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100 1  Fienga, Agnes 
245 10 Frontiers in Relativistic Celestial Mechanics :
       |bApplications and Experiments 
264  1 Berlin/Boston :|bDe Gruyter, Inc.,|c2014 
264  4 |c©2014 
300    1 online resource (320 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  De Gruyter Studies in Mathematical Physics Ser. ;|vv.22 
505 0  Intro -- Contents -- List of figures -- List of tables -- 
       Preface -- New tools for determining the light travel time
       in static, spherically symmetric spacetimes beyond the 
       order G2 -- 1 Introduction -- 2 Notations and conventions 
       -- 3 Generalities -- 4 Specific assumptions on the metric 
       and the light rays -- 4.1 Post-Minkowskian expansion of 
       the metric -- 4.2 Time transfer function for a quasi-
       Minkowskian light ray -- 5 Fundamental properties of 
       functions T(n) -- 5.1 Recurrence relation satisfied by 
       functions T(n) -- 5.2 Analyticity of the functions T(n) --
       6 First procedure: determination of the T(n)'s from the 
       recurrence relation for n = 1, 2, 3 -- 7 Second procedure:
       determination of the T(n)'s from the geodesic equations --
       7.1 Null geodesic equations -- 7.2 Post-Minkowskian 
       expansion of the impact parameter -- 7.3 Implementation of
       the method -- 8 Simplification of the second procedure -- 
       8.1 Use of a constraint equation -- 8.2 Explicit 
       calculation of T(1), T(2), and T(3) -- 9 Direction of 
       light propagation up to order G3 -- 10 Light ray emitted 
       at infinity -- 11 Enhanced terms in T(1), T(2), and T(3) -
       - 12 Application to some Solar System experiments -- 13 
       Concluding remarks -- References -- Testing relativistic 
       gravity with radio pulsars -- 1 Introduction -- 1.1 Radio 
       pulsars and pulsar timing -- 1.2 Binary pulsar motion in 
       gravity theories -- 1.3 Gravitational spin effects in 
       binary pulsars -- 1.4 Phenomenological approach to 
       relativistic effects in binary pulsar observations -- 2 
       Gravitational wave damping -- 2.1 The Hulse-Taylor pulsar 
       -- 2.2 The Double Pulsar - The best test for Einstein's 
       quadrupole formula, and more -- 2.3 PSR J1738+0333 - The 
       best test for scalar-tensor gravity -- 2.4 PSR J0348+0432 
       - A massive pulsar in a relativistic orbit -- 2.5 
       Implications for gravitational wave astronomy -- 3 
       Geodetic precession 
505 8  3.1 PSR B1534+12 -- 3.2 The Double Pulsar -- 4 The strong 
       equivalence principle -- 4.1 The Damour-Schäfer test -- 
       4.2 Direct tests -- 5 Local Lorentz invariance of gravity 
       -- 5.1 Constraints on a1 from binary pulsars -- 5.2 
       Constraints on a2 from binary and solitary pulsars -- 5.3 
       Constraints on a3 from binary pulsars -- 6 Local position 
       invariance of gravity -- 7 A varying gravitational 
       constant -- 8 Summary and outlook -- References -- Lunar 
       laser ranging and relativity -- 1 Introduction -- 2 Model 
       -- 2.1 Overview -- 2.2 Ephemerides -- 3 Analysis -- 3.1 
       Software package LUNAR -- 3.2 Newtonian parameters -- 4 
       Results for relativistic parameters -- 4.1 Gravitational 
       constant -- 4.2 Equivalence principle -- 4.3 Yukawa term -
       - 4.4 Geodetic precession -- 4.5 Metric parameter β -- 4.6
       Preferred-frame parameters α1, α2 -- 5 Summary and outlook
       -- References -- Dragging of inertial frames, fundamental 
       physics, and satellite laser ranging -- 1 Introduction -- 
       2 Dragging of inertial frames -- 3 Tests of string theory 
       and the LAGEOS and LARES space experiments -- 4 LAGEOS and
       Gravity Probe B: two independent space experiments 
       measuring frame dragging -- 5 The LARES mission -- 5.1 The
       LARES satellite -- 5.2 The LARES satellite and geodesic 
       motion -- 5.3 Preliminary orbital analyses -- 5.4 Error 
       analyses -- 5.5 Monte Carlo simulations -- 6 Conclusions -
       - References -- Elliptic functions and elliptic integrals 
       for celestial mechanics and dynamical astronomy -- 1 
       Introduction -- 2 Notations -- 2.1 Glossary -- 2.2 First 
       input argument: ϕ, u and x -- 2.3 Second input argument: 
       k, u and x -- 2.4 Sign of n -- 2.5 Third input argument: n
       and α -- 2.6 Ordering of arguments -- 2.7 Omission of 
       parameters -- 3 Elliptic functions -- 3.1 General elliptic
       function -- 3.2 Weierstrass elliptic function -- 3.3 
       Jacobian elliptic functions -- 3.4 Jacobi's amplitude 
       function 
505 8  3.5 Differential equations of Jacobian elliptic functions 
       -- 3.6 Addition theorem of Jacobian elliptic functions -- 
       3.7 Jacobi's form of incomplete elliptic integrals -- 3.8 
       Addition theorem of incomplete elliptic integrals -- 3.9 
       Jacobi's original form of incomplete elliptic integral of 
       the third kind -- 4 Elliptic integrals -- 4.1 General 
       elliptic integral -- 4.2 Legendre's form of incomplete 
       elliptic integrals -- 4.3 Associate incomplete elliptic 
       integrals -- 4.4 Complete elliptic integrals -- 4.5 
       Generalized elliptic integrals -- 4.6 Symmetric elliptic 
       integrals -- 5 Numerical computation of elliptic functions
       and elliptic integrals -- 5.1 Overview -- 5.2 
       Transformation method -- 5.3 Example of transformation 
       method -- 5.4 Simultaneous computation of Jacobian 
       elliptic functions -- 5.5 Better computation of Jacobian 
       elliptic functions -- 5.6 Computation of Jacobi's form of 
       incomplete elliptic integrals -- 5.7 Computation of 
       Legendre's form of incomplete elliptic integral of the 
       first kind -- 5.8 Computation of other incomplete elliptic
       integrals -- 5.9 Computation of complete elliptic 
       integrals other than II(n|m) and J(n|m) -- 5.10 
       Computation of complete elliptic integrals of the third 
       kind -- 5.11 CPU time comparison -- 5.12 Software -- 6 
       Conclusion -- References -- Victor Brumberg and the French
       school of analytical celestial mechanics -- 1 Introduction
       -- 2 Analytical formulism for planetary perturbations -- 
       2.1 Development of the perturbative function -- 2.2 
       Calculation of the Hansen coefficients -- 3 General 
       planetary theory (GPT) -- 3.1 Introduction -- 3.2 General 
       theory by V. Brumberg -- 4 Planetary theories with the aid
       of the expansions of elliptic functions -- 4.1 Notations -
       - 4.2 Expansion of the right-hand members of the equations
       : A change of the time variable -- 4.3 Application to 
       planetary problems 
505 8  5 Reference frames, time scales, and units for planetary 
       ephemerides -- 5.1 Victor Brumberg's contributions -- 5.2 
       Planetary ephemerides -- 5.3 Conclusions -- References -- 
       Atomic time, clocks, and clock comparisons in relativistic
       spacetime: a review -- 1 Introduction -- 2 Atomic time and
       atomic clocks -- 2.1 Atomic time scales -- 2.2 Atomic 
       clocks -- 3 Relativistic framework for time and frequency 
       comparisons -- 3.1 Introduction -- 3.2 Simultaneity and 
       synchronization -- 3.3 Relativistic definitions of 
       spacetime coordinate systems -- 3.4 Time scales in the 
       barycentric and geocentric systems -- 3.5 Relativistic 
       theory for time transformations in the Solar System (BCRS)
       -- 4 Relativistic treatment for time and frequency 
       comparisons in the vicinity of the Earth (GCRS) -- 4.1 One
       -way time transfer -- 4.2 Two-way time transfer using 
       artificial satellites -- 4.3 Frequency comparisons -- 5 
       Time and frequency transfer techniques -- 5.1 Established 
       time and frequency transfer techniques: GNSS and two-way 
       time transfer -- 5.2 Some novel two-way techniques -- 6 
       Clocks in relativistic geodesy -- 6.1 Review of 
       chronometric geodesy -- 6.2 The chronometric geoid -- 7 
       Conclusions and prospects -- References -- Index 
520    With a wide range of prominent authors from the field of 
       relativistic celestial mechanics, this first volume of a 
       two-volume series consists of reviews on a multitude of 
       advanced topics in the area, covering both classical as 
       well as modern developments, while focusing on 
       applications and experiments. On the occasion of his 80-th
       birthday this volume honors V. A. Brumberg - one of the 
       pioneers in modern relativistic celestial mechanics 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Relativistic astrophysics.;Celestial mechanics 
655  4 Electronic books 
700 1  Fukushima, Toshio 
700 1  Teyssandier, Pierre 
700 1  Müller, Jürgen 
700 1  Wex, Norbert 
700 1  Ciufolini, Ignazio 
700 1  Petit, G 
700 1  Kopeikin, Sergei M 
776 08 |iPrint version:|aFienga, Agnes|tFrontiers in Relativistic
       Celestial Mechanics : Applications and Experiments|dBerlin
       /Boston : De Gruyter, Inc.,c2014|z9783110345452 
830  3 De Gruyter Studies in Mathematical Physics Ser 
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
       detail.action?docID=1524419|zClick to View