Electric Propulsion for Small Satellites: a Case Study
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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 -
Reference System Issues in Binary Star Calculations
Reference System Issues in Binary Star Calculations Poster for Division A Meeting DAp.1.05 George H. Kaplan Consultant to U.S. Naval Observatory Washington, D.C., U.S.A. [email protected] or [email protected] IAU General Assembly Honolulu, August 2015 1 Poster DAp.1.05 Division!A! !!!!!!Coordinate!System!Issues!in!Binary!Star!Computa3ons! George!H.!Kaplan! Consultant!to!U.S.!Naval!Observatory!!([email protected][email protected])! It!has!been!es3mated!that!half!of!all!stars!are!components!of!binary!or!mul3ple!systems.!!Yet!the!number!of!known!orbits!for!astrometric!and!spectroscopic!binary!systems!together!is! less!than!7,000!(including!redundancies),!almost!all!of!them!for!bright!stars.!!A!new!genera3on!of!deep!allLsky!surveys!such!as!PanLSTARRS,!Gaia,!and!LSST!are!expected!to!lead!to!the! discovery!of!millions!of!new!systems.!!Although!for!many!of!these!systems,!the!orbits!may!be!poorly!sampled!ini3ally,!it!is!to!be!expected!that!combina3ons!of!new!and!old!data!sources! will!eventually!lead!to!many!more!orbits!being!known.!!As!a!result,!a!revolu3on!in!the!scien3fic!understanding!of!these!systems!may!be!upon!us.! The!current!database!of!visual!(astrometric)!binary!orbits!represents!them!rela3ve!to!the!“plane!of!the!sky”,!that!is,!the!plane!orthogonal!to!the!line!of!sight.!!Although!the!line!of!sight! to!stars!constantly!changes!due!to!proper!mo3on,!aberra3on,!and!other!effects,!there!is!no!agreed!upon!standard!for!what!line!of!sight!defines!the!orbital!reference!plane.!! Furthermore,!the!computa3on!of!differen3al!coordinates!(component!B!rela3ve!to!A)!for!a!given!date!must!be!based!on!the!binary!system’s!direc3on!at!that!date.!!Thus,!a!different! -
Sentinel-1 Constellation SAR Interferometry Performance Verification
Sentinel-1 Constellation SAR Interferometry Performance Verification Dirk Geudtner1, Francisco Ceba Vega1, Pau Prats2 , Nestor Yaguee-Martinez2 , Francesco de Zan3, Helko Breit3, Andrea Monti Guarnieri4, Yngvar Larsen5, Itziar Barat1, Cecillia Mezzera1, Ian Shurmer6 and Ramon Torres1 1 ESA ESTEC 2 DLR, Microwaves and Radar Institute 3 DLR, Remote Sensing Technology Institute 4 Politecnico Di Milano 5 Northern Research Institute (Norut) 6 ESA ESOC ESA UNCLASSIFIED - For Official Use Outline • Introduction − Sentinel-1 Constellation Mission Status − Overview of SAR Imaging Modes • Results from the Sentinel-1B Commissioning Phase • Azimuth Spectral Alignment Impact on common − Burst synchronization Doppler bandwidth − Difference in mean Doppler Centroid Frequency (InSAR) • Sentinel-1 Orbital Tube and InSAR Baseline • Demonstration of cross S-1A/S-1B InSAR Capability for Surface Deformation Mapping ESA UNCLASSIFIED - For Official Use ESA Slide 2 Sentinel-1 Constellation Mission Status • Constellation of two SAR C-band (5.405 GHz) satellites (A & B units) • Sentinel-1A launched on 3 April, 2014 & Sentinel-1B on 25 April, 2016 • Near-Polar, sun-synchronous (dawn-dusk) orbit at 698 km • 12-day repeat cycle (each satellite), 6 days for the constellation • Systematic SAR data acquisition using a predefined observation scenario • More than 10 TB of data products daily (specification of 3 TB) • 3 X-band Ground stations (Svalbard, Matera, Maspalomas) + upcoming 4th core station in Inuvik, Canada • Use of European Data Relay System (EDRS) provides -
Circular Orbits
ANALYSIS AND MECHANIZATION OF LAUNCH WINDOW AND RENDEZVOUS COMPUTATION PART I. CIRCULAR ORBITS Research & Analysis Section Tech Memo No. 175 March 1966 BY J. L. Shady Prepared for: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION / GEORGE C. MARSHALL SPACE FLIGHT CENTER AERO-ASTRODYNAMICS LABORATORY Prepared under Contract NAS8-20082 Reviewed by: " D. L/Cooper Technical Supervisor Director Research & Analysis Section / NORTHROP SPACE LABORATORIES HUNTSVILLE DEPARTMENT HUNTSVILLE, ALABAMA FOREWORD The enclosed presents the results of work performed by Northrop Space Laboratories, Huntsville Department, while )under contract to the Aero- Astrodynamfcs Laboratory of Marshall Space Flight Center (NAS8-20082) * This task was conducted in response to the requirement of Appendix E-1, Schedule Order No. PO. Technical coordination was provided by Mr. Jesco van Puttkamer of the Technical and Scientific Staff (R-AERO-T) ABS TRACT This repart presents Khe results of an analytical study to develop the logic for a digrtal c3mp;lrer sclbrolrtine for the automatic computationof launch opportunities, or the sequence of launch times, that rill allow execution of various mades of gross ~ircuiarorbit rendezvous. The equations developed in this study are based on tho-bady orb:taf chmry. The Earch has been assumed tcr ha.:e the shape of an oblate spheroid. Oblateness of the Earth has been accounted for by assuming the circular target orbit to be space- fixed and by cosrecring che T ational raLe of the EarKh accordingly. Gross rendezvous between the rarget vehicle and a maneuverable chaser vehicle, assumed to be a standard 3+ uprated Saturn V launched from Cape Kennedy, is in this srudy aecomplfshed by: .x> direct ascent to rendezvous, or 2) rendezvous via an intermediate circG1a.r parking orbit. -
Some of the Scientific Miracles in Brief ﻹﻋﺠﺎز اﻟﻌﻠ� ﻲﻓ ﺳﻄﻮر English [ إ�ﻠ�ي - ]
Some of the Scientific Miracles in Brief ﻟﻋﺠﺎز ﻟﻌﻠ� ﻓ ﺳﻄﻮر English [ إ���ي - ] www.onereason.org website مﻮﻗﻊ ﺳﺒﺐ وﻟﺣﺪ www.islamreligion.com website مﻮﻗﻊ دﻳﻦ ﻟﻋﺳﻼم 2013 - 1434 Some of the Scientific Miracles in Brief Ever since the dawn of mankind, we have sought to understand nature and our place in it. In this quest for the purpose of life many people have turned to religion. Most religions are based on books claimed by their followers to be divinely inspired, without any proof. Islam is different because it is based upon reason and proof. There are clear signs that the book of Islam, the Quran, is the word of God and we have many reasons to support this claim: - There are scientific and historical facts found in the Qu- ran which were unknown to the people at the time, and have only been discovered recently by contemporary science. - The Quran is in a unique style of language that cannot be replicated, this is known as the ‘Inimitability of the Qu- ran.’ - There are prophecies made in the Quran and by the Prophet Muhammad, may God praise him, which have come to be pass. This article lays out and explains the scientific facts that are found in the Quran, centuries before they were ‘discov- ered’ in contemporary science. It is important to note that the Quran is not a book of science but a book of ‘signs’. These signs are there for people to recognise God’s existence and 2 affirm His revelation. As we know, science sometimes takes a ‘U-turn’ where what once scientifically correct is false a few years later. -
Principles and Techniques of Remote Sensing
BASIC ORBIT MECHANICS 1-1 Example Mission Requirements: Spatial and Temporal Scales of Hydrologic Processes 1.E+05 Lateral Redistribution 1.E+04 Year Evapotranspiration 1.E+03 Month 1.E+02 Week Percolation Streamflow Day 1.E+01 Time Scale (hours) Scale Time 1.E+00 Precipitation Runoff Intensity 1.E-01 Infiltration 1.E-02 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Length Scale (meters) 1-2 BASIC ORBITS • Circular Orbits – Used most often for earth orbiting remote sensing satellites – Nadir trace resembles a sinusoid on planet surface for general case – Geosynchronous orbit has a period equal to the siderial day – Geostationary orbits are equatorial geosynchronous orbits – Sun synchronous orbits provide constant node-to-sun angle • Elliptical Orbits: – Used most often for planetary remote sensing – Can also be used to increase observation time of certain region on Earth 1-3 CIRCULAR ORBITS • Circular orbits balance inward gravitational force and outward centrifugal force: R 2 F mg g s r mv2 F c r g R2 F F v s g c r 2r r T 2r 2 v gs R • The rate of change of the nodal longitude is approximated by: d 3 cos I J R3 g dt 2 2 s r 7 2 1-4 Orbital Velocities 9 8 7 6 5 Earth Moon 4 Mars 3 Linear Velocity in km/sec in Linear Velocity 2 1 0 200 400 600 800 1000 1200 1400 Orbit Altitude in km 1-5 Orbital Periods 300 250 200 Earth Moon Mars 150 Orbital Period in MinutesPeriodOrbitalin 100 50 200 400 600 800 1000 1200 1400 Orbit Altitude in km 1-6 ORBIT INCLINATION EQUATORIAL I PLANE EARTH ORBITAL PLANE 1-7 ORBITAL NODE LONGITUDE SUN ORBITAL PLANE EARTH VERNAL EQUINOX 1-8 SATELLITE ORBIT PRECESSION 1-9 CIRCULAR GEOSYNCHRONOUS ORBIT TRACE 1-10 ORBIT COVERAGE • The orbit step S is the longitudinal difference between two consecutive equatorial crossings • If S is such that N S 360 ; N, L integers L then the orbit is repetitive. -
Evolution of the Rendezvous-Maneuver Plan for Lunar-Landing Missions
NASA TECHNICAL NOTE NASA TN D-7388 00 00 APOLLO EXPERIENCE REPORT - EVOLUTION OF THE RENDEZVOUS-MANEUVER PLAN FOR LUNAR-LANDING MISSIONS by Jumes D. Alexunder und Robert We Becker Lyndon B, Johnson Spuce Center ffoaston, Texus 77058 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. AUGUST 1973 1. Report No. 2. Government Accession No, 3. Recipient's Catalog No. NASA TN D-7388 4. Title and Subtitle 5. Report Date APOLLOEXPERIENCEREPORT August 1973 EVOLUTIONOFTHERENDEZVOUS-MANEUVERPLAN 6. Performing Organizatlon Code FOR THE LUNAR-LANDING MISSIONS 7. Author(s) 8. Performing Organization Report No. James D. Alexander and Robert W. Becker, JSC JSC S-334 10. Work Unit No. 9. Performing Organization Name and Address I - 924-22-20- 00- 72 Lyndon B. Johnson Space Center 11. Contract or Grant No. Houston, Texas 77058 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Technical Note I National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D. C. 20546 I 15. Supplementary Notes The JSC Director waived the use of the International System of Units (SI) for this Apollo Experience I Report because, in his judgment, the use of SI units would impair the usefulness of the report or I I result in excessive cost. 16. Abstract The evolution of the nominal rendezvous-maneuver plan for the lunar landing missions is presented along with a summary of the significant developments for the lunar module abort and rescue plan. A general discussion of the rendezvous dispersion analysis that was conducted in support of both the nominal and contingency rendezvous planning is included. -
Preparation of Papers for AIAA Technical Conferences
DUKSUP: A Computer Program for High Thrust Launch Vehicle Trajectory Design & Optimization Spurlock, O.F.I and Williams, C. H.II NASA Glenn Research Center, Cleveland, OH, 44135 From the late 1960’s through 1997, the leadership of NASA’s Intermediate and Large class unmanned expendable launch vehicle projects resided at the NASA Lewis (now Glenn) Research Center (LeRC). One of LeRC’s primary responsibilities --- trajectory design and performance analysis --- was accomplished by an internally-developed analytic three dimensional computer program called DUKSUP. Because of its Calculus of Variations-based optimization routine, this code was generally more capable of finding optimal solutions than its contemporaries. A derivation of optimal control using the Calculus of Variations is summarized including transversality, intermediate, and final conditions. The two point boundary value problem is explained. A brief summary of the code’s operation is provided, including iteration via the Newton-Raphson scheme and integration of variational and motion equations via a 4th order Runge-Kutta scheme. Main subroutines are discussed. The history of the LeRC trajectory design efforts in the early 1960’s is explained within the context of supporting the Centaur upper stage program. How the code was constructed based on the operation of the Atlas/Centaur launch vehicle, the limits of the computers of that era, the limits of the computer programming languages, and the missions it supported are discussed. The vehicles DUKSUP supported (Atlas/Centaur, Titan/Centaur, and Shuttle/Centaur) are briefly described. The types of missions, including Earth orbital and interplanetary, are described. The roles of flight constraints and their impact on launch operations are detailed (such as jettisoning hardware on heating, Range Safety, ground station tracking, and elliptical parking orbits). -
Flowers and Satellites
Flowers and Satellites G. Lucarelli, R. Santamaria, S. Troisi and L. Turturici (Naval University, Naples) In this paper some interesting properties of circular orbiting satellites' ground traces are pointed out. It will be shown how such properties are typical of some spherical and plane curves that look like flowers both in their name and shape. In addition, the choice of the best satellite constellations satisfying specific requirements is strongly facilitated by exploiting these properties. i. INTRODUCTION. Since the dawning of mathematical sciences, many scientists have attempted to emulate mathematically the beauty of nature, with particular care to floral forms. The mathematician Guido Grandi gave in the Age of Enlightenment a definitive contribution; some spherical and plane curves reproducing flowers have his name: Guido Grandi's Clelie and Rodonee. It will be deduced that the ground traces of circular orbiting satellites are described by the same equations, simple and therefore easily reproducible, and hence employable in satellite constellation designing and in other similar problems. 2. GROUND TRACE GEOMETRY. The parametric equations describing the ground trace of any satellite in circular orbit are: . ... 24(t sin <p = sin i sin tan (A-A0 + £-T0) = cos i tan — — where i = inclination of the orbital plane; <j>, A = geographic coordinates of the subsatellite point; t = time parameter, defined as angular measure of Earth rotation starting from T0 ; T0 , Ao = time and geographic longitude relative to the crossing of the satellite at the ascending node; T = orbital satellite period as expressed in hours. In the specific case of a polar-orbiting satellite, equations (i) become tan(AA + t) = where T0 = o; AA = A — Ao ; /i = 24/T. -
Low Earth Orbit Slotting for Space Traffic Management Using Flower
Low Earth Orbit Slotting for Space Traffic Management Using Flower Constellation Theory David Arnas∗, Miles Lifson†, and Richard Linares‡ Massachusetts Institute of Technology, Cambridge, MA, 02139, USA Martín E. Avendaño§ CUD-AGM (Zaragoza), Crtra Huesca s / n, Zaragoza, 50090, Spain This paper proposes the use of Flower Constellation (FC) theory to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and optimize the available space. Specifically, it proposes the use of concentric orbital shells of admissible “slots” with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D Lattice Flower Constellations (2D-LFCs), and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. In particular, capacity is evaluated for various inclinations and other parameters. Next, a rough estimate for the capacity of LEO is generated subject to certain minimum separation and station-keeping assumptions and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management. I. Introduction SpaceX, OneWeb, Telesat and other companies are currently planning mega-constellations for space-based internet connectivity and other applications that would significantly increase the number of on-orbit active satellites across a variety of altitudes [1–5]. As these and other actors seek to make more intensive use of the global space commons, there is growing need to characterize the fundamental limits to the capacity of Low Earth Orbit (LEO), particularly in high-demand orbits and altitudes, and minimize the extent to which use by one space actor hampers use by other actors. -
4. Lunar Architecture
4. Lunar Architecture 4.1 Summary and Recommendations As defined by the Exploration Systems Architecture Study (ESAS), the lunar architecture is a combination of the lunar “mission mode,” the assignment of functionality to flight elements, and the definition of the activities to be performed on the lunar surface. The trade space for the lunar “mission mode,” or approach to performing the crewed lunar missions, was limited to the cislunar space and Earth-orbital staging locations, the lunar surface activities duration and location, and the lunar abort/return strategies. The lunar mission mode analysis is detailed in Section 4.2, Lunar Mission Mode. Surface activities, including those performed on sortie- and outpost-duration missions, are detailed in Section 4.3, Lunar Surface Activities, along with a discussion of the deployment of the outpost itself. The mission mode analysis was built around a matrix of lunar- and Earth-staging nodes. Lunar-staging locations initially considered included the Earth-Moon L1 libration point, Low Lunar Orbit (LLO), and the lunar surface. Earth-orbital staging locations considered included due-east Low Earth Orbits (LEOs), higher-inclination International Space Station (ISS) orbits, and raised apogee High Earth Orbits (HEOs). Cases that lack staging nodes (i.e., “direct” missions) in space and at Earth were also considered. This study addressed lunar surface duration and location variables (including latitude, longi- tude, and surface stay-time) and made an effort to preserve the option for full global landing site access. Abort strategies were also considered from the lunar vicinity. “Anytime return” from the lunar surface is a desirable option that was analyzed along with options for orbital and surface loiter. -
Lunar Orbiting Cubesat Sensor Transport System Mike Seibert, Alejandro Levi, and Mitchell Paradis Graduate Students, Colorado School of Mines
Lunar Orbiting CubeSat Sensor Transport System Mike Seibert, Alejandro Levi, and Mitchell Paradis Graduate Students, Colorado School of Mines Concept Origin Notional Mission Evaluated Carrier Spacecraft Conceptual Design The 2018 Lunar Polar Prospecting (LPP) Workshop Objective: • Structure: Based on EELV Secondary generated a series of recommendations for Deploy a constellation of 6 sensor spacecraft in single Payload Adapter (ESPA) Grande. prospecting of lunar water. Recommendation 3 was polar low lunar orbit plane. • Propulsion: Monoprop system with 2.5 km/s for swarms CubeSats overflying polar regions at delta-V capability. altitudes below 20 km. Recommendation 3 also Cruise Phase: Includes 179 m/s for 110 days of recommended “a swarm of hundreds of low cost LOCuST is released from the launch vehicle in a GTO. orbit eccentricity control impactors instrumented for volatile detection and A series of perigee maneuvers using carrier spacecraft • Earth Telecom: Optical derived from LADEE or quantification.” [1] propulsion are used to raise apogee to lunar distance. IRIS Version 2.0 radio • Relay Telecom: IRIS Version 2.0 (multiple if all RF) The graduate student team developed both mission Lunar Orbit Insertion/Optimization • Thermal control:Accounts for challenges of low and vehicle designs that address the LPP Lunar orbit capture into an initial 200km altitude orbit over lunar day side. recommendation during the Space Resources Design I polar orbit. Orbit is lowered to 10km altitude Main Propulsion course at the Colorado School of Mines in Spring perilune, 100km apolune. All capture and initial 2019. CubeSat optimization maneuvers use carrier spacecraft Deployers propulsion. The CubeSat swarm concept was interpreted to mean a constellation of small short mission duration Deployments spacecraft with sensors optimized for localizing After each deployment orbit phasing maneuvers to Solar Array surface water ice.