Celestial Mechanics and Satellite Orbits Introduction to Space
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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 -
Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite
46th AIAA Aerospace Sciences Meeting and Exhibit AIAA 2008-1131 7 – 10 January 20006, Reno, Nevada Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite Stephen A. Whitmore* and Tyson K. Smith† Utah State University, Logan, UT, 84322-4130 A trade study investigating the economics, mass budget, and concept of operations for delivery of a small technology-demonstration satellite to a medium-altitude earth orbit is presented. The mission requires payload deployment at a 19,000 km orbit altitude and an inclination of 55o. Because the payload is a technology demonstrator and not part of an operational mission, launch and deployment costs are a paramount consideration. The payload includes classified technologies; consequently a USA licensed launch system is mandated. A preliminary trade analysis is performed where all available options for FAA-licensed US launch systems are considered. The preliminary trade study selects the Orbital Sciences Minotaur V launch vehicle, derived from the decommissioned Peacekeeper missile system, as the most favorable option for payload delivery. To meet mission objectives the Minotaur V configuration is modified, replacing the baseline 5th stage ATK-37FM motor with the significantly smaller ATK Star 27. The proposed design change enables payload delivery to the required orbit without using a 6th stage kick motor. End-to-end mass budgets are calculated, and a concept of operations is presented. Monte-Carlo simulations are used to characterize the expected accuracy of the final orbit. -
Seismic Wavefield Polarization
E3S Web of Conferences 12, 06001 (2016) DOI: 10.1051/e3sconf/20161206001 i-DUST 2016 Seismic wavefield polarization – Part I: Describing an elliptical polarized motion, a review of motivations and methods Claire Labonne1,2, a , Olivier Sèbe1, and Stéphane Gaffet2,3 1 CEA, DAM, DIF, 91297 Arpajon, France 2 Univ. Nice Sophia Antipolis, CNRS, IRD, Observatoire de la côte d’Azur, Géoazur UMR 7329, Valbonne, France 3 LSBB UMS 3538, Rustrel, France Abstract. The seismic wavefield can be approximated by a sum of elliptical polarized motions in 3D space, including the extreme linear and circular motions. Each elliptical motion need to be described: the characterization of the ellipse flattening, the orientation of the ellipse, circle or line in the 3D space, and the direction of rotation in case of non-purely linear motion. Numerous fields of study share the need of describing an elliptical motion. A review of advantages and drawbacks of each convention from electromagnetism, astrophysics and focal mechanism is done in order to thereafter define a set of parameters to fully characterize the seismic wavefield polarization. 1. Introduction The seismic wavefield is a combination of polarized waves in the three-dimensional (3D) space. The polarization is a characteristic of the wave related to the particle motion. The displacement of particles effected by elastic waves shows a particular polarization shape and a preferred direction of polarization depending on the source properties (location and characteristics) and the Earth structure. P-waves, for example, generate linear particle motion in the direction of propagation; the polarization is thus called linear. Rayleigh waves, on the other hand, generate, at the surface of the Earth, retrograde elliptical particle motion. -
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. -
Chapter 2: Earth in Space
Chapter 2: Earth in Space 1. Old Ideas, New Ideas 2. Origin of the Universe 3. Stars and Planets 4. Our Solar System 5. Earth, the Sun, and the Seasons 6. The Unique Composition of Earth Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Earth in Space Concept Survey Explain how we are influenced by Earth’s position in space on a daily basis. The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas • Why is Earth the only planet known to support life? • How have our views of Earth’s position in space changed over time? • Why is it warmer in summer and colder in winter? (or, How does Earth’s position relative to the sun control the “Earthrise” taken by astronauts aboard Apollo 8, December 1968 climate?) The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System sun • Geocentric orbit hypothesis - Ancient civilizations interpreted rising of sun in east and setting in west to indicate the sun (and other planets) revolved around Earth Earth pictured at the center of a – Remained dominant geocentric planetary system idea for more than 2,000 years The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System • Heliocentric orbit hypothesis –16th century idea suggested by Copernicus • Confirmed by Galileo’s early 17th century observations of the phases of Venus – Changes in the size and shape of Venus as observed from Earth The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System • Galileo used early telescopes to observe changes in the size and shape of Venus as it revolved around the sun The Good Earth, Chapter 2: Earth in Space Earth in Space Conceptest The moon has what type of orbit? A. -
Chapter 7 Mapping The
BASICS OF RADIO ASTRONOMY Chapter 7 Mapping the Sky Objectives: When you have completed this chapter, you will be able to describe the terrestrial coordinate system; define and describe the relationship among the terms com- monly used in the “horizon” coordinate system, the “equatorial” coordinate system, the “ecliptic” coordinate system, and the “galactic” coordinate system; and describe the difference between an azimuth-elevation antenna and hour angle-declination antenna. In order to explore the universe, coordinates must be developed to consistently identify the locations of the observer and of the objects being observed in the sky. Because space is observed from Earth, Earth’s coordinate system must be established before space can be mapped. Earth rotates on its axis daily and revolves around the sun annually. These two facts have greatly complicated the history of observing space. However, once known, accu- rate maps of Earth could be made using stars as reference points, since most of the stars’ angular movements in relationship to each other are not readily noticeable during a human lifetime. Although the stars do move with respect to each other, this movement is observable for only a few close stars, using instruments and techniques of great precision and sensitivity. Earth’s Coordinate System A great circle is an imaginary circle on the surface of a sphere whose center is at the center of the sphere. The equator is a great circle. Great circles that pass through both the north and south poles are called meridians, or lines of longitude. For any point on the surface of Earth a meridian can be defined. -
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. -
Brief Introduction to Orbital Mechanics Page 1
Brief Introduction to Orbital Mechanics Page 1 Brief Introduction to Orbital Mechanics We wish to work out the specifics of the orbital geometry of satellites. We begin by employing Newton's laws of motion to determine the orbital period of a satellite. The first equation of motion is F = ma (1) where m is mass, in kg, and a is acceleration, in m/s2. The Earth produces a gravitational field equal to Gm g(r) = − E r^ (2) r2 24 −11 2 2 where mE = 5:972 × 10 kg is the mass of the Earth and G = 6:674 × 10 N · m =kg is the gravitational constant. The gravitational force acting on the satellite is then equal to Gm mr^ Gm mr F = − E = − E : (3) in r2 r3 This force is inward (towards the Earth), and as such is defined as a centripetal force acting on the satellite. Since the product of mE and G is a constant, we can define µ = mEG = 3:986 × 1014 N · m2=kg which is known as Kepler's constant. Then, µmr F = − : (4) in r3 This force is illustrated in Figure 1(a). An equal and opposite force acts on the satellite called the centrifugal force, also shown. This force keeps the satellite moving in a circular path with linear speed, away from the axis of rotation. Hence we can define a centrifugal acceleration as the change in velocity produced by the satellite moving in a circular path with respect to time, which keeps the satellite moving in a circular path without falling into the centre. -
GPS Applications in Space
Space Situational Awareness 2015: GPS Applications in Space James J. Miller, Deputy Director Policy & Strategic Communications Division May 13, 2015 GPS Extends the Reach of NASA Networks to Enable New Space Ops, Science, and Exploration Apps GPS Relative Navigation is used for Rendezvous to ISS GPS PNT Services Enable: • Attitude Determination: Use of GPS enables some missions to meet their attitude determination requirements, such as ISS • Real-time On-Board Navigation: Enables new methods of spaceflight ops such as rendezvous & docking, station- keeping, precision formation flying, and GEO satellite servicing • Earth Sciences: GPS used as a remote sensing tool supports atmospheric and ionospheric sciences, geodesy, and geodynamics -- from monitoring sea levels and ice melt to measuring the gravity field ESA ATV 1st mission JAXA’s HTV 1st mission Commercial Cargo Resupply to ISS in 2008 to ISS in 2009 (Space-X & Cygnus), 2012+ 2 Growing GPS Uses in Space: Space Operations & Science • NASA strategic navigation requirements for science and 20-Year Worldwide Space Mission space ops continue to grow, especially as higher Projections by Orbit Type* precisions are needed for more complex operations in all space domains 1% 5% Low Earth Orbit • Nearly 60%* of projected worldwide space missions 27% Medium Earth Orbit over the next 20 years will operate in LEO 59% GeoSynchronous Orbit – That is, inside the Terrestrial Service Volume (TSV) 8% Highly Elliptical Orbit Cislunar / Interplanetary • An additional 35%* of these space missions that will operate at higher altitudes will remain at or below GEO – That is, inside the GPS/GNSS Space Service Volume (SSV) Highly Elliptical Orbits**: • In summary, approximately 95% of projected Example: NASA MMS 4- worldwide space missions over the next 20 years will satellite constellation. -
NASA Process for Limiting Orbital Debris
NASA-HANDBOOK NASA HANDBOOK 8719.14 National Aeronautics and Space Administration Approved: 2008-07-30 Washington, DC 20546 Expiration Date: 2013-07-30 HANDBOOK FOR LIMITING ORBITAL DEBRIS Measurement System Identification: Metric APPROVED FOR PUBLIC RELEASE – DISTRIBUTION IS UNLIMITED NASA-Handbook 8719.14 This page intentionally left blank. Page 2 of 174 NASA-Handbook 8719.14 DOCUMENT HISTORY LOG Status Document Approval Date Description Revision Baseline 2008-07-30 Initial Release Page 3 of 174 NASA-Handbook 8719.14 This page intentionally left blank. Page 4 of 174 NASA-Handbook 8719.14 This page intentionally left blank. Page 6 of 174 NASA-Handbook 8719.14 TABLE OF CONTENTS 1 SCOPE...........................................................................................................................13 1.1 Purpose................................................................................................................................ 13 1.2 Applicability ....................................................................................................................... 13 2 APPLICABLE AND REFERENCE DOCUMENTS................................................14 3 ACRONYMS AND DEFINITIONS ...........................................................................15 3.1 Acronyms............................................................................................................................ 15 3.2 Definitions .........................................................................................................................