Table Of ContentFundamental Theories of Physics 196
Dirk Puetzfeld
Claus Lämmerzahl Editors
Relativistic
Geodesy
Foundations and Applications
Fundamental Theories of Physics
Volume 196
Series editors
Henk van Beijeren, Utrecht, The Netherlands
Philippe Blanchard, Bielefeld, Germany
Bob Coecke, Oxford, United Kingdom
Dennis Dieks, Utrecht, The Netherlands
Bianca Dittrich, Waterloo, Canada
Detlef Dürr, Munich, Germany
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Christopher Fuchs, Boston, USA
Domenico J. W. Giulini, Bremen, Germany
Gregg Jaeger, Boston, USA
Claus Kiefer, Cologne, Germany
Nicolaas P. Landsman, Nijmegen, The Netherlands
Christian Maes, Leuven, Belgium
Mio Murao, Bunkyo-ku, Tokyo, Japan
Hermann Nicolai, Potsdam, Germany
Vesselin Petkov, Montreal, Canada
Laura Ruetsche, Ann Arbor, USA
Mairi Sakellariadou, London, UK
Alwyn van der Merwe, Denver, USA
Rainer Verch, Leipzig, Germany
Reinhard F. Werner, Hannover, Germany
Christian Wüthrich, Geneva, Switzerland
Lai-Sang Young, New York City, USA
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Dirk Puetzfeld Claus L mmerzahl
(cid:129)
Editors
Relativistic Geodesy
Foundations and Applications
123
Editors
DirkPuetzfeld ClausLämmerzahl
ZARM ZARM
University of Bremen University of Bremen
Bremen, Germany Bremen, Germany
ISSN 0168-1222 ISSN 2365-6425 (electronic)
FundamentalTheories of Physics
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Preface
Recent years have seen the advent of high precision measuring methods, in par-
ticular, modern clocks reached an unprecedented level of accuracy and stability.
This was accompanied by important developments in the fields of atom and laser
interferometry.Laserinterferometersimprovedbyseveralordersofmagnitudeand
interferometry in space nowadays is a mature technology ready for practical
applications. All this is of direct importance for many fields of physics, and con-
sequently for geodesy.
The high precision of these new experimental capabilities made clear that
geodesy can no longer rely solely on Newtonian concepts, which are still used
within the field. Geodetical models and the interpretation of data within these
models therefore inevitably require concepts which go beyond the Newtonian
pictureofspaceandtime.Thetheoreticalunderpinningofgeodesyshouldtherefore
bebasedonthespecialandthegeneraltheoryofrelativity,thelatterstillrepresents
the most successful gravity theory to the present date. This new “relativistic geo-
desy” is the topic of the present volume.
In2016,weorganized1aninternationalconferenceinBadHonnef(Germany)on
the Relativistic Geodesy: Foundations and Applications. The conference brought
togethertheleadingexpertsintheirrespectivefieldsandwasverywellreceivedby
the speakers as well as by the audience. We would like to thank the WE-Heraeus
Foundation for the generous support of this conference. Our thanks also go to the
Physikzentrum Bad Honnef where the conference took place.
The positive reception and the feedback after the conference made clear that
thereisastrongdemandforanup-to-datevolume,coveringthemethodsemployed
in current research in the context of the relativistic geodesy. This book intends to
givesuchastatusreport.Ithopefullyisofvaluefortheexpertsworkinginthisfield
and may also serve as a guideline for students. At the same time, we should warn
potential readers that it is not intended to serve as a replacement for a textbook on
either of the subjects of gravitational physics or geodesy. But we hope that it
bridges some of the gaps between the relativity and the geodesy communities, in
1http://puetzfeld.org/relgeo2016.html.
v
vi Preface
particular,whenitcomestoimplementationandapplicationofrelativisticconcepts
and methods in the field of geodesy.
Thepresentvolumeisbasedonthelecturesgivenattheconferenceandgivesan
overview over the following topics:
(cid:129) Time and frequency metrology
(cid:129) Chronometric geodesy
(cid:129) (Clock) gradiometry
(cid:129) Satellite experiments
(cid:129) Navigation systems
(cid:129) Tests of gravity by means of geodetic measurements
In covering these topics, definitions and methods from relativistic gravity are
introduced.Emphasisisputonthecoverageofthegeodeticallyrelevantconceptsin
thecontextofEinstein’stheory(e.g.,roleofobservers,useofclocks,anddefinition
of reference systems). Furthermore, fundamental questions in the context of the
measuring process, as well as approximation methods which make certain calcu-
lations feasible, are discussed in detail.
Weaseditors aredeeplyindebtedtothecontributorstothisvolume,whomade
great efforts to present their respective areas of research in an accessible way to a
broader audience. We hope that the material presented in here will prove to be
useful asa reference for experiencedresearchers, as well asserve asaninspiration
foryoungerresearcherswhowanttoentertheexcitingemergingfieldofrelativistic
geodesy.
Bremen, Germany Dirk Puetzfeld2
Claus Lämmerzahl
2D. P. acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG) through the
grantPU461/1-1.
Contents
Time and Frequency Metrology in the Context
of Relativistic Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Andreas Bauch
Chronometric Geodesy: Methods and Applications . . . . . . . . . . . . . . . . 25
Pacome Delva, Heiner Denker and Guillaume Lion
Measuring the Gravitational Field in General Relativity:
From Deviation Equations and the Gravitational Compass
to Relativistic Clock Gradiometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Yuri N. Obukhov and Dirk Puetzfeld
A Snapshot of J. L. Synge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Peter A. Hogan
General Relativistic Gravity Gradiometry . . . . . . . . . . . . . . . . . . . . . . . 143
Bahram Mashhoon
Reference-Ellipsoid and Normal Gravity Field
in Post-Newtonian Geodesy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Sergei Kopeikin
Anholonomity in Pre-and Relativistic Geodesy. . . . . . . . . . . . . . . . . . . . 229
Erik W. Grafarend
Epistemic Relativity: An Experimental Approach to Physics . . . . . . . . . 291
Bartolomé Coll
Use of Geodesy and Geophysics Measurements to Probe
the Gravitational Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Aurélien Hees, Adrien Bourgoin, Pacome Delva, Christophe Le
Poncin-Lafitte and Peter Wolf
Operationalization of Basic Relativistic Measurements. . . . . . . . . . . . . . 359
Bruno Hartmann
vii
viii Contents
Can Spacetime Curvature be Used in Future Navigation Systems? . . . . 379
Hernando Quevedo
World-Line Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
Jan-Willem van Holten
On the Applicability of the Geodesic Deviation Equation
in General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Dennis Philipp, Dirk Puetzfeld and Claus Lämmerzahl
Measurement of Frame Dragging with Geodetic Satellites Based
on Gravity Field Models from CHAMP, GRACE and Beyond . . . . . . . 453
Rolf König and Ignazio Ciufolini
Tests of General Relativity with the LARES Satellites. . . . . . . . . . . . . . 467
Ignazio Ciufolini, Antonio Paolozzi, Erricos C. Pavlis, Richard Matzner,
Rolf König, John Ries, Giampiero Sindoni, Claudio Paris
and Vahe Gurzadyan
Contributions
(cid:129) A. Bauch Time and frequency metrology in the context of relativistic geodesy
(cid:129) P.Delva,H.Denker,G.LionChronometricgeodesy:methodsandapplications
(cid:129) Y. N. Obukhov, D. Puetzfeld Measuring the gravitational field in General
Relativity: From deviation equations and the gravitational compass to rela-
tivistic clock gradiometry
(cid:129) P. A. Hogan A Snapshot of J. L. Synge
(cid:129) B. Mashhoon General Relativistic Gravity Gradiometry
(cid:129) S. Kopeikin Reference-ellipsoid and normal gravity field in post-Newtonian
geodesy
(cid:129) E. W. Grafarend Anholonomity in Pre and Relativistic Geodesy
(cid:129) B. Coll Epistemic relativity: An experimental approach to physics
(cid:129) A. Hees, A. Bourgoin, P. Delva, C. Le Poncin-Lafitte, P. Wolf Use of geodesy
and geophysics measurements to probe the gravitational interaction
(cid:129) B. Hartmann Operationalization of basic relativistic measurements
(cid:129) H. Quevedo Can spacetime curvature be used in future navigation systems?
(cid:129) J.-W. van Holten World-line perturbation theory
(cid:129) D. Philipp, D. Puetzfeld, C. Lämmerzahl On the applicability of the geodesic
deviation equation in General Relativity
(cid:129) R. König, I. Ciufolini Measurement offrame dragging with geodetic satellites
based on gravity field models from CHAMP, GRACE and beyond
(cid:129) I. Ciufolini Tests of General Relativity with the LARES satellites
ix
