Spacecraft Guidance Techniques for Maximizing Mission Success
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AAS 13-250 Hohmann Spiral Transfer with Inclination Change Performed
AAS 13-250 Hohmann Spiral Transfer With Inclination Change Performed By Low-Thrust System Steven Owens1 and Malcolm Macdonald2 This paper investigates the Hohmann Spiral Transfer (HST), an orbit transfer method previously developed by the authors incorporating both high and low- thrust propulsion systems, using the low-thrust system to perform an inclination change as well as orbit transfer. The HST is similar to the bi-elliptic transfer as the high-thrust system is first used to propel the spacecraft beyond the target where it is used again to circularize at an intermediate orbit. The low-thrust system is then activated and, while maintaining this orbit altitude, used to change the orbit inclination to suit the mission specification. The low-thrust system is then used again to reduce the spacecraft altitude by spiraling in-toward the target orbit. An analytical analysis of the HST utilizing the low-thrust system for the inclination change is performed which allows a critical specific impulse ratio to be derived determining the point at which the HST consumes the same amount of fuel as the Hohmann transfer. A critical ratio is found for both a circular and elliptical initial orbit. These equations are validated by a numerical approach before being compared to the HST utilizing the high-thrust system to perform the inclination change. An additional critical ratio comparing the HST utilizing the low-thrust system for the inclination change with its high-thrust counterpart is derived and by using these three critical ratios together, it can be determined when each transfer offers the lowest fuel mass consumption. -
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 -
Prepared by Textore, Inc. Peter Wood, David Yang, and Roger Cliff November 2020
AIR-TO-AIR MISSILES CAPABILITIES AND DEVELOPMENT IN CHINA Prepared by TextOre, Inc. Peter Wood, David Yang, and Roger Cliff November 2020 Printed in the United States of America by the China Aerospace Studies Institute ISBN 9798574996270 To request additional copies, please direct inquiries to Director, China Aerospace Studies Institute, Air University, 55 Lemay Plaza, Montgomery, AL 36112 All photos licensed under the Creative Commons Attribution-Share Alike 4.0 International license, or under the Fair Use Doctrine under Section 107 of the Copyright Act for nonprofit educational and noncommercial use. All other graphics created by or for China Aerospace Studies Institute Cover art is "J-10 fighter jet takes off for patrol mission," China Military Online 9 October 2018. http://eng.chinamil.com.cn/view/2018-10/09/content_9305984_3.htm E-mail: [email protected] Web: http://www.airuniversity.af.mil/CASI https://twitter.com/CASI_Research @CASI_Research https://www.facebook.com/CASI.Research.Org https://www.linkedin.com/company/11049011 Disclaimer The views expressed in this academic research paper are those of the authors and do not necessarily reflect the official policy or position of the U.S. Government or the Department of Defense. In accordance with Air Force Instruction 51-303, Intellectual Property, Patents, Patent Related Matters, Trademarks and Copyrights; this work is the property of the U.S. Government. Limited Print and Electronic Distribution Rights Reproduction and printing is subject to the Copyright Act of 1976 and applicable treaties of the United States. This document and trademark(s) contained herein are protected by law. This publication is provided for noncommercial use only. -
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. -
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. -
Missile Guidance and Control
CHAPTER 4 MISSILE GUIDANCE AND CONTROL INTRODUCTION in the interest of terminology standardization and to assist common understanding, we shall call the In the preceding chapters you learned that the complete system within a missile that steers and essential parts a guided missile needs to perform stabilizes it a guidance and control system. properly are: Depending on your experience with missiles, you 1. Airframe and control surfaces. may take exception to this designation. And if you 2. Propulsion system. do, there is good reason for it. The reason is shown 3. Warhead system. in figure 4-1. For example, if you have worked on 4. Guidance and control system. the Tartar or Terrier missiles you will consider the In addition, in chapter 2 you studied the basic fire system that guides and controls a missile to be its control problem, and learned how some of the steering system. On the other hand, a Talos GMM forces of nature affect the trajectory of a guided would call it a guidance and control system. We missile as it flies to its intended target. In chapter 3 will stick with the latter designation - not because you learned how wings and fins steer a missile and we favor Talos but because most manuals, and keep it pointed along its flight path. The use of many Navy publications, use this term. interior control devices by missiles without exterior control surfaces (or limited ones) was described SUBSYSTEMS AND COMPONENTS briefly. The different types of guidance systems used in missiles are inertial, command, beam-rider, In figure 4-2 we show that the complete system and homing guidance. -
Guidance, Navigation, and Control (GN&C) Efficient, Responsive, and Effective
Space Transportation Systems National Aeronautics and Space Administration Guidance, Navigation, and Control (GN&C) Efficient, Responsive, and Effective The GN&C capability is a critical enabler of • Navigation — system architecture trade every launch vehicle and spacecraft system. studies, sensor selection and modeling, posi- At-A-Glance Marshall applies a robust, responsive, team- tion/orientation determination software (filter) Guidance, navigation, and control capabilities oriented approach to the GN&C design, develop- development, architecture trade studies, auto- will be needed for today’s launch and tomor- ment, and test capabilities. From initial concept matic rendezvous and docking (AR&D), and row’s in-space applications. Marshall has through detailed mission analysis and design, Batch estimation — all mission phases. developed a GN&C capability with experience hardware development and test, verification and • Control — algorithms, vehicle and control directly supporting projects and serving as validation, and mission operations, the Center system requirements and specifications, a supplier and partner to industry, DOD, and can provide the complete end-to-end GN&C stability analyses, and controller design, academia. To achieve end-to-end develop- development and test — or provide any portion modeling and simulation. ment, this capability leverages tools such as of it — for launch vehicles or spacecraft systems the Flight Robotics Lab, specialized software • Sensor Hardware — selection, closed for any NASA mission. Recognized as the tools, and the portable SPRITE small satellite loop testing and qualification; design, build, Agency’s lead and a world-class developer of payload integration environment. The versatile and calibrate specialized sensors. Earth-to-orbit and in-space stages for GN&C, team also provides an anchor and resource Marshall is a key developer of in-space transpor- for government “smart buyer” oversight of tation, spacecraft control, automated rendezvous future space system acquisition, helping to and capture techniques, and testing. -
Ballistic Missile Defense Guidance and Control Issues
Science & Global Security, 1998, Volume 8, pp. 99-124 © 1998 OPA (Overseas Publishers Association) Reprints available directly from the publisher Amsterdam B.V. Photocopying permitted by license only Published under license by Gordon and Breach Science Publishers SA Printed in the United States of America Ballistic Missile Defense Guidance and Control Issues Paul Zarchana Ballistic targets can be more difficult to hit than aircraft targets. If the intercept takes place out of the atmosphere and if no maneuvering is taking place, the ballistic target motion can be fairly predictable since the only force acting on the target is that of grav- ity. In all cases an exoatmospheric interceptor will need fuel to maneuver in order to hit the target. The long engagement times will require guidance and control strategies which conserve fuel and minimize the acceleration levels for a successful intercept. If the intercept takes place within the atmosphere, the ballistic target is not as predict- able because asymmetries within the target structure may cause it to spiral. In addi- tion, the targets’ high speed means that very large decelerations will take place and appear as a maneuver to the pursuing endoatmospheric interceptor. In this case advanced guidance and control strategies are required to insure that the target can be hit even when the missile is out maneuvered. This tutorial will attempt to highlight the major guidance and control challenges facing ballistic missile defense. PREDICTING WHERE THE TARGET WILL BE Before an interceptor can be launched at a ballistic target, a sensor is first required to track the threat. For example, if the sensor is a ground radar, the range and angle from the radar to the target are measured. -
The Future of the U.S. Intercontinental Ballistic Missile Force
CHILDREN AND FAMILIES The RAND Corporation is a nonprofit institution that EDUCATION AND THE ARTS helps improve policy and decisionmaking through ENERGY AND ENVIRONMENT research and analysis. HEALTH AND HEALTH CARE This electronic document was made available from INFRASTRUCTURE AND www.rand.org as a public service of the RAND TRANSPORTATION Corporation. INTERNATIONAL AFFAIRS LAW AND BUSINESS NATIONAL SECURITY Skip all front matter: Jump to Page 16 POPULATION AND AGING PUBLIC SAFETY SCIENCE AND TECHNOLOGY Support RAND Purchase this document TERRORISM AND HOMELAND SECURITY Browse Reports & Bookstore Make a charitable contribution For More Information Visit RAND at www.rand.org Explore RAND Project AIR FORCE View document details Limited Electronic Distribution Rights This document and trademark(s) contained herein are protected by law as indicated in a notice appearing later in this work. This electronic representation of RAND intellectual property is provided for non-commercial use only. Unauthorized posting of RAND electronic documents to a non-RAND website is prohibited. RAND electronic documents are protected under copyright law. Permission is required from RAND to reproduce, or reuse in another form, any of our research documents for commercial use. For information on reprint and linking permissions, please see RAND Permissions. This product is part of the RAND Corporation monograph series. RAND monographs present major research findings that address the challenges facing the public and private sectors. All RAND mono- graphs undergo rigorous peer review to ensure high standards for research quality and objectivity. C O R P O R A T I O N The Future of the U.S. Intercontinental Ballistic Missile Force Lauren Caston, Robert S.