Driven by discoveries, and enabled by leaps in technology and imagination, our understanding of the universe has changed dramatically during the course of the last few decades. The fields of astronomy and astrophysics are making new connections to physics, chemistry, biology, and computer science. Based on a broad and comprehensive survey of scientific opportunities, infrastructure, and organization in a national and international context, New Worlds, New Horizons in Astronomy and Astrophysics outlines a plan for ground- and space- based astronomy and astrophysics for the decade of the 2010's. Realizing these scientific opportunities is contingent upon maintaining and strengthening the foundations of the research enterprise including technological development, theory, computation and data handling, laboratory experiments, and human resources. New Worlds, New Horizons in Astronomy and Astrophysics proposes enhancing innovative but moderate-cost programs in space and on the ground that will enable the community to respond rapidly and flexibly to new scientific discoveries. The book recommends beginning construction on survey telescopes in space and on the ground to investigate the nature of dark energy, as well as the next generation of large ground-based giant optical telescopes and a new class of space-based gravitational observatory to observe the merging of distant black holes and precisely test theories of gravity. New Worlds, New Horizons in Astronomy and Astrophysics recommends a balanced and executable program that will support research surrounding the most profound questions about the cosmos. The discoveries ahead will facilitate the search for habitable planets, shed light on dark energy and dark matter, and aid our understanding of the history of the universe and how the earliest stars and galaxies formed. The book is a useful resource for agencies supporting the field of astronomy and astrophysics, the Congressional committees with jurisdiction over those agencies, the scientific community, and the public.

Lixourion, Kefallinia Island, Greece, 8-11 September 2005

IX LIST OF PRINCIPAL SPEAKERS XI LIST OF PARTICIPANTS 1. REGULARIZATION E. STIEFEL / A Linear Theory of the Perturbed Two-Body Problem (Regul- ization) 3 J. WALDVOGEL / Collision Singularities in Gravitational Problems 21 D. C. HEGGIE / Regularization Using a Time-Transformation Only 34 J. BAUMGAR TE / Stabilization of the Differential Equations of Keplerian Motion 38 F. NAHON / The Particular Solutions of Levi-Civita 45 O. GODAR T / Example ofIntegration of Strongly Oscillating Systems 53 w. BLACK / The Application of Recurrence Relations to Special Perturbation Methods 61 D. G. BETTIS / Numerical Solution of Ordinary Differential Equations (Abstract) 71 II. THE THREE-BODY PROBLEM V. SZEBEHELY / Recent Advances in the Problem of Three Bodies 75 R. F. ARENSTORF / Periodic Elliptic Motion in the Problem of Three Bodies (Abstract) 107 G. KATSIARIS and c. L. GOUDAS / On a Conjecture by Poincare 109 G. KATSIARIS / The Three-Dimensional Elliptic Problem 118 P. G. KAZANTZIS / Second and Third Order Variations of the Three Dimensional Restricted Problem 135 c. G. ZAGOURAS / Planar Periodic Orbits Using Second and Third Variations 146 E. RABE / Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points 156 P. GUILLAUME / A Linear Description of the Second Species Solutions 161 III. THE N-BODY PROBLEM AND STELLAR DYNAMICS G. CONTOPOULOS / Problems of Stellar Dynamics 177 w. T. KYNER / Invariant Manifolds in Celestial Mechanics 192 s. J.

This book discusses many of the recent theoretical and observational developments that have significant implications for astronomy and astrophysics. The main themes are (i) cosmology, (ii) gravitational wave astronomy and gravitational physics, (iii) stellar astrophysics, and (iv) active galactic nuclei and disk accretion. There are also contributions on the solar system.

Astronomers and astrophysicists are making revolutionary advances in our understanding of planets, stars, galaxies, and even the structure of the universe itself. The Decade of Discovery presents a survey of this exciting field of science and offers a prioritized agenda for space- and ground-based research into the twenty-first century. The book presents specific recommendations, programs, and expenditure levels to meet the needs of the astronomy and astrophysics communities. Accessible to the interested lay reader, the book explores: The technological investments needed for instruments that will be built in the next century. The importance of the computer revolution to all aspects of astronomical research. The potential usefulness of the moon as an observatory site. Policy issues relevant to the funding of astronomy and the execution of astronomical projects. The Decade of Discovery will prove valuable to science policymakers, research administrators, scientists, and students in the physical sciences, and interested lay readers.