ORBIT MANOUVERS • Orbital Plane Change (Inclination) It Is an Orbital
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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. -
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 -
Uncommon Sense in Orbit Mechanics
AAS 93-290 Uncommon Sense in Orbit Mechanics by Chauncey Uphoff Consultant - Ball Space Systems Division Boulder, Colorado Abstract: This paper is a presentation of several interesting, and sometimes valuable non- sequiturs derived from many aspects of orbital dynamics. The unifying feature of these vignettes is that they all demonstrate phenomena that are the opposite of what our "common sense" tells us. Each phenomenon is related to some application or problem solution close to or directly within the author's experience. In some of these applications, the common part of our sense comes from the fact that we grew up on t h e surface of a planet, deep in its gravity well. In other examples, our mathematical intuition is wrong because our mathematical model is incomplete or because we are accustomed to certain kinds of solutions like the ones we were taught in school. The theme of the paper is that many apparently unsolvable problems might be resolved by the process of guessing the answer and trying to work backwards to the problem. The ability to guess the right answer in the first place is a part of modern magic. A new method of ballistic transfer from Earth to inner solar system targets is presented as an example of the combination of two concepts that seem to work in reverse. Introduction Perhaps the simplest example of uncommon sense in orbit mechanics is the increase of speed of a satellite as it "decays" under the influence of drag caused by collisions with the molecules of the upper atmosphere. In everyday life, when we slow something down, we expect it to slow down, not to speed up. -
Maneuver Detection of Space Object for Space Surveillance
MANEUVER DETECTION OF SPACE OBJECT FOR SPACE SURVEILLANCE Jian Huang*, Weidong Hu, Lefeng Zhang $756WDWH.H\/DE1DWLRQDO8QLYHUVLW\RI'HIHQVH7HFKQRORJ\&KDQJVKD+XQDQ3URYLQFH&KLQD (PDLOKXDQJMLDQ#QXGWHGXFQ ABSTRACT on the technique of a moving window curve fit. Holzinger & Scheeres presented an object correlation Maneuver detection is a very important task for and maneuver detection method using optimal control maintaining the catalog of the orbital objects and space performance metrics [5]. Kelecy & Jah focused on the situational awareness. This paper mainly focuses on the detection and reconstruction of single low thrust in- typical maneuver scenario where space objects only track maneuvers by using the orbit determination perform tangential orbital maneuvers during a relative strategies based on the batch least-squares and long gap. Particularly, only two classical and extended Kalman filter (EKF) [6]. However, these commonly applied orbital transition manners are methods are highly relevant to the presupposed considered, i.e. the twice tangential maneuvers at the maneuvering mode and a relative short observation gap. apogee and the perigee or one tangential maneuver at In this paper, to address the real observed data, we only an arbitrary time. Based on this, we preliminarily consider the common maneuvering modes and estimate the maneuvering mode and parameters by observation scenarios in practical. For an orbital analyzing the change of semi-major axis and maneuver, minimization of fuel consumption is eccentricity. Furthermore, if only one tangential essential because the weight of a payload that can be maneuver happened, we can formulate the estimation carried to the desired orbit depends on this problem of maneuvering parameters as a non-linear minimization. -
Reduction of Saturn Orbit Insertion Impulse Using Deep-Space Low Thrust
Reduction of Saturn Orbit Insertion Impulse using Deep-Space Low Thrust Elena Fantino ∗† Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates. Roberto Flores‡ International Center for Numerical Methods in Engineering, 08034 Barcelona, Spain. Jesús Peláez§ and Virginia Raposo-Pulido¶ Technical University of Madrid, 28040 Madrid, Spain. Orbit insertion at Saturn requires a large impulsive manoeuver due to the velocity difference between the spacecraft and the planet. This paper presents a strategy to reduce dramatically the hyperbolic excess speed at Saturn by means of deep-space electric propulsion. The inter- planetary trajectory includes a gravity assist at Jupiter, combined with low-thrust maneuvers. The thrust arc from Earth to Jupiter lowers the launch energy requirement, while an ad hoc steering law applied after the Jupiter flyby reduces the hyperbolic excess speed upon arrival at Saturn. This lowers the orbit insertion impulse to the point where capture is possible even with a gravity assist with Titan. The control-law algorithm, the benefits to the mass budget and the main technological aspects are presented and discussed. The simple steering law is compared with a trajectory optimizer to evaluate the quality of the results and possibilities for improvement. I. Introduction he giant planets have a special place in our quest for learning about the origins of our planetary system and Tour search for life, and robotic missions are essential tools for this scientific goal. Missions to the outer planets arXiv:2001.04357v1 [astro-ph.EP] 8 Jan 2020 have been prioritized by NASA and ESA, and this has resulted in important space projects for the exploration of the Jupiter system (NASA’s Europa Clipper [1] and ESA’s Jupiter Icy Moons Explorer [2]), and studies are underway to launch a follow-up of Cassini/Huygens called Titan Saturn System Mission (TSSM) [3], a joint ESA-NASA project. -
Orbital Mechanics
Orbital Mechanics These notes provide an alternative and elegant derivation of Kepler's three laws for the motion of two bodies resulting from their gravitational force on each other. Orbit Equation and Kepler I Consider the equation of motion of one of the particles (say, the one with mass m) with respect to the other (with mass M), i.e. the relative motion of m with respect to M: r r = −µ ; (1) r3 with µ given by µ = G(M + m): (2) Let h be the specific angular momentum (i.e. the angular momentum per unit mass) of m, h = r × r:_ (3) The × sign indicates the cross product. Taking the derivative of h with respect to time, t, we can write d (r × r_) = r_ × r_ + r × ¨r dt = 0 + 0 = 0 (4) The first term of the right hand side is zero for obvious reasons; the second term is zero because of Eqn. 1: the vectors r and ¨r are antiparallel. We conclude that h is a constant vector, and its magnitude, h, is constant as well. The vector h is perpendicular to both r and the velocity r_, hence to the plane defined by these two vectors. This plane is the orbital plane. Let us now carry out the cross product of ¨r, given by Eqn. 1, and h, and make use of the vector algebra identity A × (B × C) = (A · C)B − (A · B)C (5) to write µ ¨r × h = − (r · r_)r − r2r_ : (6) r3 { 2 { The r · r_ in this equation can be replaced by rr_ since r · r = r2; and after taking the time derivative of both sides, d d (r · r) = (r2); dt dt 2r · r_ = 2rr;_ r · r_ = rr:_ (7) Substituting Eqn. -
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019 Term Description AEHF Advanced Extremely High Frequency AFB / AFS Air Force Base / Air Force Station AOC Air Operations Center AOI Area of Interest The point in the orbit of a heavenly body, specifically the moon, or of a man-made satellite Apogee at which it is farthest from the earth. Even CAP rockets experience apogee. Either of two points in an eccentric orbit, one (higher apsis) farthest from the center of Apsis attraction, the other (lower apsis) nearest to the center of attraction Argument of Perigee the angle in a satellites' orbit plane that is measured from the Ascending Node to the (ω) perigee along the satellite direction of travel CGO Company Grade Officer CLV Calculated Load Value, Crew Launch Vehicle COP Common Operating Picture DCO Defensive Cyber Operations DHS Department of Homeland Security DoD Department of Defense DOP Dilution of Precision Defense Satellite Communications Systems - wideband communications spacecraft for DSCS the USAF DSP Defense Satellite Program or Defense Support Program - "Eyes in the Sky" EHF Extremely High Frequency (30-300 GHz; 1mm-1cm) ELF Extremely Low Frequency (3-30 Hz; 100,000km-10,000km) EMS Electromagnetic Spectrum Equitorial Plane the plane passing through the equator EWR Early Warning Radar and Electromagnetic Wave Resistivity GBR Ground-Based Radar and Global Broadband Roaming GBS Global Broadcast Service GEO Geosynchronous Earth Orbit or Geostationary Orbit ( ~22,300 miles above Earth) GEODSS Ground-Based Electro-Optical Deep Space Surveillance -
The Speed of a Geosynchronous Satellite Is ___
Physics 106 Lecture 9 Newton’s Law of Gravitation SJ 7th Ed.: Chap 13.1 to 2, 13.4 to 5 • Historical overview • N’Newton’s inverse-square law of graviiitation Force Gravitational acceleration “g” • Superposition • Gravitation near the Earth’s surface • Gravitation inside the Earth (concentric shells) • Gravitational potential energy Related to the force by integration A conservative force means it is path independent Escape velocity Example A geosynchronous satellite circles the earth once every 24 hours. If the mass of the earth is 5.98x10^24 kg; and the radius of the earth is 6.37x10^6 m., how far above the surface of the earth does a geosynchronous satellite orbit the earth? G=6.67x10-11 Nm2/kg2 The speed of a geosynchronous satellite is ______. 1 Goal Gravitational potential energy for universal gravitational force Gravitational Potential Energy WUgravity= −Δ gravity Near surface of Earth: Gravitational force of magnitude of mg, pointing down (constant force) Æ U = mgh Generally, gravit. potential energy for a system of m1 & m2 G Gmm12 mm F = Attractive force Ur()=− G12 12 r 2 g 12 12 r12 Zero potential energy is chosen for infinite distance between m1 and m2. Urg ()012 = ∞= Æ Gravitational potential energy is always negative. 2 mm12 Urg ()12 =− G r12 r r Ug=0 1 U(r1) Gmm U =− 12 g r Mechanical energy 11 mM EKUrmvMVG=+ ( ) =22 + − mech 22 r m V r v M E_mech is conserved, if gravity is the only force that is doing work. 1 2 MV is almost unchanged. If M >>> m, 2 1 2 mM ÆWe can define EKUrmvG=+ ( ) = − mech 2 r 3 Example: A stone is thrown vertically up at certain speed from the surface of the Moon by Superman. -
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. -
Flight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics AE2-104, lecture hours 21-24: Interplanetary flight Ron Noomen October 25, 2012 AE2104 Flight and Orbital Mechanics 1 | Example: Galileo VEEGA trajectory Questions: • what is the purpose of this mission? • what propulsion technique(s) are used? • why this Venus- Earth-Earth sequence? • …. [NASA, 2010] AE2104 Flight and Orbital Mechanics 2 | Overview • Solar System • Hohmann transfer orbits • Synodic period • Launch, arrival dates • Fast transfer orbits • Round trip travel times • Gravity Assists AE2104 Flight and Orbital Mechanics 3 | Learning goals The student should be able to: • describe and explain the concept of an interplanetary transfer, including that of patched conics; • compute the main parameters of a Hohmann transfer between arbitrary planets (including the required ΔV); • compute the main parameters of a fast transfer between arbitrary planets (including the required ΔV); • derive the equation for the synodic period of an arbitrary pair of planets, and compute its numerical value; • derive the equations for launch and arrival epochs, for a Hohmann transfer between arbitrary planets; • derive the equations for the length of the main mission phases of a round trip mission, using Hohmann transfers; and • describe the mechanics of a Gravity Assist, and compute the changes in velocity and energy. Lecture material: • these slides (incl. footnotes) AE2104 Flight and Orbital Mechanics 4 | Introduction The Solar System (not to scale): [Aerospace -
Lesson 3: Moons, Rings Relationships
GETTING TO KNOW SATURN LESSON Moons, Rings, and Relationships 3 3–4 hrs Students design their own experiments to explore the fundamental force of gravity, and then extend their thinking to how gravity acts to keep objects like moons and ring particles in orbit. Students use the contexts of the Solar System and the Saturn system MEETS NATIONAL to explore the nature of orbits. The lesson SCIENCE EDUCATION enables students to correct common mis- STANDARDS: conceptions about gravity and orbits and to Science as Inquiry • Abilities learn how orbital speed decreases as the dis- Prometheus and Pandora, two of Saturn’s moons, “shepherd” necessary to Saturn’s F ring. scientific inquiry tance from the object being orbited increases. Physical Science • Motions and PREREQUISITE SKILLS BACKGROUND INFORMATION forces Working in groups Background for Lesson Discussion, page 66 Earth and Space Science Reading a chart of data Questions, page 71 • Earth in the Plotting points on a graph Answers in Appendix 1, page 225 Solar System 1–21: Saturn 22–34: Rings 35–50: Moons EQUIPMENT, MATERIALS, AND TOOLS For the teacher Materials to reproduce Photocopier (for transparencies & copies) Figures 1–10 are provided at the end of Overhead projector this lesson. Chalkboard, whiteboard, or large easel FIGURE TRANSPARENCY COPIES with paper; chalk or markers 11 21 For each group of 3 to 4 students 31 Large plastic or rubber ball 4 1 per student Paper, markers, pencils 5 1 1 per student 6 1 for teacher 7 1 (optional) 1 for teacher 8 1 per student 9 1 (optional) 1 per student 10 1 (optional) 1 for teacher 65 Saturn Educator Guide • Cassini Program website — http://www.jpl.nasa.gov/cassini/educatorguide • EG-1999-12-008-JPL Background for Lesson Discussion LESSON 3 Science as inquiry The nature of Saturn’s rings and how (See Procedures & Activities, Part I, Steps 1-6) they move (See Procedures & Activities, Part IIa, Step 3) Part I of the lesson offers students a good oppor- tunity to experience science as inquiry.