Orbit Design Marcelo Suárez
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
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 -
Mission Design for the Lunar Reconnaissance Orbiter
AAS 07-057 Mission Design for the Lunar Reconnaissance Orbiter Mark Beckman Goddard Space Flight Center, Code 595 29th ANNUAL AAS GUIDANCE AND CONTROL CONFERENCE February 4-8, 2006 Sponsored by Breckenridge, Colorado Rocky Mountain Section AAS Publications Office, P.O. Box 28130 - San Diego, California 92198 AAS-07-057 MISSION DESIGN FOR THE LUNAR RECONNAISSANCE ORBITER † Mark Beckman The Lunar Reconnaissance Orbiter (LRO) will be the first mission under NASA’s Vision for Space Exploration. LRO will fly in a low 50 km mean altitude lunar polar orbit. LRO will utilize a direct minimum energy lunar transfer and have a launch window of three days every two weeks. The launch window is defined by lunar orbit beta angle at times of extreme lighting conditions. This paper will define the LRO launch window and the science and engineering constraints that drive it. After lunar orbit insertion, LRO will be placed into a commissioning orbit for up to 60 days. This commissioning orbit will be a low altitude quasi-frozen orbit that minimizes stationkeeping costs during commissioning phase. LRO will use a repeating stationkeeping cycle with a pair of maneuvers every lunar sidereal period. The stationkeeping algorithm will bound LRO altitude, maintain ground station contact during maneuvers, and equally distribute periselene between northern and southern hemispheres. Orbit determination for LRO will be at the 50 m level with updated lunar gravity models. This paper will address the quasi-frozen orbit design, stationkeeping algorithms and low lunar orbit determination. INTRODUCTION The Lunar Reconnaissance Orbiter (LRO) is the first of the Lunar Precursor Robotic Program’s (LPRP) missions to the moon. -
Positioning: Drift Orbit and Station Acquisition
Orbits Supplement GEOSTATIONARY ORBIT PERTURBATIONS INFLUENCE OF ASPHERICITY OF THE EARTH: The gravitational potential of the Earth is no longer µ/r, but varies with longitude. A tangential acceleration is created, depending on the longitudinal location of the satellite, with four points of stable equilibrium: two stable equilibrium points (L 75° E, 105° W) two unstable equilibrium points ( 15° W, 162° E) This tangential acceleration causes a drift of the satellite longitude. Longitudinal drift d'/dt in terms of the longitude about a point of stable equilibrium expresses as: (d/dt)2 - k cos 2 = constant Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF EARTH ASPHERICITY VARIATION IN THE LONGITUDINAL ACCELERATION OF A GEOSTATIONARY SATELLITE: Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN & MOON ATTRACTION Gravitational attraction by the sun and moon causes the satellite orbital inclination to change with time. The evolution of the inclination vector is mainly a combination of variations: period 13.66 days with 0.0035° amplitude period 182.65 days with 0.023° amplitude long term drift The long term drift is given by: -4 dix/dt = H = (-3.6 sin M) 10 ° /day -4 diy/dt = K = (23.4 +.2.7 cos M) 10 °/day where M is the moon ascending node longitude: M = 12.111 -0.052954 T (T: days from 1/1/1950) 2 2 2 2 cos d = H / (H + K ); i/t = (H + K ) Depending on time within the 18 year period of M d varies from 81.1° to 98.9° i/t varies from 0.75°/year to 0.95°/year Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN RADIATION PRESSURE Due to sun radiation pressure, eccentricity arises: EFFECT OF NON-ZERO ECCENTRICITY L = difference between longitude of geostationary satellite and geosynchronous satellite (24 hour period orbit with e0) With non-zero eccentricity the satellite track undergoes a periodic motion about the subsatellite point at perigee. -
Satellite Orbits
Course Notes for Ocean Colour Remote Sensing Course Erdemli, Turkey September 11 - 22, 2000 Module 1: Satellite Orbits prepared by Assoc Professor Mervyn J Lynch Remote Sensing and Satellite Research Group School of Applied Science Curtin University of Technology PO Box U1987 Perth Western Australia 6845 AUSTRALIA tel +618-9266-7540 fax +618-9266-2377 email <[email protected]> Module 1: Satellite Orbits 1.0 Artificial Earth Orbiting Satellites The early research on orbital mechanics arose through the efforts of people such as Tyco Brahe, Copernicus, Kepler and Galileo who were clearly concerned with some of the fundamental questions about the motions of celestial objects. Their efforts led to the establishment by Keppler of the three laws of planetary motion and these, in turn, prepared the foundation for the work of Isaac Newton who formulated the Universal Law of Gravitation in 1666: namely, that F = GmM/r2 , (1) Where F = attractive force (N), r = distance separating the two masses (m), M = a mass (kg), m = a second mass (kg), G = gravitational constant. It was in the very next year, namely 1667, that Newton raised the possibility of artificial Earth orbiting satellites. A further 300 years lapsed until 1957 when the USSR achieved the first launch into earth orbit of an artificial satellite - Sputnik - occurred. Returning to Newton's equation (1), it would predict correctly (relativity aside) the motion of an artificial Earth satellite if the Earth was a perfect sphere of uniform density, there was no atmosphere or ocean or other external perturbing forces. However, in practice the situation is more complicated and prediction is a less precise science because not all the effects of relevance are accurately known or predictable. -
Sun-Synchronous Satellites
Topic: Sun-synchronous Satellites Course: Remote Sensing and GIS (CC-11) M.A. Geography (Sem.-3) By Dr. Md. Nazim Professor, Department of Geography Patna College, Patna University Lecture-3 Concept: Orbits and their Types: Any object that moves around the Earth has an orbit. An orbit is the path that a satellite follows as it revolves round the Earth. The plane in which a satellite always moves is called the orbital plane and the time taken for completing one orbit is called orbital period. Orbit is defined by the following three factors: 1. Shape of the orbit, which can be either circular or elliptical depending upon the eccentricity that gives the shape of the orbit, 2. Altitude of the orbit which remains constant for a circular orbit but changes continuously for an elliptical orbit, and 3. Angle that an orbital plane makes with the equator. Depending upon the angle between the orbital plane and equator, orbits can be categorised into three types - equatorial, inclined and polar orbits. Different orbits serve different purposes. Each has its own advantages and disadvantages. There are several types of orbits: 1. Polar 2. Sunsynchronous and 3. Geosynchronous Field of View (FOV) is the total view angle of the camera, which defines the swath. When a satellite revolves around the Earth, the sensor observes a certain portion of the Earth’s surface. Swath or swath width is the area (strip of land of Earth surface) which a sensor observes during its orbital motion. Swaths vary from one sensor to another but are generally higher for space borne sensors (ranging between tens and hundreds of kilometers wide) in comparison to airborne sensors. -
SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS
www.myreaders.info www.myreaders.info Return to Website SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS RC Chakraborty (Retd), Former Director, DRDO, Delhi & Visiting Professor, JUET, Guna, www.myreaders.info, [email protected], www.myreaders.info/html/orbital_mechanics.html, Revised Dec. 16, 2015 (This is Sec. 5, pp 164 - 192, of Orbital Mechanics - Model & Simulation Software (OM-MSS), Sec 1 to 10, pp 1 - 402.) OM-MSS Page 164 OM-MSS Section - 5 -------------------------------------------------------------------------------------------------------43 www.myreaders.info SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS Satellite Ephemeris is Expressed either by 'Keplerian elements' or by 'State Vectors', that uniquely identify a specific orbit. A satellite is an object that moves around a larger object. Thousands of Satellites launched into orbit around Earth. First, look into the Preliminaries about 'Satellite Orbit', before moving to Satellite Ephemeris data and conversion utilities of the OM-MSS software. (a) Satellite : An artificial object, intentionally placed into orbit. Thousands of Satellites have been launched into orbit around Earth. A few Satellites called Space Probes have been placed into orbit around Moon, Mercury, Venus, Mars, Jupiter, Saturn, etc. The Motion of a Satellite is a direct consequence of the Gravity of a body (earth), around which the satellite travels without any propulsion. The Moon is the Earth's only natural Satellite, moves around Earth in the same kind of orbit. (b) Earth Gravity and Satellite Motion : As satellite move around Earth, it is pulled in by the gravitational force (centripetal) of the Earth. Contrary to this pull, the rotating motion of satellite around Earth has an associated force (centrifugal) which pushes it away from the Earth. -
The UCS Satellite Database
UCS Satellite Database User’s Manual 1-1-17 The UCS Satellite Database The UCS Satellite Database is a listing of active satellites currently in orbit around the Earth. It is available as both a downloadable Excel file and in a tab-delimited text format, and in a version (tab-delimited text) in which the "Name" column contains only the official name of the satellite in the case of government and military satellites, and the most commonly used name in the case of commercial and civil satellites. The database is updated roughly quarterly. Our intent in producing the Database is to create a research tool by collecting open-source information on active satellites and presenting it in a format that can be easily manipulated for research and analysis. The Database includes basic information about the satellites and their orbits, but does not contain the detailed information necessary to locate individual satellites. The UCS Satellite Database can be accessed at www.ucsusa.org/satellite_database. Using the Database The Database is free and its use is unrestricted. We request that its use be acknowledged and referenced in written materials. References should include the version of the Database that was used, which is indicated by the name of the Excel file, and a link to or URL for the webpage www.ucsusa.org/satellite_database. We welcome corrections, additions, and suggestions. These can be emailed to the Database manager at [email protected] If you would like to be notified when updated versions of the Database are completed, please send an email request to this address. -
Evolution of a Terrestrial Multiple Moon System
THE ASTRONOMICAL JOURNAL, 117:603È620, 1999 January ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A. EVOLUTION OF A TERRESTRIAL MULTIPLE-MOON SYSTEM ROBIN M. CANUP AND HAROLD F. LEVISON Southwest Research Institute, 1050 Walnut Street, Suite 426, Boulder, CO 80302 AND GLEN R. STEWART Laboratory for Atmospheric and Space Physics, University of Colorado, Campus Box 392, Boulder, CO 80309-0392 Received 1998 March 30; accepted 1998 September 29 ABSTRACT The currently favored theory of lunar origin is the giant-impact hypothesis. Recent work that has modeled accretional growth in impact-generated disks has found that systems with one or two large moons and external debris are common outcomes. In this paper we investigate the evolution of terres- trial multiple-moon systems as they evolve due to mutual interactions (including mean motion resonances) and tidal interaction with Earth, using both analytical techniques and numerical integra- tions. We Ðnd that multiple-moon conÐgurations that form from impact-generated disks are typically unstable: these systems will likely evolve into a single-moon state as the moons mutually collide or as the inner moonlet crashes into Earth. Key words: Moon È planets and satellites: general È solar system: formation INTRODUCTION 1. 1000 orbits). This result was relatively independent of initial The ““ giant-impact ÏÏ scenario proposes that the impact of disk conditions and collisional parameterizations. Pertur- a Mars-sized body with early Earth ejects enough material bations by the largest moonlet(s) were very e†ective at clear- into EarthÏs orbit to form the Moon (Hartmann & Davis ing out inner disk materialÈin all of the ICS97 simulations, 1975; Cameron & Ward 1976). -
Mission Concept for a Satellite Mission to Test Special Relativity
Mission Concept for a Satellite Mission to Test Special Relativity VOLKAN ANADOL Space Engineering, masters level 2016 Luleå University of Technology Department of Computer Science, Electrical and Space Engineering LULEÅ UNIVERSITY of TECHNOLOGY Master Thesis SpaceMaster Mission Concept for a Satellite Mission to Test Special Relativity Supervisors: Author : Dr. Thilo Schuldt Volkan Anadol Dr. Norman Gürlebeck Examiner : Assoc. Prof. Thomas Kuhn September 29, 2016 Abstract In 1905 Albert Einstein developed the theory of Special Relativity. This theory describes the relation between space and time and revolutionized the understanding of the universe. While the concept is generally accepted new experimental setups are constantly being developed to challenge the theory, but so far no contradictions have been found. One of the postulates Einsteins theory of Relativity is based on states that the speed of light in vac- uum is the highest possible velocity. Furthermore, it is demanded that the speed of light is indepen- dent of any chosen frame of reference. If an experiment would find a contradiction of these demands, the theory as such would have to be revised. To challenge the constancy of the speed of light the so- called Kennedy Thorndike experiment has been developed. A possible setup to conduct a Kennedy Thorndike experiment consists of comparing two independent clocks. Likewise experiments have been executed in laboratory environments. Within the scope of this work, the orbital requirements for the first space-based Kennedy Thorndike experiment called BOOST will be investigated. BOOST consists of an iodine clock, which serves as a time reference, and an optical cavity, which serves as a length reference. -
Remote Sensing I: Basics
Remote Sensing I: Basics Kelly M. Brunt Earth System Science Interdisciplinary Center, University of Maryland Cryospheric Science Laboratory, NASA Goddard Space Flight Center [email protected] (Based on Nick Barrand’s UAF Summer School in Glaciology 2014 lecture) ROUGH Outline: Electromagnetic Radiation Electromagnetic Spectrum NASA Satellites and the Electromagnetic Spectrum Passive & Active instruments Types of Survey Methods Types of Orbits Resolution Platforms & Sensors (Speaker’s bias: NASA, lidar, and Antarctica…) Electromagnetic Radiation - Energy derived from oscillating magnetic and electrostatic fields - Properties include wavelength (, in m) and frequency (, in Hz) related to (speed of light, 299,792,458 m/s) by: Wikipedia Electromagnetic Radiation Electromagnetic Spectrum NASA (increasing frequency…) Electromagnetic Radiation Electromagnetic Spectrum NASA (increasing wavelength…) Radiation in the Atmosphere NASA Cryosphere Specular: Smooth surface; energy reflected in 1 direction (e.g., sea ice lead) Diffuse: Rough surface; energy reflected in many directions (e.g., pressure ridges) Nick Barrand, UAF Summer School in Glaciology, 2014 NASA Earth-orbiting Satellites (‘observatory’ or ‘bus’) NASA Satellite, observatory, or bus: everything (i.e., instrument, thrust, power, and navigation components…) e.g., Terra Instrument: the part making the measurement; often satellites have suites of instruments e.g., ASTER, MODIS (on satellite Terra) NASA Earth-orbiting Satellites (‘observatory’ or ‘bus’) Radio & Optical; weather Optical; -
Types of Orbit
Types of Orbit drishtiias.com/printpdf/types-of-orbit An orbit is a regular, repeating path that an object in space takes around another one. An object moving around a planet in an orbit is called a satellite. According to the height of satellites from the earth, the orbits can be classified as High Earth orbit, Medium Earth orbit, and Low Earth orbit. High Earth orbit begins about one-tenth of the way to the moon. Many kinds of weather and some communications satellites tend to have a high Earth orbit, furthest away from the surface. Satellites that orbit in a medium (mid) Earth orbit include navigation satellites, designed to monitor a particular region. Most scientific satellites, including NASA’s Earth Observing System fleet, have a low Earth orbit. Path of a Satellite in an Orbit Together, the satellite’s height, eccentricity, and inclination determine the satellite’s path in an orbit. Height of Satellite The height of the orbit, or distance between the satellite and Earth’s surface, determines how quickly the satellite moves around the Earth. Higher a satellite’s orbit, the slower it moves. 1/6 An Earth-orbiting satellite’s motion is mostly controlled by Earth’s gravity. As satellites get closer to Earth, the pull of gravity gets stronger, and the satellite moves more quickly. For Example, NASA’s Aqua satellite requires about 99 minutes to orbit the Earth at about 705 kilometres height from Earth’s surface. A communication satellite about 36,000 kilometres from Earth’s surface takes 23 hours, 56 minutes, and 4 seconds to complete an orbit. -
Providing Orbit Information with Predetermined Bounded Accuracy Λογος
Providing orbit information with predetermined bounded accuracy λογος Vitali Braun December 5, 2016 Providing orbit information with predetermined bounded accuracy Von der Fakultät für Maschinenbau der Technischen Universität Carolo-Wilhelmina zu Braunschweig zur Erlangung der Würde eines Doktor-Ingenieurs (Dr.-Ing.) genehmigte Dissertation von: Vitali Braun aus: Pleschanowo eingereicht am: 04.04.2016 mündliche Prüfung am: 26.08.2016 Gutachter: Prof. Dr.-Ing. Enrico Stoll, B. Sc. Prof. Dr.-Ing. Heiner Klinkrad Prof. Dr.-Ing. Joachim Block Ph.D. Moriba K. Jah 2016 Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet uber¨ http://dnb.d-nb.de abrufbar. c Copyright Logos Verlag Berlin GmbH 2016 Alle Rechte vorbehalten. ISBN 978-3-8325-4405-8 Logos Verlag Berlin GmbH Comeniushof, Gubener Str. 47, 10243 Berlin Tel.: +49 (0)30 42 85 10 90 Fax: +49 (0)30 42 85 10 92 INTERNET: http://www.logos-verlag.de Abstract The exchange of orbit information is becoming more important in view of the increasing population of objects in space as well as the increase in parties involved in space opera- tions. The US Space Surveillance Network is an example for a system which obtains orbit data from measurements provided by a network of globally distributed sensors. The aim of this thesis was to highlight how the orbit information maintained by a surveillance system is provided to the users of such a system. Services like collision avoid- ance require very accurate information, while other services might work with less accurate data.