LIBRARYSeries Editors:

ASTRONOMY A T

ST OPHYS CS -lIB ARY

1. Appen zeller, Heidelberg, GermanyG. Bomer, Garching, GermanyM. Harwit, Washington, DC, USAR. Kippenhahn, Gottingen, GermanyJ. Lequeux, Paris, FranceP.A. Strittmatter, Tucson, AZ, USAV. Trimble, College Park, MD, and Irvine, CA, USA

Springer-Verlag Berlin Heidelberg GmbH

Physics and AstronomyONLINE LIBRARY

http://www.springer.de/phys/

Jean Kovalevsky

ModemAstrometry

Second EditionWith 139 Figures and 5 Tables

Springer

ProfessorJean KovalevskyObservatoire de la Cote d' AzurDepartement CERGAAvenue Copemic06130 Grasse, France

Cover picture :General aerial overview of the Navy Protopype Optical Interferometer (NPOI) at the Lowell Observatorynear Flagstaff (Arizona , USA). Courtesy US Naval Observatory.

Library of Congress Cataloging-in-Publication Data.

Kovalevsky, Jean .Modem astrometry/Jean Kovalevsky. - 2nd ed.p.cm. - (Astronomy and astrophysics library, ISSN 0941-7834)I. Astrometry. I. Title. n. Series.QB807. K683 2001 522--<1c21 2001049830

ISSN 0941-7834ISBN 978-3-642-07619-0 ISBN 978-3-662-04730-9 (eBook)DOI 10.1007/978-3-662-04730-9

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© Springer-Verlag Berlin Heidelberg 1994,2002Originally published by Springer-Verlag Berlin Heidelberg New York in 2002.Softcover reprint of the hardcover 2nd edition 2002

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Preface to the Second Edition

On the occasion of the second edit ion of the book, it appeared necessary to up­date information that was already seven years old. Astrometry has recordedtremendous advances during these last years , so that , in addition to cor­recting identified errors and misprints, there are many major modifications.Among the events that forced me to modify significantly the contents of thebook, the most important are the release of the Hipparcos and Tycho cata­logues, the introduction of CCD astrometry, the decision of the InternationalAstronomical Union to adopt a new celestial reference frame, the dramaticimprovement of accurate time and frequency standards, the decision takenby space agencies to prepare several new space astrometry satellites and thedevelopment of optical interferometry. The description and the consequencesof these events have been included in this edition. One of them is that a mi­crosecond of arc or microarcsecond (uas) has become a widely used unit .

On the contrary, the result was also that the importance of some in­struments such as astrolabes or transit circles has decreased. However, I lefttheir description unchanged, not only for their historical interest, but becausenewer techniques often use similar data reduction methods so that one canrefer to them. Conversely, some methods or instruments have evolved andnew information is included. Finally, many new references were added to theoriginal list .

The last chapter was almost completely rewritten. On one side, someof the announced prospects have indeed come into existence and are nowincluded in the core of the book. Others that were described will never mate­rialise, so they have been removed . They are replaced by the account of newprogrammes that have been approved and are in various stages of develop­ment or realisation.

In addition to those colleagues who have been mentioned in the preface,I wish to thank Drs C. Delmas and P.K. Seidelmann who provided me withvery useful information.

Grasse, November 2001 Jean Kovalevsky

Preface to the First Edition

Astromet ry is the domain of ast ronomy devoted to the determination of po­sitions and their tim e-variations, and by extension, the apparent dimensionsand shapes of celesti al bodies. Although several books describe the theoret icalfoundations of positional ast ronomy, they touch only slight ly on the descrip­tion of instrument s and the pro cedures for obt aining act ual geomet rical orkinematic quantities, which are amon g the basic observational data in thest udy of the Universe and of its components. The goal of the present book is,in cont rast, to provide an up-to-dat e description of ast rometric techniques,par ticularly the most recent and powerful ones, whether the instruments areon the ground or in space.

Until the end of the 19th cent ury, before the development of physical as­tronomy, all astronomical observations were directed towards obt aining posi­tions of celest ial bodies. Since then astrophysics has become the most impor­tant domain of ast ronomy. With the extension of observations to almost allwavelengths from radio waves to gamma rays, with the use of very sensit ivenew receivers and the development of fast computers, remarkable progresshas been made in the description and the und erstanding of the Universe.

Until about 1970, ast rometry did not take part in this general develop­ment of ast ronomy, and yet trigonometric parallaxes, proper motions, andsizes of st ars, which can be obtained only by ast romet ric techniques, arefundament al quantities in many domains of ast rophysics. As a consequence,some basic domains of ast rophysics became conspicuously uncertain in com­parison with progess achieved elsewhere. Since 1970, ast romet ry has st artedto make up for lost t ime and its contribut ions to astronomy are dispropor­t ionate ly increasing . New techniques such as radio and optical ast rometry,CCD receivers, astrometric satellites , chronometric methods, and computershave drasti cally changed ast romet ry, leading to gains of one, two, and some­times several orders of magnitude in precision and accuracy. Thanks to them,ast rometry has become a completely renovated science. It is this new sciencet hat is describ ed in this book, which is a development of several years ofpostgraduate courses at Paris Observatory.

A first draft - in French - of the mat erial presented here was published bySpringer in its Lecture Notes series (Kovalevsky, 1990). However, the presentbook is not simply an enlarged and updated version of the latter . Several

VIII Preface to the First Edition

chapters are almost completely rewritten. New material is introduced in mostsections and a chapter on future projects is added. Results from the HubbleSpace Telescope and Hipparcos, now available , are presented as well as newdevelopments in other techniques.

The first chapter is a general introduction to astrometry emphasising itsobjectives and general methods. The next two chapters present a synthesisof the main results in physical optics necessary to understand the generalprop erties of astrometric instruments and of the atmosphere - an unavoidablemedium for ground-based astrometry which strongly affects the observations.Chapter 4 presents a resume of the main results of spherical astronomy thatare constantly used in the reduction of observations; this is not an attemptto write a new treatise in fundamental astronomy but this chapter was addedto have at hand in the book all the necessary formulae referred to. The sameconcern led to a short presentation of the main tools for data reduction andevaluation of uncertainties as well as a sketch of the physical background oftechniques used.

The next seven chapters are devoted to presentation of the instrumentsused in astrometric observations of celestial bodies and of the Earth-Moonsystem. The objective is to present a brief summary description of the instru­ments and of their principles, to discuss the origins of errors, to describe thecalibrations, and to give some indication of the methods used to reduce theobservations. Besides classical astrometric instruments such as astrographs,meridian circles, and astrolabes with their latest improvements, we presentall the new techniques which appeared in the last 10-20 years , and con­tributed to the high precision of modern astrometric data (CCD receivers,Hubble Space Telescope, Hipparcos, optical interferometry, VLBI, laser rang­ing, GPS pulsar timing). In the last chapter, after a summary description ofthe main achievements of modern astrometry, we present the need for evenbetter precision and projects which aim at meeting these requirements.

Throughout the book, we have used systematically the international sys­tem of units (SI). However, with the great increase in precision , the unit ofangle, the second (If) is too large . Several notations for a thousandth of a sec­ond are found in the literature. It is either called milliarcsecond abbreviated"mas" or millisecond of arc (actually the correct term should be millisecondof degree or millisecond of angle since the quantity measured is not an arcbut an angle) . I have chosen to use millisecond of arc systematically andintroduced the corresponding abbreviation "mas" .

It is my pleasure to acknowledge the very competent and efficient typingby Mrs Jeanne Falin. I thank Dr D. Bonneau for his very thorough reading ofthe chapter on interferometry: actually some paragraphs were written by him.I thank Drs M. Froeschle, F . Laclare, F. Mignard, and C. Thomas for readingseveral chapters, correcting errors, and suggesting pertinent modifications.

Grasse , May 1994 Jean Kovalevsky

Contents

1 Pres entation of Astrometry 1

1.1 Ast rometry in Ast ronomy 11.2 Goals of Astrometry 2

1.2.1 Extragalactic Obj ects 31.2.2 Stars 31.2.3 Objects in the Solar System 51.2.4 Earth-Moon System 61.2.5 Conclusion 7

1.3 Astromet ric Techniques 81.3.1 Small-Field Astrometry 81.3.2 Semi-global Astrometry 91.3.3 Dist ance Measurements 91.3.4 Other Techniques 91.3.5 Ground-Based or Space Astromet ry? 10

2 Image Formation 11

2.1 Basic Principles 112.1.1 Propagation of a Light Ray 122.1.2 The Fermat Principle 122.1.3 Propagation of a Monochromatic Light Wave 132.1.4 Superposition Principle 152.1.5 T he Huygens Principle 15

2.2 Diffract ion 152.2.1 Propagation of a Limited P lane Wave 162.2.2 Diffraction by a Circular Aperture 182.2.3 Point Spread Function of a Circular Aperture 192.2.4 Resolving Power 20

2.3 Coherence of Light 212.3.1 Bandwidth 212.3.2 Coherence Time and Length 23

2.4 Instrumental Defects 242.4.1 Conventio nal Image 242.4.2 Defocus 262.4.3 Spherical Aberration 26

X Contents

2.4.4 Coma 272.4.5 Ast igmatism and Field Curvature 282.4.6 Distortion 292.4.7 Chromatic Aberration 302.4.8 Diffract ion Chromatism 31

3 Atmospheric Effects on Image Formation 33

3.1 Monochromatic At mospheric Refraction 333.1.1 Approximate Theory of Atmospheric Refract ion 333.1.2 Spherical Atmosphere Approximation 343.1.3 Laplace Formula 363.1.4 Normal Refraction 383.1.5 Temperat ure and Pressure Dependence 383.1.6 Differential Refractio n 39

3.2 Chromatic Refraction 403.2.1 Chromatic Refract ion Correction 403.2.2 App licat ion to Star Observations 403.2.3 Empirical Correction 413.2.4 Simplified Empirical Correction 43

3.3 Refraction in Distance 443.3.1 Dist ance Measurements in Optical Wavelengt hs 443.3.2 Refract ion of Radio Waves 45

3.4 Heterogeneity of the Atmosphere 483.4.1 Structure of the Atmosphere 483.4.2 Effects of TUrbulence 503.4.3 Statistical P ropert ies of a TUrbulent Atmosphere 513.4.4 Wave Propagation in the Atmosphere 523.4.5 Seeing . . . . . . . . .. . . . ... . . . . . . . . . . .... . . . . . . . . . . . 533.4.6 Instantaneous Image 543.4.7 Resolving Power of Telescopes 563.4.8 Adaptive Optics 58

4 R eduction of Observations 61

4.1 Reference Systems and Frames 614.1.1 Ideal Reference System 624.1.2 Reference System 634.1.3 Conventio nal Reference System 634.1.4 Conventio nal Reference Frames 644.1.5 Change of Reference Coordinates 654.1.6 Application to Local Coordinates 664.1.7 Relat ion with the Celestial Reference Frame 684.1.8 New Intermediary System 704.1.9 Satellite Astrometry 71

Contents XI

4.2 Geometrical Effects 714.2.1 Field-to-Focus Transformation 714.2.2 Annual Parallax 744.2.3 Other Parallactic Corrections 754.2.4 Proper Motions 76

4.3 Optical Effects 774.3.1 Aberr ation 774.3.2 Relativistic Light Deflection 794.3.3 Relativistic Light-Time Delay 804.3.4 Doppler Shift 80

4.4 Reduction of Observations 814.4.1 Position of the Problem 824.4.2 Modelling 834.4.3 Calibration 84

4.5 Estimation of Parameters 844.5.1 Notion of Uncertainty 844.5.2 Evaluation of the Uncertainty 864.5.3 Method of Least Squares 874.5.4 Variance and Covariances in Least Squares 89

5 Small-Field Astrometry 91

5.1 Photographic Astrometry 915.1.1 Telescopes for Small-Fi eld Astrometry 925.1.2 Properti es of Photographic Plat es 955.1.3 Image of a Star 995.1.4 Photographic Plate Measurements 1015.1.5 Determination of Image Positions 1025.1.6 Plate Reduction 1035.1.7 Star Catalogues 107

5.2 Photoel ectri city in Astrometry 1095.2.1 Photomultipliers 1095.2.2 CCD Receivers 1105.2.3 CCD Calibration 1125.2.4 CCD Astrometric Observations 1135.2.5 CCD Scan Mode 114

5.3 Grid-Modulation Astrometry 1175.3.1 Grid-Modulation Theory 1175.3.2 Reduct ion of a Grid-Modulated Signal 1185.3.3 Multichannel Astrometric Photometer 119

5.4 Astrometry with the Hubble Space Telescope 1215.4.1 Description of the HST 1225.4.2 Degradation of the HST Optics 1225.4.3 Description of the Fine Guid ance Sensors 1245.4.4 Reduction of FGS Dat a in Transfer-Function Mode . 127

XII Contents

5.4.5 Reduction of FGS Data in Astrometric Mode 1295.4.6 Astrometric Use of the WF fPC 131

5.5 Radial Velocities 1325.5.1 Spect roscopy 1335.5.2 Determinat ion of Radial Velocities: CORAVEL 1335.5.3 Objective Prism 135

6 Meridian C ircles 139

6.1 Measurement of Large Angles 1396.1.1 Measuring Angles by a Rotation 1396.1.2 Materialised Representation of Angles 140

6.2 The Meridian Circle 1426.2.1 Principle of a Meridian Circle 1426.2.2 Descript ion of the Meridian Circle 144

6.3 Determination of Celestial Coordinates 1446.3.1 Right Ascensions 1456.3.2 Collimation 1466.3.3 Inclination of the Rotation Axis 1476.3.4 Azimuth of the Rotation Axis 1486.3.5 Calibration of the Instrumental Constants 1496.3.6 Bessel's Formula 1506.3.7 Determination of Declinations 1516.3.8 Geometric Corrections for Declinat ions 1516.3.9 Flexure of the Tube 1526.3.10 Errors in Refraction 1526.3.11 Summary of Corrections in Declination 153

6.4 Micrometers 1546.4.1 Rotating Mask Micrometer 1546.4.2 Oscillating Grid Micrometer 1566.4.3 Use of an Image Dissector 1616.4.4 CCD Micrometer 1626.4.5 CCD Telescopes 163

6.5 Horizontal Meridian Circles 1636.5.1 Pulkovo Horizontal Meridian Circle 1646.5.2 Axial Meridian Circle 165

6.6 Reduction of Meridian Observations 1666.6.1 Relative Observations 1666.6.2 Global Reduction 1676.6.3 Precisions of Observations 169

7 Equal A ltitude Inst rum ent s 1717.1 Principle of Astrolabes 171

7.1.1 Geometry of the Observation 1727.1.2 Curvature of the Parallel 173

Contents XIII

7.2 Descript ion of an Astrolabe 1747.2.1 Principle of the Danjon Prism Astrolabe 1757.2.2 Principle of a Full Pupil Astrolabe 1767.2.3 Description of a Full Pupil Astrolabe 1777.2.4 The Mark 4 Ast rolabe 1807.2.5 Instrumental Parameters 181

7.3 Met hod of Equal Alti tudes 1827.3.1 Fundamental Formu la 1837.3.2 Observational Procedures 1847.3.3 Determination of Inst rumental Parameters 1857.3.4 Determination of Star Posit ions 1867.3.5 Astrolabe Star Catalogues 186

7.4 Solar Astrolabe 1877.4.1 Principle of a Solar Astrolabe 1877.4.2 Description of the Mult iprism Solar Astrolabe 1897.4.3 Reduction of Observat ions 1907.4.4 Variable Prism Solar Astrolabe 192

7.5 The Photographi c Zenith Tube 193

8 Hipparcos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

8.1 Hipparcos Mission 1978.1.1 General Principle of Hipparcos 1988.1.2 Descrip tion of the Satellite 1988.1.3 Input Catalogue 2018.1.4 Nominal Scanning Law 2038.1.5 At titude Control 2038.1.6 Observing Strategy 2048.1.7 Operation of the Satellite 2058.1.8 Data Reduction 206

8.2 Photon Count Treatment 2068.2.1 Single-Slit Response 2068.2.2 Transit Time on the Star-Mapper 2088.2.3 Grid-to-Field Transformat ion 2098.2.4 Reference Great Circles 2108.2.5 At t it ude Determination 2128.2.6 Representat ion of the Att itude 2138.2.7 Main Grid Photon Counts 2158.2.8 Main Grid Coordinates 2168.2.9 Case of Double and Multiple Stars 218

8.3 Reduct ion on a Great Circle 2198.3.1 Geometry of the Reduct ion 2198.3.2 Equations of Condition 2208.3.3 Design Matrix and Solutio n 221

8.4 Astromet ric Parameter Determination 223

XIV Contents

8.4.1 Basic Equations 2238.4.2 Sphere Reconstitution 2258.4.3 Astrometric Parameter Determination 227

8.5 Iterations and Results for Single Stars 2278.6 Special Tasks 229

8.6.1 Double and Multiple Stars 2298.6.2 Hipparcos Photometry 2318.6.3 Solar System Objects 2328.6.4 Link to the Extragalactic Reference Frame 233

8.7 Hipparcos Final Catalogue 2358.7.1 Merging of the Catalogues 2358.7.2 Contents of the Hipp arcos Catalogue 236

8.8 Tycho 2388.8.1 Principle of Tycho 2388.8.2 Detection of Stars 2388.8.3 Star Identification 2398.8.4 Equations for the Astrometric Parameters 2408.8.5 Astrometric Parameter Determination 2418.8.6 Tycho Cat alogue 242

8.9 Tycho-2 Cat alogue 2438.9.1 Identification of Transits 2438.9.2 Estimation of Stellar Positions 2438.9.3 Tycho-2 Catalogue 245

9 Very Small Field Astrometry 2479.1 Stellar Amplitude Int erferometry 247

9.1.1 Interference Fringes 2479.1.2 Michelson Interferometry 2499.1.3 Fundamental Equ at ion of Stellar Int erferometry 2519.1.4 Description of Int erferometers 2549.1.5 Double Star Observation 2599.1.6 Int erferometry of Extended Sources 2619.1.7 Resolving Power of an Interferometer 2659.1.8 Other Optical Int erferometers 265

9.2 Speckle Int erferometry 2679.2.1 Reduction by the Autocorrelation Method 2679.2.2 Reduction in a Fourier Space 2689.2.3 Operations 269

9.3 Occultat ions by the Moon 2709.3.1 Diffraction by a Half-Plane 2709.3.2 Application to Lunar Occultations 2729.3.3 Observation of Occultat ions 2739.3.4 Reduction of Observations 2749.3.5 Precisions Achieved 276

Contents XV

10 Phase Interferometry 277

10.1 Optical Phase Int erferometry 27710.1.1 General Theory 27710.1.2 Reduction of Observations 27910.1.3 Refraction Correct ion in the Mark III Int erferometer 28010.1.4 Astrometry with the NPOI 28210.1.5 Astrometric Precision 283

10.2 Radio Interferometry 28410.2.1 Radio Telescopes 28410.2.2 Interferometry in Radio Waves 28610.2.3 Very Long Baseline Int erferometry 28810.2.4 VLBI Data Reduction 29010.2.5 Observation of Stars by VLBI 29210.2.6 Space VLBI 293

11 Timing Techniques 295

11.1 Chronometry 29511.1.1 Oscillators 29511.1.2 Quartz Oscillators 29711.1.3 Stimulated Emissions 29911.1.4 Caesium Atomic Frequency Standards 30111.1.5 Atomic Clocks 30511.1.6 Atomi c Time Scales 307

11.2 Lasers 30911.2.1 The Laser Effect 30911.2.2 Implement ation for Telemetry 311

11.3 Laser Ranging 31111.3.1 Lunar Laser Ranging Equipment 31311.3.2 Photon Efficiency of Lunar Lasers 31511.3.3 Return Recognition and Data Reduction 31711.3.4 Satellite Laser Ranging 319

11.4 Global Positioning System 32011.4.1 Principle of the System 32111.4.2 Description of the GPS 32111.4.3 Measurements with GPS Receivers 32211.4.4 Extensions 324

11.5 Planetary Radars 32511.5.1 Radar Ranging Measurements 32511.5.2 Application to Planets 32711.5.3 Ranging to Asteroids 328

11.6 Pulsar Timing 32911.6.1 Timing Pulses 33011.6.2 Propagation Time of Pulsar Signals 33211.6.3 Interpretation of the Observations 332

XVI Contents

11.6.4 Astrometric Results 334

12 Future of Astrometry 337

12.1 Achievements of Present Astrometry 33712.1.1 Extragalactic Obj ects 33712.1.2 Stars 33812.1.3 Objects in the Solar System 339

12.2 Need for Better Astrometry 34112.2.1 Extragalactic Objects 34312.2.2 Stars 34412.2.3 The Galaxy 346

12.3 Space Global Astrometry Projects 34712.3.1 DIVA 34812.3.2 FAME 34912.3.3 GAIA 350

12.4 Space Interferometry 35212.4.1 SIM 35212.4.2 Space VLBI 35312.4.3 Astrometry from the Moon? 353

12.5 Prospects of Ground-Based Astrometry 35412.5.1 CCD Astrometry 35412.5.2 Very Small Field Astrometry 35512.5.3 Role of Ground-Based Astrometry 355

12.6 As a Conclusion 356

References 359

Index 371