On The Geodetic Measurements ; Dangaus kūnų įtakos geodeziniams matavimams vertinimas
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VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Darius POPOVAS THE ASSESSMENT OF THE CELESTIAL BODY INFLUENCE ON THE GEODETIC MEASUREMENTS SUMMARY OF DOCTORAL DISSERTATION TECHNOLOGICAL SCIENCES, MEASUREMENT ENGINEERING (10T) Vilnius 2011 Scientific Supervisor Prof Dr Habil Petras PETROŠKEVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T). The dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T). Members: Assoc Prof Dr Vladislovas Česlovas AKSAMITAUSKAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T), Prof Dr Habil Ramutis Petras BANSEVIČIUS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T), Prof Dr Habil Vytautas GINIOTIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T), Prof Dr Habil Kazys KAZLAUSKAS (Vilnius University, Physical Sciences, Informatics – 09P). Opponents: Dr Habil Saulius ŠLIAUPA (Nature Research Center, Physical Sciences, Geology – 05P), Prof Dr Habil Algimantas ZAKAREVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T).
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01 janvier 2012
VILNIUS GEDIMINAS TECHNICAL UNIVERSITY
Darius POPOVAS
THE ASSESSMENT OF THE CELESTIAL BODY INFLUENCE ON THE GEODETIC MEASUREMENTS
SUMMARY OF DOCTORAL DISSERTATION
TECHNOLOGICAL SCIENCES, MEASUREMENT ENGINEERING (10T)
Vilnius
2011
Scientific Supervisor Prof Dr Habil Petras PETROŠKEVIČIUS(Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T). The dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T). Members: Assoc Prof Dr Vladislovas Česlovas AKSAMITAUSKAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T), Prof Dr Habil Ramutis Petras BANSEVIČIUS University of (Kaunas Technology, Technological Sciences, Mechanical Engineering – 09T), Prof Dr Habil Vytautas GINIOTIS(Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T), Prof Dr Habil Kazys KAZLAUSKAS University, Physical (Vilnius Sciences, Informatics – 09P). Opponents: Dr Habil Saulius ŠLIAUPA(Nature Research Center, Physical Sciences, Geology – 05P), Prof Dr Habil Algimantas ZAKAREVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T). The dissertation will be defended at the public meeting of the Council of Scientific Field of Measurement Engineering in the Senate Hall of Vilnius Gediminas Technical University at 2 p. m. on 19 December 2011. Address: Saul4tekio al. 11, LT-10223 Vilnius, Lithuania. Tel.: +370 5 27 952, +370 5 27 956; fax +370 5 270 0112; e-mail: doktor@vgtu.lt The summary of the doctoral dissertation was distributed on 18 November 2011. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saul4tekio al. 1, LT-10223 Vilnius, Lithuania). © Darius Popovas, 2011
VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS
Darius POPOVAS
DANGAUS KŪNŲ ĮTAKOS GEODEZINIAMS MATAVIMAMS VERTINIMAS
DAKTARO DISERTACIJOS SANTRAUKA TECHNOLOGIJOS MOKSLAI, MATAVIMŲ INŽINERIJA (10T)
Vilnius
2011
Disertacija rengta 2006–2011 metais Vilniaus Gedimino technikos universitete. Mokslinis vadovas: prof. habil. dr. Petras PETROŠKEVIČIUS Gedimino (Vilniaus technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T). Disertacija ginama Vilniaus Gedimino technikos universiteto Matavimų inžinerijos mokslo krypties taryboje: Pirmininkas: prof. habil. dr. Vladas VEKTERIS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T). Nariai: doc. dr. Vladislovas Česlovas AKSAMITAUSKAS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T), prof. habil. dr. Ramutis Petras BANSEVIČIUS technologijos (Kauno universitetas, technologijos mokslai, mechanikos inžinerija – 09T), prof. habil. dr. Vytautas GINIOTIS(Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T), prof. habil. dr. Kazys KAZLAUSKAS universitetas, fiziniai (Vilniaus mokslai, informatika – 09P). Oponentai: habil. dr. Saulius ŠLIAUPA(Gamtos tyrimų centras, fiziniai mokslai, geologija – 05P), prof. habil. dr. Algimantas ZAKAREVIČIUS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimų inžinerija – 10T). Disertacija bus ginama viešame Matavimų inžinerijos mokslo krypties tarybos pos4dyje 2011 m. gruodžio 19 d. 1 val. Vilniaus Gedimino technikos universiteto senato pos4džių sal4je. Adresas: Saul4tekio al. 11, LT-10223 Vilnius, Lietuva. Tel.: (8 5) 27 952, (8 5) 27 956; faksas (8 5) 270 0112; el. paštas doktor@vgtu.lt Disertacijos santrauka išsiuntin4ta 2011 m. lapkričio 18 d. Disertaciją galima peržiūr4ti Vilniaus Gedimino technikos universiteto bibliotekoje (Saul4tekio al. 1, LT-10223 Vilnius, Lietuva). VGTU leidyklos „Technika“ 1936-M mokslo literatūros knyga. © Darius Popovas, 2011
Introduction Topicality of the problem.Geodetic measurements are interrelated with the gravitational field which tend to vary within the time running. The major influence makes such celestial bodies as the Sun and Moon. The gravitational pull of the moving celestial bodies alternate the field of the Earth’s gravity as well as its form. The effect of the Sun and the Moon cause periodical and constant deformations of the Earth. The mentioned above deformations influence the direction of the vertical, the gravity, the equipotential surfaces of the gravity field and etc., what in its turn induces the results of geodetic measurements. To calculate the corrections of the tides there are applied the spherical function series of the tide generating potential. Modern accurate calculations on the tide potential by means of the Sun’s and Moon’s coordinates allow to assess precisely the variation of the gravity field to a rigid Earth. However, the Earth is not rigid and homogenic body and be able to react on to the effect of the celestials bodies in a more complex way, that is why the available models of the tides and the algorithms diverge in between more or less. The classical geodesy use simpler and unlike methods (in levelling, gravimetry) of the tide corrections which have to be revised and specified when more precise measurements are introduced. Relevance of the work.The effect of the celestial bodies has to be assessed when carrying out geodetic measurements, determining the coordinates of the benchmarks and the parameters of the Earth’s gravity field. These issues are significant when solving geodetic tasks not only by the classical methods but the methods of cosmic geodesy. The data obtained by the cosmic geodesy methods are mostly applied for the solution of the tasks of geophysics and geodynamics, for compiling global and regional geodetic networks, that is why tide models to be used for the corrections of these data have to satisfy the required accuracy typical for these data. The increased accuracy of geodetic and gravimetric measurements requires more precise and detailed investigation of the effect of the celestial bodies as well as more precise its assessment. The mentioned above are significant for the geodetic works executed in Lithuania which are considered to be essential to be able to establish modern geodetic reference frame. Objective of the work.The effect of the celestial bodies on to the elements of the gravity field and the methodology of the assessment of the changes of the gravity field in the geodetic measurements.
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Aim of the work.and assess the effect of the celestial bodiesTo investigate on to the elements of the gravity field and to upgrade the methodology of the assessment of the celestial bodies effect on the geodetic measurements. Tasks of the work 1. To carry out the research on the potential of the tide caused by the celestial bodies. 2. To analyse the effect of the celestial bodies on to the gravity field elements. 3. To assess and investigate the effect of the celestial bodies on to the geodetic measurements. . To improve the methodology of the assessment of the celestial bodies effect on to the geodetic measurements. Methods of the work.Theoretical and experimental research of Earth’s gravity change applying the theory of the tide potential, spherical function series, horizontal and equatorial coordinate systems and assessing the rigidity of the Earth. Scientific novelty 1. analysed, assessed and investigated the effect of theThere was celestial bodies on to the elements of the gravity field instead of the elements of the orbit making use of the known coordinates of the celestial bodies. 2. The zonal waves of the tide potential were analysed in a detailed way, their effect to the gravity field elements was evaluated. 3. The methodology of the assessment of the tide effect on to the geodetic measurements was advanced. . Methodology to specify the geoid surface and gravity system assessing the permanent part of the tide generating potential. 5. The effect of the celestial bodies on to the gravity field elements in the territory of Lithuania and their dispersion. Practical value.The results of the research work could be applied for the assessment of the celestial bodies effect on the geodetic, gravimetric and
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geodetic astronomy measurements as well as when selecting the surfaces of the Earth’s and geoid and the system of the gravity in cases of the assessment of the celestial bodies effect. The presented methodology of the Lunisolar effect on the height differences was applied for the geodetic vertical first class Lithuanian network measurements. Defended propositions 1. The new series of the tide potential preconditioned by the impact of the celestial bodies and expressed by the spherical functions, where the arguments are the celestial body coordinates, allows to asses the impact of the celestial bodies by using the finite equations for each member of the series. 2. The use of the coordinates of the celestial bodies allows to carry out the assessment of the long period waves. It allows the selection of the gravity system and equipotential surfaces for geoid determination. 3. the improved methodology regarding the impact of theThe use of celestial bodies on the geodetic measurements allows to carry out the assessment of the permanent and variable part of the impact of the celestial bodies. . Presented methodology allows the reduction of the data of various geodetic measurements to be introduced into the uniform assessment system dealing with the impact of the celestial bodies. The scope of the scientific work.The research consists of the following parts, namely the introduction, four chapters and summary of the results, two supplements are included as well. The research contains 108 pages, apart from the supplements; there were used 138 numbered equations, 5 figures and 1 table. There were used 153 literature sources when working on the research. 1. Celestial bodies effect to the gravity field and geodetic measurements valuation problems The chapter deals with the review of the development of the theory of the effect of the celestial bodies, the analysis of the contemporary methods used in the assessments of the tides and the reliability of the assessments made. The scientific literature issues on the research theme concerning the effect of the celestial bodies on the Earth’s gravity field and geodetic measurements are
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analysed. The problems regarding the assessment of the effect of the celestial bodies are named and classified. In executing the assessment of the celestial bodies on the geodetic measurements, the research very often is limited only to the first member of the tide potential. Together with the increase in the accuracy of the measurements it is advisable to assess the members of the higher series, n=3; n= of the tide potential. The geodetic experiences indicate mostly single Love number used, which after the perfection of the accuracy of the measurements inadequately represents the elasticity of the Earth. In accordance with the methodology of the assessment of the zonal waves there could be applied different conceptions regarding the Earth’s surface, geoid and gravity. The contemporary used geodetic data present the uneven assessment of the effect of the celestial bodies, which is why the general implementation of various geodetic data requires their reduction into the unanimous system for the assessment of the effect of the celestial bodies to be made. 2. Theoretical research of the effect of the celestial bodies on the gravity field The effect of the celestial bodies on the gravity field is presented by using the series of the spherical functions of the tide potential: =Gm∞Rrn VTrn∑= Pn(cosz), (1) 2 wherePn(cosz) −is the Legendre polynomials,Gis a gravitational constant,m is the mass of the celestial body,r the geocentric distance to the celestial is body,Ris the geocentric distance to the point of the Earth’s surface, andzis the geocentric zenith distance of the celestial body. Taking into consideration only the first three members of the series it is possible to express the following: VT=rGm3R232soc2z−12+rmG4R32soc53z−2cos3z+
Gmr5R453cos84z−803cos2z+83.
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(2)
The derivative of the tide potential towards the vertical direction is equal to the projection of the tide force onto the vertical. It expresses the changeδg′of the gravity due to the effect of the celestial body: ′ ∂VT δg. (3) = − ∂ By differentiating (2) it is received in the following way: δ′ =Gm3R1−3cos2z+3Gm4R23cosz−5 cos3z+ r2r G2m5R330 cos2z−35 cos4z−3. () r By applying the theorem of the sum of the spherical functions there have been written the equation for the gravity change expressed by the equatorial coordinates: Whenn=2: δT2= −G2rm3R3sin2δ−1 3sin2Φ−1+3sin 2δsin 2Φcost+ 3cos2δcos2Φcos 2t, (5) whereδ,andtis the declination of the celestial body and hour angle,Φis the geocentric latitude of the point. Whenn=3: δg3T= −3Gm4R25sin3δ−3sinδ5sin3Φ−3sinΦ+ 4r s3coδ5sin2δ−1 cosΦ5sin2Φ −1 cost+ 2
15 cos2δsinδcos2ΦsinΦcos 2t+c5so23δcos3Φcos 3t.
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(6)
Whenn=4: TGmRn 3 δg4= −4r3546135sin4δ−30 si2δ+35 sin4Φ−30 sin2Φ+3+ 5cosδ7 sin3δ−3sinδ 8 cosΦ7 sin3Φ −3sinΦcost+
ocs52δ7 sin2δ−1 cos2Φ7 sin2Φ −1 cos 2t+ 16 35cos3δsin cos3 3sin cost53ocs4cos4cos 4t7 8δΦ Φ +64δΦ. ( ) Then the change of the gravity is equal to: δg′ =δg2T+δg3T+δg4T. (8) The constant part of the regional waves on the gravity which depends only on the latitude, it is possible to determine from the equation: δgzTΦ=G2m3R3sin2Φ−1−31G6m5R335sin4Φ−30 sin2Φ+3. (9) r r This part of the gravity change in the given latitude tends not to vary in the course of time. The other part of the zonal waves depends not only on the latitude, but also on the declination of the celestial body. To assess its effect it is possible to use the mean integral values ofδ functions. Thus, the effect on the gravity could be expressed by the following: δgvTz=GmR1−3isn2ε3sin2Φ −1− 2r32
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13G6rm5R38in5s34ε−5sinε+135 sin4Φ −30 sin2Φ +3, (10) whereεinclination of the celestial body orbit to the equator.is the By applying the potential of the tide there were received not only the above presented equations expressing the change of the gravity but the equations describing the deviation of the vertical, the deformations of the equipotential surface and the components of the tide force. For the assessment of the whole elements of the gravity field there were obtained the equations by applying the first three members of the tide potential as well as there were carried out the transitions from the horizontal to the equatorial coordinates. There were analysed in a detailed way the zonal waves which depend on the latitude of the point and declination of the celestial body. There were selected two forms for the assessment of the zonal waves. The first form is the one which evaluates the effect depending on the latitude, the second form is the one additionally evaluating the average integral effect of the functions depending on the declination of the celestial body. The formulas of the zonal waves were specified and they could be applied when selecting various surfaces of the Earth’s and geoid as well as gravity system. The effect of the celestial body on the gravity field and its elements of the real Earth were analysed. The Love numbers dependant on the degree of tide potential was used when evaluating the elasticity of the Earth. 3. The research of the effect of the Moon and Sun on the gravity field elements The chapter presents the analysis of the Moon and Sun effect on the elements of the gravity field when the zenith distance of the celestial body is changing, submits the assessment of the effect of the constant part of the zonal waves and carries out the research on the general effect of both the celestial bodies. The equations received in the second chapter are used. Due to the effect of the celestial body when the potential of the gravity of the Earth is changing there are proceeded the deformation of the equipotential surface of the gravity field. ζT=γ2Ggm3R23cos22z−12+γ3rgmG4R3523z−32z+ r cos cos
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