Modern Astrodynamics

In recent years, an unprecedented interest in novel and revolutionary space missions has risen out of the advanced NASA and ESA programs. Astrophysicists, astronomers, space systems engineers, mathematicians and scientists have been cooperating to implement novel and ground-breaking space missions. Recent progress in mathematical dynamics has enabled development of specialised spacecraft orbits and propulsion systems. Recently, the concept of flying spacecraft in formation has gained a lot of interest within the community. These progresses constitute the background to a significant renaissance of research dealing with astrodynamics and its applications. Modern Astrodynamics is designed as a stepping stone for the exposition of modern astrodynamics to students, researchers, engineers and scientists. This volume will present the main constituents of the astrodynamical science in an elaborate, comprehensive and rigorous manner. Although the volume will contain a few distinct chapters, it will render a coherent portrayal of astrodynamics. Encompasses the main constituents of the astrodynamical sciences in an elaborate, comprehensive and rigorous manner Presents recent astrodynamical advances and describes the challenges ahead The first volume of a series designed to give scientists and engineers worldwide an opportunity to publish their works in this multi-disciplinary field

Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

Beginning from an understanding of Hamiltonian dynamics, Modern Astrodynamics blends the modern methods of dynamical system theory with the classical perturbation methods. Emphasizing earth satellite motion, the work also explores planetary motion. The text concludes with nonlinear resonance and relative motion of satellites. A Windows PC program disk suppliments the text.

Beginning with Hamiltonian dynamics, Modern Astrodynamics blends the modern methods of dynamical systems theory with the perturbation theory methods of the last century. With an emphasis on earth satellite motion, the derivation of the geopotential expansion is covered, and the motion of an object under the influence of the Earth's equatorial oblateness is derived to the first order. The structure of the phase space of Hamiltonian systems is explored both with modern numerical techniques (the surface of section) periodic orbit theory, and nonlinear resonance methods. The text concludes with applications of these modern methods to the problem of the relative motion of satellites in orbit about the earth, and the application of KAM tori to earth satellite motion. The text is suitable for a semester course at the introductory graduate level. Topics covered include: (1) Modern Numerical Methods, (2) Transformation Theory, (3) Variation of Elements, (4) Perturbing Forces, (5) General Perturbations, (6) Nonlinear Resonance, (7) Relative Satellite Motion, and (8) KAM Tori.

Fundamentals of Astrodynamics and Applications is rapidly becoming the standard astrodynamics reference for those involved in the business of spaceflight. What sets this book apart is that nearly all of the theoretical mathematics is followed by discussions of practical applications implemented in tested software routines. For example, the book includes a compendium of algorithms that allow students and professionals to determine orbits with high precision using a PC. Without a doubt, when an astrodynamics problem arises in the future, it will become standard practice for engineers to keep this volume close at hand and `look it up in Vallado'. While the first edition was an exceptionally useful and popular book throughout the community, there are a number of reasons why the second edition will be even more so. There are many reworked examples and derivations. Newly introduced topics include ground illumination calculations, Moon rise and set, and a listing of relevant Internet sites. There is an improved and expanded discussion of coordinate systems, orbit determination, and differential correction. Perhaps most important is that all of the software routines described in the book are now available for free in FORTRAN, PASCAL, and C. This makes the second edition an even more valuable text and superb reference.

Focusing on the orbital mechanics tools and techniques necessary to design, predict, and guide a trajectory of a spacecraft traveling between two or more bodies in a Solar System, this book covers the dynamical theory necessary for describing the motion of bodies in space, examines the N-body problem, and shows applications using this theory for designing interplanetary missions. While most orbital mechanics books focus primarily on Earth-orbiting spacecraft, with a brief discussion of interplanetary missions, this book reverses the focus and emphasizes the interplanetary aspects of space missions. Written for instructors, graduate students, and advanced undergraduate students in Aerospace and Mechanical Engineering, this book provides advanced details of interplanetary trajectory design, navigation, and targeting.