FUNDAMENTALS OF ASTRODYNAMICS (original) (raw)
General-relativistic celestial mechanics. IV. Theory of satellite motion
Physical Review D, 1994
The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealt with in our approach thanks to the use of previously developed tools: the definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.
Modern Celestial Mechanics: From Theory to Applications
2002
t the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events
Analysis of Kepler’s law to the movement of celestial bodies
Journal of Physics: Conference Series, 2019
Unity of planetary movement theory from Newton's law and Kepler's law shows the orbiting motion of the planet to the sun. Kepler's law illustrates the movement of planets orbiting the sun, assuming the sun is silent, thereby exposing the path of the orbits of planets that are often encountered so far. In fact, the sun also moves towards a certain center, so that the form of a planetary orbital path that is so closed is not a reflection of the actual movement of the planet. When the sun moves then the movement of the planet is not an elliptical but rigid. In addition the earths movement orbiting the sun is not as simple as it is described, because it is not just the earth that orbits the sun but there are other celestial bodies that also orbits the sun. So it is necessary to show the relationship of the movement of other planets to the movement of the earth around the sun. The purpose of this study is to find out the relation between the movement of other planets to the earths motion orbiting the sun and to know the true orbit path of the planets as the sun moves too. From this study, it can be seen that the use of Kepler's law equations and Newton's laws that have existed so far is not for the actual movement of the solar system, because many factors influence. During this time, the use of Kepler's law and Newton's law for the movement of the earth and the sun always considered their physical conditions ideal, assuming the sun was silent. The actual conditions of the sun moving, the shape of the trajectory of the movement of celestial bodies is not elliptical but rigid.
Unity of planetary movement theory from Newton's law and Kepler's law shows the orbiting motion of the planet to the sun. Kepler's law illustrates the movement of planets orbiting the sun, assuming the sun is silent, thereby exposing the path of the orbits of planets that are often encountered so far. In fact, the sun also moves towards a certain center, so that the form of a planetary orbital path that is so closed is not a reflection of the actual movement of the planet. When the sun moves then the movement of the planet is not an elliptical but rigid. In addition the earths movement orbiting the sun is not as simple as it is described, because it is not just the earth that orbits the sun but there are other celestial bodies that also orbits the sun. So it is necessary to show the relationship of the movement of other planets to the movement of the earth around the sun. The purpose of this study is to find out the relation between the movement of other planets to the earths motion orbiting the sun and to know the true orbit path of the planets as the sun moves too. From this study, it can be seen that the use of Kepler's law equations and Newton's laws that have existed so far is not for the actual movement of the solar system, because many factors influence. During this time, the use of Kepler's law and Newton's law for the movement of the earth and the sun always considered their physical conditions ideal, assuming the sun was silent. The actual conditions of the sun moving, the shape of the trajectory of the movement of celestial bodies is not elliptical but rigid.
New methods in celestial mechanics and mission design
Bulletin of the American Mathematical Society, 2005
The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three-body problem. Since then, many researchers have contributed to his legacy by developing and applying these methods to problems in celestial mechanics and, more recently, with the design of space missions. This paper will give a survey of some of these exciting ideas, and we would especially like to acknowledge the work of Michael Dellnitz, Frederic Gabern, Katalin Grubits, Oliver Junge, Wang-Sang Koon, François Lekien, Martin Lo, Sina Ober-Blöbaum, Kathrin Padberg, Robert Preis, and Bianca Thiere. One of the purposes of the AMS Current Events session is to discuss work of others. Even though we were involved in the research reported on here, this short paper is intended to survey many ideas due to our collaborators and others. This survey is by no means complete, and we apologize for not having...
Notes on the Motion of Celestial Bodies
JAMP, 2020
A novel method for the computation of the motion of multi-body systems is proposed against the traditional one, based on the dynamic exchange of attraction forces or using complex field equations, that hardly face two-body problems. The Newton gravitational model is interpreted as the emission of neutrino/gravitons from celestial bodies that combine to yield a cumulative flux that interacts with single bodies through a momentum balance. The neu-trino was first found by Fermi to justify the energy conservation in β decay and, using his model; we found that the emission of neutrino from matter is almost constant independently from the nuclides involved. This flux can be correlated to Gauss constant G, allowing the rebuilding of Newton law on the basis of nuclear data, the neutrino weight and the speed of light. Similarly to nature, we can therefore separate in the calculations the neutrino flux, that represents the gravitational field, is dependent on masses and is not bound to the number of bodies involved, from the motion of each body that, given the field, is independent of the mass of bodies themselves. The conflict between exchanges of forces is avoided, the mathematics is simplified, the computational time is reduced to seconds and the stability of result is guaranteed. The example of computation of the solar system including the Sun and eight planets over a period of one to one hundred years is reported, together with the evolution of the shape of the orbits.
Mathematical Methods Applied to the Celestial Mechanics of Artificial Satellites
Mathematical Problems in Engineering, 2012
Celestial mechanics is a science that comes from the more general field of astronomy. It is devoted to the study of the motion of the planets, moons, asteroids, comets, and other celestial bodies. Some of the main researchers involved in this field are well-known names in history, like Johannes Kepler and Isaac Newton, who wrote the basic laws that govern these motions. With the advances of technology, the world entered the so-called "Space Age," where artificial artifacts started to be built and launched into space. To perform those tasks, the same laws used to describe the motion of the natural celestial bodies can be used to study the motion of those manmade spacecrafts. Although it is not the beginning of the space activities, the launch of the satellite Sputnik in 1957, by the former Soviet Union, is an important mark of this age. This launch was then followed by the United States of America USA that, among other space activities, landed a man on the Moon in 1969. Nowadays, after those first historical events, the activities related to artificial satellites are one of the most important fields in science and technology. It includes several important applications of engineering that improved the life of everybody in the entire world. Communications by satellite are well established for many years, and it is hard to imagine a world without this capability. Another field that has been helped by the space activities is the field related to the exploration of resources on Earth. Images from satellites can generate important maps to find their locations, and this can make the difference for a sustainable use of our resources. The use of location devices based on the GPS constellation is also everyday
Orbital Mechanics for Engineering Students
This textbook evolved from a formal set of notes developed over nearly ten years of teaching an introductory course in orbital mechanics for aerospace engineering students. These undergraduate students had no prior formal experience in the subject, but had completed courses in physics, dynamics and mathematics through differential equations and applied linear algebra. That is the background I have presumed for readers of this book. This is by no means a grand, descriptive survey of the entire subject of astronautics. It is a foundations text, a springboard to advanced study of the subject. I focus on the physical phenomena and analytical procedures required to understand and predict, to first order, the behavior of orbiting spacecraft. I have tried to make the book readable for undergraduates, and in so doing I do not shy away from rigor where it is needed for understanding. Spacecraft operations that take place in earth orbit are considered as are interplanetary missions. The important topic of spacecraft control systems is omitted. However, the material in this book and a course in control theory provide the basis for the study of spacecraft attitude control. A brief perusal of the Contents shows that there are more than enough topics to cover in a single semester or term. Chapter 1 is a review of vector kinematics in three dimensions and of Newton's laws of motion and gravitation. It also focuses on the issue of relative motion, crucial to the topics of rendezvous and satellite attitude dynamics. Chapter 2 presents the vector-based solution of the classical two-body problem, coming up with a host of practical formulas for orbit and trajectory analysis. The restricted three-body problem is covered in order to introduce the notion of Lagrange points. Chapter 3 derives Kepler's equations, which relate position to time for the different kinds of orbits. The concept of 'universal variables' is introduced. Chapter 4 is devoted to describing orbits in three dimensions and accounting for the major effects of the earth's oblate, non-spherical shape. Chapter 5 is an introduction to preliminary orbit determination, including Gibbs' and Gauss's methods and the solution of Lambert's problem. Auxiliary topics include topocentric coordinate systems, Julian day numbering and sidereal time. Chapter 6 presents the common means of transferring from one orbit to another by impulsive delta-v maneuvers, including Hohmann transfers, phasing orbits and plane changes. Chapter 7 derives and employs the equations of relative motion required to understand and design two-impulse rendezvous maneuvers. Chapter 8 explores the basics of interplanetary mission analysis. Chapter 9 presents those elements of rigid-body dynamics required to characterize the attitude of an orbiting satellite. Chapter 10 describes the methods of controlling, changing and stabilizing the attitude of spacecraft by means of thrusters, gyros and other devices. Finally, Chapter 11 is a brief introduction to the characteristics and design of multi-stage launch vehicles. Chapters 1 through 4 form the core of a first orbital mechanics course. The time devoted to Chapter 1 depends on the background of the student. It might be surveyed xi xii Preface briefly and used thereafter simply as a reference. What follows Chapter 4 depends on the objectives of the course. Chapters 5 through 8 carry on with the subject of orbital mechanics. Chapter 6 on orbital maneuvers should be included in any case. Coverage of Chapters 5, 7 and 8 is optional. However, if all of Chapter 8 on interplanetary missions is to form a part of the course, then the solution of Lambert's problem (Section 5.3) must be studied beforehand. Chapters 9 and 10 must be covered if the course objectives include an introduction to satellite dynamics. In that case Chapters 5, 7 and 8 would probably not be studied in depth. Chapter 11 is optional if the engineering curriculum requires a separate course in propulsion, including rocket dynamics. To understand the material and to solve problems requires using a lot of undergraduate mathematics. Mathematics, of course, is the language of engineering. Students must not forget that Sir Isaac Newton had to invent calculus so he could solve orbital mechanics problems precisely. Newton (1642-1727) was an English physicist and mathematician, whose 1687 publication Mathematical Principles of Natural Philosophy ('the Principia') is one of the most influential scientific works of all time. It must be noted that the German mathematician Gottfried Wilhelm von Leibniz (1646-1716) is credited with inventing infinitesimal calculus independently of Newton in the 1670s. In addition to honing their math skills, students are urged to take advantage of computers (which, incidentally, use the binary numeral system developed by Leibniz). There are many commercially available mathematics software packages for personal computers. Wherever possible they should be used to relieve the burden of repetitive and tedious calculations. Computer programming skills can and should be put to good use in the study of orbital mechanics. Elementary MATLAB® programs (M-files) appear at the end of this book to illustrate how some of the procedures developed in the text can be implemented in software. All of the scripts were developed using MATLAB version 5.0 and were successfully tested using version 6.5 (release 13). Information about MATLAB, which is a registered trademark of The MathWorks, Inc.
Orbital Mechanics Course - Final Group Report
Orbital Mechanics Course - Final Group Report , 2020
The report was divided into two main parts: the purpose of the first assignment was to design an interplanetary transfer of a spacecraft that minimised the delta-V required to get from Mercury, the starting planet, to Neptune, the target one, performing a flyby on Mars, in a time window of 40 years. To obtain this result two main methods were used: a brut force triple loop routine process and a secondary approach through genetic algorithm. The second assignment involved the propagation analysis of a given nominal orbit affected by some perturbations (J2 and Moon), through two main method: using Cartesian coordinates in the "ECI" frame and Gauss Planetary Equations centered in "rsw" local frame. Furthermore was carried out a frequency analysis and a filter process. Finally this methods were applied to a real satellite data to asses its accuracy and limits. Co-Authors: Apparenza Lucia Bassissi Enrico Di Trocchio Marco Lane John Matthew Peter