AAS 13-250 Hohmann Spiral Transfer with Inclination Change Performed
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
Low-Energy Lunar Trajectory Design
LOW-ENERGY LUNAR TRAJECTORY DESIGN Jeffrey S. Parker and Rodney L. Anderson Jet Propulsion Laboratory Pasadena, California July 2013 ii DEEP SPACE COMMUNICATIONS AND NAVIGATION SERIES Issued by the Deep Space Communications and Navigation Systems Center of Excellence Jet Propulsion Laboratory California Institute of Technology Joseph H. Yuen, Editor-in-Chief Published Titles in this Series Radiometric Tracking Techniques for Deep-Space Navigation Catherine L. Thornton and James S. Border Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation Theodore D. Moyer Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communication Marvin K. Simon Large Antennas of the Deep Space Network William A. Imbriale Antenna Arraying Techniques in the Deep Space Network David H. Rogstad, Alexander Mileant, and Timothy T. Pham Radio Occultations Using Earth Satellites: A Wave Theory Treatment William G. Melbourne Deep Space Optical Communications Hamid Hemmati, Editor Spaceborne Antennas for Planetary Exploration William A. Imbriale, Editor Autonomous Software-Defined Radio Receivers for Deep Space Applications Jon Hamkins and Marvin K. Simon, Editors Low-Noise Systems in the Deep Space Network Macgregor S. Reid, Editor Coupled-Oscillator Based Active-Array Antennas Ronald J. Pogorzelski and Apostolos Georgiadis Low-Energy Lunar Trajectory Design Jeffrey S. Parker and Rodney L. Anderson LOW-ENERGY LUNAR TRAJECTORY DESIGN Jeffrey S. Parker and Rodney L. Anderson Jet Propulsion Laboratory Pasadena, California July 2013 iv Low-Energy Lunar Trajectory Design July 2013 Jeffrey Parker: I dedicate the majority of this book to my wife Jen, my best friend and greatest support throughout the development of this book and always. -
Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Optimisation of Propellant Consumption for Power Limited Rockets
Delft University of Technology Faculty Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics Optimisation of Propellant Consumption for Power Limited Rockets. What Role do Power Limited Rockets have in Future Spaceflight Missions? (Dutch title: Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten. De rol van deze raketten in toekomstige ruimtevlucht missies. ) A thesis submitted to the Delft Institute of Applied Mathematics as part to obtain the degree of BACHELOR OF SCIENCE in APPLIED MATHEMATICS by NATHALIE OUDHOF Delft, the Netherlands December 2017 Copyright c 2017 by Nathalie Oudhof. All rights reserved. BSc thesis APPLIED MATHEMATICS \ Optimisation of Propellant Consumption for Power Limited Rockets What Role do Power Limite Rockets have in Future Spaceflight Missions?" (Dutch title: \Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten De rol van deze raketten in toekomstige ruimtevlucht missies.)" NATHALIE OUDHOF Delft University of Technology Supervisor Dr. P.M. Visser Other members of the committee Dr.ir. W.G.M. Groenevelt Drs. E.M. van Elderen 21 December, 2017 Delft Abstract In this thesis we look at the most cost-effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the Hohmann Transfer Orbit, will be explained. Using Optimal Control Theory, the optimal trajectory for power limited rockets can be found. Three trajectories will be discussed: Low Earth Orbit to Geostationary Earth Orbit, Earth to Mars and Earth to Saturn. After this we compare the propellant use of the thrust limited rockets for these trajectories with the power limited rockets. -
A Strategy for the Eigenvector Perturbations of the Reynolds Stress Tensor in the Context of Uncertainty Quantification
Center for Turbulence Research 425 Proceedings of the Summer Program 2016 A strategy for the eigenvector perturbations of the Reynolds stress tensor in the context of uncertainty quantification By R. L. Thompsony, L. E. B. Sampaio, W. Edeling, A. A. Mishra AND G. Iaccarino In spite of increasing progress in high fidelity turbulent simulation avenues like Di- rect Numerical Simulation (DNS) and Large Eddy Simulation (LES), Reynolds-Averaged Navier-Stokes (RANS) models remain the predominant numerical recourse to study com- plex engineering turbulent flows. In this scenario, it is imperative to provide reliable estimates for the uncertainty in RANS predictions. In the recent past, an uncertainty estimation framework relying on perturbations to the modeled Reynolds stress tensor has been widely applied with satisfactory results. Many of these investigations focus on perturbing only the Reynolds stress eigenvalues in the Barycentric map, thus ensuring realizability. However, these restrictions apply to the eigenvalues of that tensor only, leav- ing the eigenvectors free of any limiting condition. In the present work, we propose the use of the Reynolds stress transport equation as a constraint for the eigenvector pertur- bations of the Reynolds stress anisotropy tensor once the eigenvalues of this tensor are perturbed. We apply this methodology to a convex channel and show that the ensuing eigenvector perturbations are a more accurate measure of uncertainty when compared with a pure eigenvalue perturbation. 1. Introduction Turbulent flows are present in a wide number of engineering design problems. Due to the disparate character of such flows, predictive methods must be robust, so as to be easily applicable for most of these cases, yet possessing a high degree of accuracy in each. -
Up, Up, and Away by James J
www.astrosociety.org/uitc No. 34 - Spring 1996 © 1996, Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, CA 94112. Up, Up, and Away by James J. Secosky, Bloomfield Central School and George Musser, Astronomical Society of the Pacific Want to take a tour of space? Then just flip around the channels on cable TV. Weather Channel forecasts, CNN newscasts, ESPN sportscasts: They all depend on satellites in Earth orbit. Or call your friends on Mauritius, Madagascar, or Maui: A satellite will relay your voice. Worried about the ozone hole over Antarctica or mass graves in Bosnia? Orbital outposts are keeping watch. The challenge these days is finding something that doesn't involve satellites in one way or other. And satellites are just one perk of the Space Age. Farther afield, robotic space probes have examined all the planets except Pluto, leading to a revolution in the Earth sciences -- from studies of plate tectonics to models of global warming -- now that scientists can compare our world to its planetary siblings. Over 300 people from 26 countries have gone into space, including the 24 astronauts who went on or near the Moon. Who knows how many will go in the next hundred years? In short, space travel has become a part of our lives. But what goes on behind the scenes? It turns out that satellites and spaceships depend on some of the most basic concepts of physics. So space travel isn't just fun to think about; it is a firm grounding in many of the principles that govern our world and our universe. -
Spacecraft Guidance Techniques for Maximizing Mission Success
Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2014 Spacecraft Guidance Techniques for Maximizing Mission Success Shane B. Robinson Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Robinson, Shane B., "Spacecraft Guidance Techniques for Maximizing Mission Success" (2014). All Graduate Theses and Dissertations. 2175. https://digitalcommons.usu.edu/etd/2175 This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. SPACECRAFT GUIDANCE TECHNIQUES FOR MAXIMIZING MISSION SUCCESS by Shane B. Robinson A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering Approved: Dr. David K. Geller Dr. Jacob H. Gunther Major Professor Committee Member Dr. Warren F. Phillips Dr. Charles M. Swenson Committee Member Committee Member Dr. Stephen A. Whitmore Dr. Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2013 [This page intentionally left blank] iii Copyright c Shane B. Robinson 2013 All Rights Reserved [This page intentionally left blank] v Abstract Spacecraft Guidance Techniques for Maximizing Mission Success by Shane B. Robinson, Doctor of Philosophy Utah State University, 2013 Major Professor: Dr. David K. Geller Department: Mechanical and Aerospace Engineering Traditional spacecraft guidance techniques have the objective of deterministically min- imizing fuel consumption. -
Richard Dalbello Vice President, Legal and Government Affairs Intelsat General
Commercial Management of the Space Environment Richard DalBello Vice President, Legal and Government Affairs Intelsat General The commercial satellite industry has billions of dollars of assets in space and relies on this unique environment for the development and growth of its business. As a result, safety and the sustainment of the space environment are two of the satellite industry‘s highest priorities. In this paper I would like to provide a quick survey of past and current industry space traffic control practices and to discuss a few key initiatives that the industry is developing in this area. Background The commercial satellite industry has been providing essential space services for almost as long as humans have been exploring space. Over the decades, this industry has played an active role in developing technology, worked collaboratively to set standards, and partnered with government to develop successful international regulatory regimes. Success in both commercial and government space programs has meant that new demands are being placed on the space environment. This has resulted in orbital crowding, an increase in space debris, and greater demand for limited frequency resources. The successful management of these issues will require a strong partnership between government and industry and the careful, experience-based expansion of international law and diplomacy. Throughout the years, the satellite industry has never taken for granted the remarkable environment in which it works. Industry has invested heavily in technology and sought out the best and brightest minds to allow the full, but sustainable exploitation of the space environment. Where problems have arisen, such as space debris or electronic interference, industry has taken 1 the initiative to deploy new technologies and adopt new practices to minimize negative consequences. -
Perturbation Theory in Celestial Mechanics
Perturbation Theory in Celestial Mechanics Alessandra Celletti Dipartimento di Matematica Universit`adi Roma Tor Vergata Via della Ricerca Scientifica 1, I-00133 Roma (Italy) ([email protected]) December 8, 2007 Contents 1 Glossary 2 2 Definition 2 3 Introduction 2 4 Classical perturbation theory 4 4.1 The classical theory . 4 4.2 The precession of the perihelion of Mercury . 6 4.2.1 Delaunay action–angle variables . 6 4.2.2 The restricted, planar, circular, three–body problem . 7 4.2.3 Expansion of the perturbing function . 7 4.2.4 Computation of the precession of the perihelion . 8 5 Resonant perturbation theory 9 5.1 The resonant theory . 9 5.2 Three–body resonance . 10 5.3 Degenerate perturbation theory . 11 5.4 The precession of the equinoxes . 12 6 Invariant tori 14 6.1 Invariant KAM surfaces . 14 6.2 Rotational tori for the spin–orbit problem . 15 6.3 Librational tori for the spin–orbit problem . 16 6.4 Rotational tori for the restricted three–body problem . 17 6.5 Planetary problem . 18 7 Periodic orbits 18 7.1 Construction of periodic orbits . 18 7.2 The libration in longitude of the Moon . 20 1 8 Future directions 20 9 Bibliography 21 9.1 Books and Reviews . 21 9.2 Primary Literature . 22 1 Glossary KAM theory: it provides the persistence of quasi–periodic motions under a small perturbation of an integrable system. KAM theory can be applied under quite general assumptions, i.e. a non– degeneracy of the integrable system and a diophantine condition of the frequency of motion. -
Session 6:Analytical Approximations for Low Thrust Maneuvers
Session 6: Analytical Approximations for Low Thrust Maneuvers As mentioned in the previous lecture, solving non-Keplerian problems in general requires the use of perturbation methods and many are only solvable through numerical integration. However, there are a few examples of low-thrust space propulsion maneuvers for which we can find approximate analytical expressions. In this lecture, we explore a couple of these maneuvers, both of which are useful because of their precision and practical value: i) climb or descent from a circular orbit with continuous thrust, and ii) in-orbit repositioning, or walking. Spiral Climb/Descent We start by writing the equations of motion in polar coordinates, 2 d2r �dθ � µ − r + = a (1) 2 2 r dt dt r 2 d θ 2 dr dθ aθ + = (2) 2 dt r dt dt r We assume continuous thrust in the angular direction, therefore ar = 0. If the acceleration force along θ is small, then we can safely assume the orbit will remain nearly circular and the semi-major axis will be just slightly different after one orbital period. Of course, small and slightly are vague words. To make the analysis rigorous, we need to be more precise. Let us say that for this approximation to be valid, the angular acceleration has to be much smaller than the corresponding centrifugal or gravitational forces (the last two terms in the LHS of Eq. (1)) and that the radial acceleration (the first term in the LHS in the same equation) is negligible. Given these assumptions, from Eq. (1), dθ r µ d2θ 3 r µ dr ≈ ! ≈ − (3) 3 2 5 dt r dt 2 r dt Substituting into Eq. -
Spacex Rocket Data Satisfies Elementary Hohmann Transfer Formula E-Mail: [email protected] and [email protected]
IOP Physics Education Phys. Educ. 55 P A P ER Phys. Educ. 55 (2020) 025011 (9pp) iopscience.org/ped 2020 SpaceX rocket data satisfies © 2020 IOP Publishing Ltd elementary Hohmann transfer PHEDA7 formula 025011 Michael J Ruiz and James Perkins M J Ruiz and J Perkins Department of Physics and Astronomy, University of North Carolina at Asheville, Asheville, NC 28804, United States of America SpaceX rocket data satisfies elementary Hohmann transfer formula E-mail: [email protected] and [email protected] Printed in the UK Abstract The private company SpaceX regularly launches satellites into geostationary PED orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper 10.1088/1361-6552/ab5f4c this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit around the Earth to enter a Hohmann transfer orbit, an elliptical orbit on which the spacecraft reaches 1361-6552 a high altitude. A simple derivation is given for the Hohmann transfer velocity boost that introductory students can derive on their own with a little teacher guidance. They can then use the SpaceX telemetry data to verify the Published theoretical results, finding the discrepancy between observation and theory to be 3% or less. The students will love the rocket videos as the launches and 3 transfer burns are very exciting to watch. 2 Introduction Complex 39A at the NASA Kennedy Space Center in Cape Canaveral, Florida. This launch SpaceX is a company that ‘designs, manufactures and launches advanced rockets and spacecraft. -
Results of Long-Duration Simulation of Distant Retrograde Orbits
aerospace Article Results of Long-Duration Simulation of Distant Retrograde Orbits Gary Turner Odyssey Space Research, 1120 NASA Pkwy, Houston, TX 77058, USA; [email protected] Academic Editor: Konstantinos Kontis Received: 31 July 2016; Accepted: 26 October 2016; Published: 8 November 2016 Abstract: Distant Retrograde Orbits in the Earth–Moon system are gaining in popularity as stable “parking” orbits for various conceptual missions. To investigate the stability of potential Distant Retrograde Orbits, simulations were executed, with propagation running over a thirty-year period. Initial conditions for the vehicle state were limited such that the position and velocity vectors were in the Earth–Moon orbital plane, with the velocity oriented such that it would produce retrograde motion about Moon. The resulting trajectories were investigated for stability in an environment that included the eccentric motion of Moon, non-spherical gravity of Earth and Moon, gravitational perturbations from Sun, Jupiter, and Venus, and the effects of radiation pressure. The results indicate that stability may be enhanced at certain resonant states within the Earth–Moon system. Keywords: Distant Retrograde Orbit; DRO; orbits-stability; radiation pressure; orbits-resonance; dynamics 1. Introduction 1.1. Overview The term Distant Retrograde Orbit (DRO) was introduced by O’Campo and Rosborough [1] to describe a set of trajectories that appeared to orbit the Earth–Moon system in a retrograde sense when compared with the motion of the Earth/Moon around the solar-system barycenter. It has since been extended to be a generic term applied to the motion of a minor body around the three-body system-barycenter where such motion gives the appearance of retrograde motion about the secondary body in the system. -
ORBIT MANOUVERS • Orbital Plane Change (Inclination) It Is an Orbital
UNIVERSITY OF ANBAR ADVANCED COMMUNICATIONS SYSTEMS FOR 4th CLASS STUDENTS COLLEGE OF ENGINEERING by: Dr. Naser Al-Falahy ELECTRICAL ENGINEERING WE EK 4 ORBIT MANOUVERS Orbital plane change (inclination) It is an orbital maneuver aimed at changing the inclination of an orbiting body's orbit. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector (delta v) at the orbital nodes (i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes). In general, inclination changes can take a very large amount of delta v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize any inclination change required over the duration of the spacecraft life. When both orbits are circular (i.e. e = 0) and have the same radius the Delta-v (Δvi) required for an inclination change (Δvi) can be calculated using: where: v is the orbital velocity and has the same units as Δvi (Δi ) inclination change required. Example Calculate the velocity change required to transfer a satellite from a circular 600 km orbit with an inclination of 28 degrees to an orbit of equal size with an inclination of 20 degrees. SOLUTION, r = (6,378.14 + 600) × 1,000 = 6,978,140 m , ϑ = 28 - 20 = 8 degrees Vi = SQRT[ GM / r ] Vi = SQRT[ 3.986005×1014 / 6,978,140 ] Vi = 7,558 m/s Δvi = 2 × Vi × sin(ϑ/2) Δvi = 2 × 7,558 × sin(8/2) Δvi = 1,054 m/s 18 UNIVERSITY OF ANBAR ADVANCED COMMUNICATIONS SYSTEMS FOR 4th CLASS STUDENTS COLLEGE OF ENGINEERING by: Dr.