Signal in Space Error and Ephemeris Validity Time Evaluation of Milena and Doresa Galileo Satellites †
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Analysis of Perturbations and Station-Keeping Requirements in Highly-Inclined Geosynchronous Orbits
ANALYSIS OF PERTURBATIONS AND STATION-KEEPING REQUIREMENTS IN HIGHLY-INCLINED GEOSYNCHRONOUS ORBITS Elena Fantino(1), Roberto Flores(2), Alessio Di Salvo(3), and Marilena Di Carlo(4) (1)Space Studies Institute of Catalonia (IEEC), Polytechnic University of Catalonia (UPC), E.T.S.E.I.A.T., Colom 11, 08222 Terrassa (Spain), [email protected] (2)International Center for Numerical Methods in Engineering (CIMNE), Polytechnic University of Catalonia (UPC), Building C1, Campus Norte, UPC, Gran Capitan,´ s/n, 08034 Barcelona (Spain) (3)NEXT Ingegneria dei Sistemi S.p.A., Space Innovation System Unit, Via A. Noale 345/b, 00155 Roma (Italy), [email protected] (4)Department of Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ (United Kingdom), [email protected] Abstract: There is a demand for communications services at high latitudes that is not well served by conventional geostationary satellites. Alternatives using low-altitude orbits require too large constellations. Other options are the Molniya and Tundra families (critically-inclined, eccentric orbits with the apogee at high latitudes). In this work we have considered derivatives of the Tundra type with different inclinations and eccentricities. By means of a high-precision model of the terrestrial gravity field and the most relevant environmental perturbations, we have studied the evolution of these orbits during a period of two years. The effects of the different perturbations on the constellation ground track (which is more important for coverage than the orbital elements themselves) have been identified. We show that, in order to maintain the ground track unchanged, the most important parameters are the orbital period and the argument of the perigee. -
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 -
Ephemeris Time, D. H. Sadler, Occasional
EPHEMERIS TIME D. H. Sadler 1. Introduction. – At the eighth General Assembly of the International Astronomical Union, held in Rome in 1952 September, the following resolution was adopted: “It is recommended that, in all cases where the mean solar second is unsatisfactory as a unit of time by reason of its variability, the unit adopted should be the sidereal year at 1900.0; that the time reckoned in these units be designated “Ephemeris Time”; that the change of mean solar time to ephemeris time be accomplished by the following correction: ΔT = +24°.349 + 72s.318T + 29s.950T2 +1.82144 · B where T is reckoned in Julian centuries from 1900 January 0 Greenwich Mean Noon and B has the meaning given by Spencer Jones in Monthly Notices R.A.S., Vol. 99, 541, 1939; and that the above formula define also the second. No change is contemplated or recommended in the measure of Universal Time, nor in its definition.” The ultimate purpose of this article is to explain, in simple terms, the effect that the adoption of this resolution will have on spherical and dynamical astronomy and, in particular, on the ephemerides in the Nautical Almanac. It should be noted that, in accordance with another I.A.U. resolution, Ephemeris Time (E.T.) will not be introduced into the national ephemerides until 1960. Universal Time (U.T.), previously termed Greenwich Mean Time (G.M.T.), depends both on the rotation of the Earth on its axis and on the revolution of the Earth in its orbit round the Sun. There is now no doubt as to the variability, both short-term and long-term, of the rate of rotation of the Earth; U.T. -
Electric Propulsion System Scaling for Asteroid Capture-And-Return Missions
Electric propulsion system scaling for asteroid capture-and-return missions Justin M. Little⇤ and Edgar Y. Choueiri† Electric Propulsion and Plasma Dynamics Laboratory, Princeton University, Princeton, NJ, 08544 The requirements for an electric propulsion system needed to maximize the return mass of asteroid capture-and-return (ACR) missions are investigated in detail. An analytical model is presented for the mission time and mass balance of an ACR mission based on the propellant requirements of each mission phase. Edelbaum’s approximation is used for the Earth-escape phase. The asteroid rendezvous and return phases of the mission are modeled as a low-thrust optimal control problem with a lunar assist. The numerical solution to this problem is used to derive scaling laws for the propellant requirements based on the maneuver time, asteroid orbit, and propulsion system parameters. Constraining the rendezvous and return phases by the synodic period of the target asteroid, a semi- empirical equation is obtained for the optimum specific impulse and power supply. It was found analytically that the optimum power supply is one such that the mass of the propulsion system and power supply are approximately equal to the total mass of propellant used during the entire mission. Finally, it is shown that ACR missions, in general, are optimized using propulsion systems capable of processing 100 kW – 1 MW of power with specific impulses in the range 5,000 – 10,000 s, and have the potential to return asteroids on the order of 103 104 tons. − Nomenclature -
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 -
Handbook of Satellite Orbits from Kepler to GPS Michel Capderou
Handbook of Satellite Orbits From Kepler to GPS Michel Capderou Handbook of Satellite Orbits From Kepler to GPS Translated by Stephen Lyle Foreword by Charles Elachi, Director, NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA 123 Michel Capderou Universite´ Pierre et Marie Curie Paris, France ISBN 978-3-319-03415-7 ISBN 978-3-319-03416-4 (eBook) DOI 10.1007/978-3-319-03416-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014930341 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this pub- lication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permis- sions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. -
Orbit and Spin
Orbit and Spin Overview: A whole-body activity that explores the relative sizes, distances, orbit, and spin of the Sun, Earth, and Moon. Target Grade Level: 3-5 Estimated Duration: 2 40-minute sessions Learning Goals: Students will be able to… • compare the relative sizes of the Earth, Moon, and Sun. • contrast the distance between the Earth and Moon to the distance between the Earth and Sun. • differentiate between the motions of orbit and spin. • demonstrate the spins of the Earth and the Moon, as well as the orbits of the Earth around the Sun, and the Moon around the Earth. Standards Addressed: Benchmarks (AAAS, 1993) The Physical Setting, 4A: The Universe, 4B: The Earth National Science Education Standards (NRC, 1996) Physical Science, Standard B: Position and motion of objects Earth and Space Science, Standard D: Objects in the sky, Changes in Earth and sky Table of Contents: Background Page 1 Materials and Procedure 5 What I Learned… Science Journal Page 14 Earth Picture 15 Sun Picture 16 Moon Picture 17 Earth Spin Demonstration 18 Moon Orbit Demonstration 19 Extensions and Adaptations 21 Standards Addressed, detailed 22 Background: Sun The Sun is the center of our Solar System, both literally—as all of the planets orbit around it, and figuratively—as its rays warm our planet and sustain life as we know it. The Sun is very hot compared to temperatures we usually encounter. Its mean surface temperature is about 9980° Fahrenheit (5800 Kelvin) and its interior temperature is as high as about 28 million° F (15,500,000 Kelvin). -
Calculation of Moon Phases and 24 Solar Terms
Calculation of Moon Phases and 24 Solar Terms Yuk Tung Liu (廖²棟) First draft: 2018-10-24, Last major revision: 2021-06-12 Chinese Versions: ³³³qqq---文文文 简简简SSS---文文文 This document explains the method used to compute the times of the moon phases and 24 solar terms. These times are important in the calculation of the Chinese calendar. See this page for an introduction to the 24 solar terms, and this page for an introduction to the Chinese calendar calculation. Computation of accurate times of moon phases and 24 solar terms is complicated, but today all the necessary resources are freely available. Anyone familiar with numerical computation and computer programming can follow the procedure outlined in this document to do the computation. Before stating the procedure, it is useful to have a basic understanding of the basic concepts behind the computation. I assume that readers are already familiar with the important astronomy concepts mentioned on this page. In Section 1, I briefly introduce the barycentric dynamical time (TDB) used in modern ephemerides, and its connection to terrestrial time (TT) and international atomic time (TAI). Readers who are not familiar with general relativity do not have to pay much attention to the formulas there. Section 2 introduces the various coordinate systems used in modern astronomy. Section 3 lists the formulas for computing the IAU 2006/2000A precession and nutation matrices. One important component in the computation of accurate times of moon phases and 24 solar terms is an accurate ephemeris of the Sun and Moon. I use the ephemerides developed by the Jet Propulsion Laboratory (JPL) for the computation. -
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 ......................................................................................................................... -
Analysis of Transfer Maneuvers from Initial
Revista Mexicana de Astronom´ıa y Astrof´ısica, 52, 283–295 (2016) ANALYSIS OF TRANSFER MANEUVERS FROM INITIAL CIRCULAR ORBIT TO A FINAL CIRCULAR OR ELLIPTIC ORBIT M. A. Sharaf1 and A. S. Saad2,3 Received March 14 2016; accepted May 16 2016 RESUMEN Presentamos un an´alisis de las maniobras de transferencia de una ´orbita circu- lar a una ´orbita final el´ıptica o circular. Desarrollamos este an´alisis para estudiar el problema de las transferencias impulsivas en las misiones espaciales. Consideramos maniobras planas usando ecuaciones reci´enobtenidas; con estas ecuaciones se com- paran las maniobras circulares y el´ıpticas. Esta comparaci´on es importante para el dise˜no´optimo de misiones espaciales, y permite obtener mapeos ´utiles para mostrar cu´al es la mejor maniobra. Al respecto, desarrollamos este tipo de comparaciones mediante 10 resultados, y los mostramos gr´aficamente. ABSTRACT In the present paper an analysis of the transfer maneuvers from initial circu- lar orbit to a final circular or elliptic orbit was developed to study the problem of impulsive transfers for space missions. It considers planar maneuvers using newly derived equations. With these equations, comparisons of circular and elliptic ma- neuvers are made. This comparison is important for the mission designers to obtain useful mappings showing where one maneuver is better than the other. In this as- pect, we developed this comparison throughout ten results, together with some graphs to show their meaning. Key Words: celestial mechanics — methods: analytical — space vehicles 1. INTRODUCTION The large amount of information from interplanetary missions, such as Pioneer (Dyer et al. -
The Calendars of India
The Calendars of India By Vinod K. Mishra, Ph.D. 1 Preface. 4 1. Introduction 5 2. Basic Astronomy behind the Calendars 8 2.1 Different Kinds of Days 8 2.2 Different Kinds of Months 9 2.2.1 Synodic Month 9 2.2.2 Sidereal Month 11 2.2.3 Anomalistic Month 12 2.2.4 Draconic Month 13 2.2.5 Tropical Month 15 2.2.6 Other Lunar Periodicities 15 2.3 Different Kinds of Years 16 2.3.1 Lunar Year 17 2.3.2 Tropical Year 18 2.3.3 Siderial Year 19 2.3.4 Anomalistic Year 19 2.4 Precession of Equinoxes 19 2.5 Nutation 21 2.6 Planetary Motions 22 3. Types of Calendars 22 3.1 Lunar Calendar: Structure 23 3.2 Lunar Calendar: Example 24 3.3 Solar Calendar: Structure 26 3.4 Solar Calendar: Examples 27 3.4.1 Julian Calendar 27 3.4.2 Gregorian Calendar 28 3.4.3 Pre-Islamic Egyptian Calendar 30 3.4.4 Iranian Calendar 31 3.5 Lunisolar calendars: Structure 32 3.5.1 Method of Cycles 32 3.5.2 Improvements over Metonic Cycle 34 3.5.3 A Mathematical Model for Intercalation 34 3.5.3 Intercalation in India 35 3.6 Lunisolar Calendars: Examples 36 3.6.1 Chinese Lunisolar Year 36 3.6.2 Pre-Christian Greek Lunisolar Year 37 3.6.3 Jewish Lunisolar Year 38 3.7 Non-Astronomical Calendars 38 4. Indian Calendars 42 4.1 Traditional (Siderial Solar) 42 4.2 National Reformed (Tropical Solar) 49 4.3 The Nānakshāhī Calendar (Tropical Solar) 51 4.5 Traditional Lunisolar Year 52 4.5 Traditional Lunisolar Year (vaisnava) 58 5.