An atmospheric phenomenon is considered as 'explained' when we have succeeded in deducing it on the basis of accepted principles of physics. (H. Ertel, Methods and problems of dynamical meteorolo gy,p. l) Until recently, noctilucent clouds were regarded merely as a curious atmos pheric phenomenon, the occurrence of which aroused only limited scientific attention. However, in the last two decades the interest they have been given has markedly increased. The clouds, usually pale blue in colour, may be seen on a clear night at high latitudes. Typical examples are illustrated in the book. Clouds looking like these in daytime would be classified as cirrostratus. What sets noctilucent clouds apart is their occurrence in the middle of the night, their very obvious pale blue colour, and their disappearance into the dawn close to the onset of civil twilight when the Sun is 6 Degrees below the horizon. as being set apart from ordinary Noctilucent clouds were first recognized clouds in 1884/1885 and in a series of sightings that followed their return in the summer of 1885. That year marked the beginning of observations and the interpretation of twilight phenomena. The impetus came from the extraordi nary Krakatoa eruption, which was not only one of the most spectacular volcanic eruptions in recorded history, but which also turned out to be a startling event in atmospheric science with repercussions even in our time.

Modem dynamics is increasingly participating in the solution of problems raised by as tronomical observations. This new relationship is being fostered on one side by the im provements in the observations, which in recent years contributed several discoveries of new systems, such as the objects in the Kuiper belt, the pulsar and star companions, to speak only of the most striking ones, and, on the other hand, by the progresses in modem dynamics. The progresses in modem dynamics are due to two factors: the dissemination of fast computers, allowing the numerical studies of very complex systems by a large number of scientists, and the improvement in our understanding of the complex behaviour of Hamiltonian systems. KAM and Nekhorochev theories have shed a light on the subtle and surprizing interplays between regular and chaotic motions; numerical experiments and analytical approximations have shown how these peculiarities are indeed present in astronomically important systems and are instrumental in understanding their formation and evolution.

Three years ago the Reports on Astronomy were for the first time published in three separate parts whereby related astronomical topics were collected in one volume and each volume was kept to a size of no more than about 250 pages. The a m was to facilitate a wider distribution of individual volumes among astronomers and other scientists interested in specific subjects of astronomy. The same system was adopted for the present volume A of the IAU Transactions which covers the activities in astronomical research from January 1976 to December 1978. The Commission Presidents were invited to restrict their reports, to present a selection of the most important developments in the field of astronomy covered by their Commission, and to avoid overlaps with other Commission reports. As a re sult of the restriction in the number of pages some Commissions presen.t a large, concentrated list of references with little discussion, whereas others review some of the most exciting recent research developments in their subject. The distribution of the Commission Reports into the three parts of volume XVII A is as follows: VOL. XVII A PART 1 commission 4. Ephemerides 5. Documentation 6. Astronomical Telegrams " 7. Celestial Hechanics " 9. Instruments and Techniques 14. Fundamental Spectroscopic Data " 15. Physical Study of Cornets, Hinor Planets and Meteorites 16. Physical Study of Planets and Satellites " Working Group on Planetary System Nomenclature 17. The Moon " 19. Rotation of the Earth " 20."

This book, which has been in the making for some eighteen years, would never have begun were it not for Dr. David Dewhirst in 1976 kindly having shown the author a packet of papers in the archives of the Cambridge Obser vatories. These letters and miscellaneous papers of Fearon Fallows sparked an interest in the history of the Royal Observatory at the Cape of Good Hope which, after the diversion of producing several books on later phases of the Observatory, has finally resulted in a detailed study of the origin and first years of the Observatory's life. Publication of this book coincides with the 175th anniversary of the founding of the Royal Observatory, e.G.H. Observatories are built for the use of astronomers. They are built through astronomers, architects, engineers and contractors acting in concert (if not always in harmony). They are constructed, with whatever techniques and skills are available, from bricks, stones and mortar; but their construction may take a toll of personal relationships, patience, and flesh and blood.

Research of the interstellar medium (ISM) has been advancing rapidly during the last 10 years, mainly due to immensely improved observational facilities and techniques in all wavelength ranges. We are now able to investigate the ISM in external galaxies and even the intergalactic and intracluster medium in great detail. Increased spatial and spectral resolution have provided us with a great deal of information on the interstellar gas in its various phases, the magnetic field and the cosmic rays, and of course, also the stellar component, which is the driving agent of the interstellar matter cycle.
Since only fairly recently, a sufficient amount of computing power has become available to tackle these problems with some prospect of obtaining a self-consistent picture of the ISM, a major goal of this workshop was to bring together observers and theoreticians sufficiently close, so that intense discussions about the necessities and desiderata of modelling the ISM could be stimulated. Observers have shown in great detail on this conference of what is seen on all scales of the ISM, near and far, and what boundary conditions would be appropriate for realistic models, and theoreticians pointed out what assumptions and simplifications their codes need, and how future observations could test their models. As a first step towards this goal, some self-consistent numerical simulations with a minimum number of relevant physical processes were also presented on this meeting. There was wide agreement, that this approach - to keep observers and theoreticians in close contact and also in sometimes quite controversial discussions - will bear fruitful results in the near future.

InMay1988,theFirstInternationalConferenceonDissociativeRecombination:Theory, ExperimentandApplicationswasheldatChateauLakeLouise,Alberta,Canada. Thismeeting gaveaconsiderableimpetustothissubject,whichisofparticularinterestforalargevarietyof fieldsincludinginterstellarclouds,planetaryatmospheres,gaslasers,plasmaprocessing,ion sourcesandthermonuclearplasmas. Sincethen,indeed,severalcollaborationswereinitiated betweenexperimentalistsworkingwithdifferenttechniques,betweentheoreticiansdealingwith molecularstructureononehandanddynamicsontheotherhandandalsobetween experimentalistsandtheoreticians. Duringthelastfouryears,therefore,alargenumberof studieswerecarriedoutandraisedanewsetofquestions. Moreparticularly,theresultsthat wereobtainedconcerningcontroversialspeciessuchasH!andHeir,castingsomedoubton theverymechanismsbywhichdissociativerecombinationproceeds. The Second International Conference on Dissociative Recombination: Theory, ExperimentandApplications heldat"I'AbbayedeSaintJacutdelaMer",Brittany,France, May3-8,1992,camethereforeattherighttimetosurveythecurrentstateofthesubject. The symposiumbroughttogetherleadinginvestigatorsinthefieldsofmolecularionrecombination research,atomicandmoleculartheoryandexperiment,plasmasphysics,astrochemistryand aeronomy. Speakerspresentedtalksreviewingtheirownworkandthesewerefollowedby livelydiscussionsessions. Freetimeperiodsallowedparticipantstodiscoveranenchanting peninsulaofNorthBrittanywhilepursuingstimulatingscientificdiscussions. Thepapersinthis volumearebasedonthesetalksandfurtherdiscussions,withtheexceptionofcontributions fromT. AmanoandB. M. McLaughlinwhowereunabletoattend. Alistofparticipantsas wellasasouvenirgroupphotoisgivenattheendofthebook. WeareindebtedtoNATOforitsfinancialsupportwhichcontributedtothegreat successofthissecondmeeting. TheUniversityofRennesIandtheBalzerscompanyarealso acknowledgedfortheiradditionalsupportManythankstothewholestaffoftheabbeyforits kindnessandeffortsinprovidinguswithapropitiousenvironmentforsuchaworkshop. We arealsogratefultoL. Caubetforhervaluableadministrativeassistanceduringthepreparation ofthemeeting. Finallyaspecialmentionmustbegiventoallthesessionchairpersonsfortheir skillinorchestratingthediscussions. Lookingforwardtoattendingthethirdmeeting. TheEditors Bertrand R. Rowe J. Bria/l A. Mitchell Andre Callosa DepartementdePhysique DepartmentofPhysics DepartementdePhysique AtomiqueetMoleculaire TheUniversityofWesternOntario AtomiqueetMoleculaire UniversitedeRennesI London,Canada,N6A3K7 UniversitedeRennesI CampusdeBeaulieu CampusdeBeaulieu 35042RennesCedex, 35042RennesCedex, France France v CONTENTS ORALCONTRIBUTIONS PolyatomicIonDissociativeRecombination . 1 D. R. Bates RecentDevelopmentsandPerspectivesintheTreatmentofDissociative RecombinationandRelatedProcesses...11 A. Giusti-Suzor, I. F Schneider, and 0. Dulieu CharacteristicsofSuperexcitedStatesofMoleculesandMQDTStudiesofNO+ DissociativeRecombination...25 H. Sun, K. Nakashima, and H. Nakamura CalculationsforAr +Xe*andArXe+ +e 35 A. P. Hickman, DL Huestis, and R. P. Saxon Electron-IonContinuum-ContinuumMixinginDissociativeRecombination 47 s. L. Guberman ATheoreticalStudyoftheHCO+andHCS+ElectronicDissociativeRecombinations. . 59 D. Talbi, and Y Ellinger DissociativeRecombinationofCH;:SomeBasicInformationfromElectronic 2 StructureCalculations. 67 WP. Kraemer TheoreticalProblemsintheDissociativeRecombinationofH~ +e...75 H. Takagi RecentMergedBeamsInvestigationsofHydrogenMolecularIonRecombination...87 J B. A. Mitchell, F B. Yousif, P. Van der Donk, and T. J Morgan vii FlowingAfterglowStudiesofElectron-IonRecombinationusingLangmuirProbesand OpticalSpectroscopy...99 NG. Adams RecentFlowingAfterglowMeasurements . 113 B. R. Rowe InfraredSpectroscopicStudiesoftheDissociativeRecombinationProcessesofH...127 3 T. Amano RecombinationofClusterIons . 135 R. Johnsen PredissociationofExcitedStatesofH . . 145 3 H. Helm AStudyofHe e,3I,;)BoundandContinuumStates...155 2 CJ Gillan, B. M McLaughlin. and P. G. Burke ElectronCollisionInducedExcitationsandDissociationofHeH+usingthe R-MatrixMethod . . 163 BK Sarpal, J Tennyson, and L. A. Morgan AssociativeIonisationofHydrogen:ExperimentswithFastMergedBeams...173 F Brouillard, andX Urbain TheoryoftheAsssociativeIonisationReactionbetweenTwoLaser-Excited . 187 SodiumAtoms 0. Du!ieu, A. Giusti-Suzor, andF Masnou-Seeuws ResonantTheoryofDissociativeAttachment...195 J. J. Fabrikant MicroscopicandMacroscopicTheoriesofTermolecularRecombinationbetween AtomicIons...205 MR. Flannery DissociativeRecombinationinPlanetaryIonospheres . . 219 JL. Fox ChemistryofSupernova1987a . 243 A. Dalgarno DissociativeRecombinationinInterstellarClouds . .

IAU Transactions are published as a volume corresponding to each General Assembly. Volume A is produced prior to the Assembly and contains Reports on Astronomy, prepared by each Commission President. The intention is to summarize the astronomical results that have affected the work of the Commission since the production of the previous Reports up to a time which is about one year prior to the General Assembly. Volume B is produced after the Assembly and contains accounts of Commission Meetings which were held, together with other material. The reports included in the present volume range from outline summaries to lengthy compilations and references. Most reports are in English.

Neutrinos play a fundamental role in the latest particle physics theories, such as Grand Unified Theories, theories of supersymmetry, and superstring theory. Their mass yields an important boundary condition for grand unification models. They are the best candidates for dark matter in the universe, and their mass could determine its large scale structure and evolution. Neutrinos probe the interior of collapsing stars, and understanding them may lead to a solution of the solar neutrino problem. In ten chapters written by experts in each of these fields this book gives a comprehensive presentation of our current knowledge of the neutrino, of its role in nuclear particle and astrophysics theories, and of ongoing experimental efforts to learn more about its own nature. Graduate students and researchers in these fields will find this book a reliable advanced text and source of reference.

The present set of chapters by members of the staff of the National Radio Astronomy Observatory deals with the basic fields of research concerned with radio astronomy outside the solar system. The emphasis in this volume is on the type of data available and its interpretation. Basic theory is considered only where absolutely necessary, and little discussion of receivers or techniques is entered into in most of the chapters. The book is intended to take over where most textbooks on radio astronomy leave off, that is, in the discussion of what is actually known from the research done. In addition there is a chapter on the technical aspects of inter ferometry and aperture synthesis, since so much of modern radio astronomy depends, and will depend in an ever increasing manner, on such tools. The editors want to stress that the chapters were not necessarily expected to be compre hensive reviews of any of the fields being covered, but rather, overall outlines which the in dividual authors felt would be suitable for graduate students and interested workers in other fields. As a result, the lists of references are not complete. This only reflects the preferences of the individual authors and not the relative merit of those references included or omitted.

Nobel Symposium No 31 on The Impact of Space Science on Man kind was held at Spatind, Norway, September 7 - 12, 1975. Twenty seven leading experts from the United States, the U. S. S. R. and Western Europe attended the Symposium. Four main subjects were discussed: The Impact of Space Science, introduced by Profe. ssor Reimar Lust; The Impact of Space Communica tion, ihtroduced by Dr Joseph Charyk; The Impact of Earth Resources Exploration from Space, introduced by Dr William Nordberg; and The Impact of Space Assisted Meteorology, introduced by Dr Robert M White. This book contains edited summaries of the papers presented at the Symposium and summaries of the discussions. The Symposium was financed by the Nobel Foundation through grants from the Tercentenary Foundation of the Bank of Sweden and organized by a special committee appointed by the Norwegian Nobel Institute. Tim Greve Finn Lied Erik Tandberg vii CONTENTS The Impact of Space Science 1 R. Lust The Impact of Space Science on Mankind (Discussion) 13 T. R. Larsen (ed. ) Satellite Communications 25 J. V. Charyk The Impact of Space Communication (Discussion) 57 G. Rosenberg (ed. ) The Impact of Earth Resources Exploration from Space 67 W. Nordberg The Impact of Earth Resources Exploration from Space 79 (Discussion) E. Tandberg (ed. ) The Environmental Satellite: What It Means for Man 91 R. M. White The Impact of Space Assisted Meteorology (Discussion) 111 E. Tandberg (ed.

Since the 1970s symposia or colloquia devoted to recent research on close binaries have been held around the world almost annually. At meetings of the General Assembly of the International Astronomical Union this topic has also been discussed in detail at presentations in various commission meetings and also as invited talks by leading astronomers in the field. In recent years, fundamental changes have taken place in the study of close binaries due to the improvements in observational techniques, extension of observations from X-ray to radio regions of the electromagnetic spectrum, and advances in theoretical studies. For more than a decade, a group of astronomers at Ege University Observatory has been concentrating on active close binaries with particular emphasis on the behaviour of the light curves of chromospherically active systems. Thus, we decided to organize an international meeting in Western Anatolia, where this part of Turkey had been the cradle for great developments in science during antiquity. KUljadasi, located only minutes away from Ephesus, one of the seven wonders of the world, was selected to be the meeting site. Close binary systems constitute a very rich source of information about the physical properties of the component stars. Some systems are eclipsing variables, where periodic recurrences of eclipses are observed as comparatively brief decreases in the total brightness of the binary system. Precise methods of photometric observations make it possible to obtain the light variations of these systems because of eclipses and other phenomena.

During the past few decades we have witnessed at least two major innovations in science which have had substantial impact on technology as well as science itself, pervasive enough to modify many facets of our daily lives. We refer, of course, to the tran sistor and the laser. It is striking that now with the advent of optical bistability we may have opened the door to another such field, which combines these two aspects (transistor and laser) and has the possibility for important device applications as well as providing a unique window into the as yet not thoroughly explored frontiers of nonequilibrium statistical physics. This has prompted us to organize an international conference on the subject of optical bistability to provide an adequate means for assessing the current state of the art of this important field and to stimulate further significant developments by means of in tense technical exchange and interaction among the leading scien tists in this subject area.

It is a 10ng-standing tradition in this country for any event re1ated to solar activity to enjoy special importance. Because we enjoy the advantage of pro10nged sunny periods, we consider the incidence of some thirty c10udy days each year as a personal af- front. I cannot say that we have the facu1ty to produce solar ec1ipses in order to justify an Institute on this subject to be held in Athens, but I can say that the occurrence of a solar ec1ipse over Greece wou1d present, for optica1 and solar astronomers, the highest possibi1ity of exce11ent conditions for observation. We had this opportunity during the May 20, 1966 annu1ar solar ec1ipse over North Africa and southern Europe. At that time we had the p1easure to co11aborate with a 1arge number of research groups of various nationa1ities, who insta11ed optica1 and radio instru- ments near or in Lagonissi, which 1ay a10ng the centra1 path, in order to fo110w the ec1ipse. A first meeting was then organized in order to discuss methods of data handling and avai1abi1ity of resu1ts. After a pre1iminary discussion it was suggested that a 1ater meeting shou1d be organized when final resu1ts were avai1ab1e.

This volume consists of invited lectures and seminars presented at the NATO Advanced Study Institute "The Gamma Ray Sky with COMPTON GRO and SIGMA," which was held at the Centre de Physique Theorique of Les Houches (France) in January / February 1994. The school has been planned by a Scientific Organizing Committee. It was organized with the aim of providing students and young researchers with an up-to-date account of the high-energy phenomena in the vicinity of compact objets and the diffuse gamma-ray backgrounds after the early results from the gamma-ray telescope SIGMA and the four instruments onboard COMPTON GRO (Gamma Ray Observatory): BATSE (Burst and Transient Source Experiment), COMPTEL(Compto'l Telescope), EGRET (Energetic Gamma Ray Experiment Telescope) and OS SE(Oriented Scintillation Spectrometer Experiment) . It was attended by more than sixty researchers from many countries. The lectures and seminars represent a complete coverage of our present knowledge and understanding of: Gamma-ray backgrounds, Gamma-ray Burts, Active Galactic Nuclei, Galactic Compact Objects, Gamma-ray Spectroscopy, Instrumentation and observation techniques, etc ... Most of these lectures are reproduced in this volume. Unfortunately, a few lecturers have chosen not to submit their manuscript.

The launch in October 1990 of the joint ESA-NASA Ulysses mission marked the start of a new era in the study of the heliosphere. For the fIrst time, in-situ observations are being made covering the full range of heliographic latitudes. Following the successful gravity-assist manoeuvre at Jupiter in February 1992, Ulysses left the ecliptic plane in a southerly direction and headed back toward the Sun, passing over the southern solar pole in mid-1994. To mark these unique events, the 28th ESLAB Symposium, held in Friedrichs hafen, Germany, on 19-21 April 1994, was devoted to "The High Latitude Helio sphere." Following on from the highly successful 19th ESLAB Symposium "The Sun and the Heliosphere in Three Dimensions" (Les Diablerets, 1985), the purpose of the meeting was to review out-of-ecliptic results from the Ulysses mission obtained to date, and to provide a focus for the fIrst polar pass. Relevant results from other space missions, as well as ground-based and theoretical studies, were also included. Attended by 130 scientists, the main themes of the Symposium were The Sun and Corona, Large-Scale Heliospheric Structure, Energetic Particles in the Heliosphere, Cosmic Rays in the Heliosphere, and Interstellar Gas and Cosmic Dust. The scientifIc programme consisted of a number of Topical Review papers introducing various as pects of these themes, supplemented by a large number of contributed papers (72 in to tal) presented either orally or as posters. Undoubtedly, the excellent poster sessions formed one of the highlights of the meeting."

The conference recorded in this volume was one of the events organised to celebrate the centenary of the (re)establishment of the Royal Observatory, Edinburgh, on Blackford Hill in 1884. Circumstellar Matter was selected as the topic because of important contributions toward research in the field by recent observations in the infrared and submillimetre, particularly with the two telescopes which the Observatory has both operated and built instru mentation for - the United Kingdom Infrared Telescope (UKIRT) and the James Clerk Maxwell Telescope (JCMT). The programme aimed to cover as many aspects of circumstellar matter as could fit into a one-week meeting, omitting only planetary nebulae, which had been well served by meetings in the previous two years. We thank the international scientific advisory com mittee (overleaf) for their help in selecting the Invited Reviewers around which the programme was built. The Invited Reviews and oral contributions are included in the order and sections in which they were presented, even where re-ordering might have been more logical. We did not attempt to categorise the poster contributions but have included them in alphabetical order. An evening session for viewing and discussing posters in an unhurried atmosphere was very successful. A competition for the best poster was held and the prize was awarded for that by Lindqvist, Lucas, Olofsson, Omont, Eriksson & Gustafsson."

Ptolemy was the most important physical scientist of the Roman Empire, and for a millennium and a half his writings on astronomy, astrology, and geography were models for imitation, resources for new work, and targets of criticism. Ptolemy in Perspective traces reactions to Ptolemy from his own times to ours. The nine studies show the complex processes by which an ancient scientist and his work gained and subsequently lost an overreaching reputation and authority.

The physical processes driving the different manifestations of the phe nomenon of active galactic nuclei have been studied extensively during the last decade. A major obstacle in all attempts to understand the relevant pro cesses has always been the wide range of frequencies over which significant fractions of the total power are emitted. During the last decade, orbiting telescopes and instrumental improvements for ground-based instrumenta tion provided the means for major advancements on the observational side. The organizers felt that it was timely to organize a meeting to discuss the impact of this new situation on the understanding of the relevant physical processes. More then 400 astrophysicists were interested in participating in the meeting, in spite of the constraints on overseas travel which were imposed in early 1991. Unfortunately only 220 participants could be hosted by the Max-Planck-Haus, the site of the 1991 Heidelberg conference. The meet ing was organized by Sonderforschungsbereich 328 "Evolution of Galaxies". During 5 sessions, most of which lasted for one day each, 47 invited and con tributed talks and 150 poster papers were given, most, but not all, of which are included in these proceedings. With a few exceptions the order of the written texts follows that of the oral contributions during the meeting. The arrangement of posters into the five sections was not always unambiguous. We hope to have placed them in the most appropriate sections, in which they are listed in alphabetical order.

Because of recent progress in the development of quasistationary toroidal mag- netic confinement systems, especially tokamaks, these systems are at the center of research on controlled thermonuclear fusion. Tokamaks were proposed and first built at the Kurchatov Institute of Atomic Energy. In the 1960s the basic features of plasma behavior in toroidal magnetic confinement systems were investigated in ex- periments on the first tokamaks and the possibility of obtaining effective confine- ment in them was demonstrated. The successes of this first stage led to a rapid ex- pansion in tokamak research around the world. The development of a thermonu- clear power reactor based on the tokamak is now actively under way. During the earliest phase of research on tokamaks, it was already clear that the ohmic heating used in them was not sufficient to obtain the temperatures needed for initiation of a self-sustaining thermonuclear reaction. At the beginning of the 1970s, therefore, a search was begun for methods of heating which could supple- ment ohmic heating. The best of these auxiliary heating techniques are neutral beam injection, various methods based on the collisionless absorption of rf (radio fre- quency) waves, and adiabatic compression of the plasma by a rising magnetic field.

A wealth of material on practically every aspect of astronomy, beginning from the first principles. It is quite unique in providing a level of scientific accuracy and detail to be found in no other introductory book, including coverage of instruments, theory, observation, space exploration and cosmology. Encyclopaedic in its breadth, the book still contains in-depth explanations of the underlying theories. The illustrations - many of them colour photographs - animate the text, itself so clear and concise that it will fascinate readers of every discipline.
Winner of the Rapportryers Prize for "most meritorious popular science book."

Ram accelerators are among the most advanced tools for generating fluid dynamcis data in supersonic reacting systems. They require the combined action of combustion, wave systems and turbulence and are still a serious challenge for physicists and engineers. This book will serve as an introductionary textbook on ram accelerators and gives a thorough overview on research activities, performance modeling and high-pressure detonation dynamics.

This volume of Astrophysical Data deals with Planets and Stars; a second volume, Part II, will give data for Galaxies and the Universe. They both pro vide basic data for use by all scientists, from the amateur astronomer to the professional astrophysicist. In this first volume, we not only provide physical parameters of planets, stars and their environment, but we also provide the celestial coordinates required to observe them. Here we use c.g.s. units, for they are the most commonly used in astron omy and astrophysics; but our volume begins with astronomical and physical constants and the conversion factors needed for other units. The next section concerns the planets and their satellites; it singles out the Earth and Moon for special treatment. Spacecraft rendezvous with the planets and satellites have led to improved values for their atmospheric compositions, orbital parameters, magnetic fields, masses, radii, rotation periods, and surface pressures and temperatures. This section also contains data for the asteroids, comets and their debris. We then discuss everyday stars, beginning with the Sun, and continuing with basic stellar data, the brightest stars and nearby stars. Special categories of stars, such as the Wolf-Rayet stars, magnetic stars, flare stars, and RS CVn binary stars, are included.

After the launching of the first artificial satellites preceding interplanetary vehicles, celestial mechanics is no longer a science of interest confined to a small group of astronomers and mathematicians; it becomes a special engineering technique. I have tried to set this book in this new perspective, by severely limiting the choice of examples from classical celestial mechanics and by retaining only those useful in calculating the trajectory of a body in space. The main chapter in this book is the fifth, where a detailed solution is given of the problem of motion of an artificial satellite in the Earth's gravitational field, using the methods of Von Zeipel and of Brouwer. It is shown how Lagrange's equations can be applied to this problem. The first four chapters contain proofs of the main results useful for these two methods: the elliptical solution of the two-body problem and the basic algebra of celestial mechanics; some theorems of analytical mechanics; the Delaunay variables and the Lagrangian equations of variation of elements; the expansion of the disturbing function and the Bessel functions necessary for this expansion. The last two chapters are more descriptive in character. In them I have summarized briefly some of the classical theories of celestial mechanics, and have tried to show their distinctive characteristics without going into details.