Libration Orbit Mission Design: Applications of Numerical and Dynamical Methods
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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 -
AAS/AIAA Astrodynamics Specialist Conference
DRAFT version: 7/15/2011 11:04 AM http://www.alyeskaresort.com AAS/AIAA Astrodynamics Specialist Conference July 31 ‐ August 4, 2011 Girdwood, Alaska AAS General Chair AIAA General Chair Ryan P. Russell William Todd Cerven Georgia Institute of Technology The Aerospace Corporation AAS Technical Chair AIAA Technical Chair Hanspeter Schaub Brian C. Gunter University of Colorado Delft University of Technology DRAFT version: 7/15/2011 11:04 AM http://www.alyeskaresort.com Cover images: Top right: Conference Location: Aleyska Resort in Girdwood Alaska. Middle left: Cassini looking back at an eclipsed Saturn, Astronomy picture of the day 2006 Oct 16, credit CICLOPS, JPL, ESA, NASA; Middle right: Shuttle shadow in the sunset (in honor of the end of the Shuttle Era), Astronomy picture of the day 2010 February 16, credit: Expedition 22 Crew, NASA. Bottom right: Comet Hartley 2 Flyby, Astronomy picture of the day 2010 Nov 5, Credit: NASA, JPL-Caltech, UMD, EPOXI Mission DRAFT version: 7/15/2011 11:04 AM http://www.alyeskaresort.com Table of Contents Registration ............................................................................................................................................... 5 Schedule of Events ................................................................................................................................... 6 Conference Center Layout ........................................................................................................................ 7 Conference Location: The Hotel Alyeska ............................................................................................... -
Aas 11-509 Artemis Lunar Orbit Insertion and Science Orbit Design Through 2013
AAS 11-509 ARTEMIS LUNAR ORBIT INSERTION AND SCIENCE ORBIT DESIGN THROUGH 2013 Stephen B. Broschart,∗ Theodore H. Sweetser,y Vassilis Angelopoulos,z David C. Folta,x and Mark A. Woodard{ As of late-July 2011, the ARTEMIS mission is transferring two spacecraft from Lissajous orbits around Earth-Moon Lagrange Point #1 into highly-eccentric lunar science orbits. This paper presents the trajectory design for the transfer from Lissajous orbit to lunar orbit in- sertion, the period reduction maneuvers, and the science orbits through 2013. The design accommodates large perturbations from Earth’s gravity and restrictive spacecraft capabili- ties to enable opportunities for a range of heliophysics and planetary science measurements. The process used to design the highly-eccentric ARTEMIS science orbits is outlined. The approach may inform the design of future eccentric orbiter missions at planetary moons. INTRODUCTION The Acceleration, Reconnection, Turbulence and Electrodynamics of the Moons Interaction with the Sun (ARTEMIS) mission is currently operating two spacecraft in lunar orbit under funding from the Heliophysics and Planetary Science Divisions with NASA’s Science Missions Directorate. ARTEMIS is an extension to the successful Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission [1] that has relocated two of the THEMIS spacecraft from Earth orbit to the Moon [2, 3, 4]. ARTEMIS plans to conduct a variety of scientific studies at the Moon using the on-board particle and fields instrument package [5, 6]. The final portion of the ARTEMIS transfers involves moving the two ARTEMIS spacecraft, known as P1 and P2, from Lissajous orbits around the Earth-Moon Lagrange Point #1 (EML1) to long-lived, eccentric lunar science orbits with periods of roughly 28 hr. -
Applications of Multi-Body Dynamical Environments: the ARTEMIS Transfer Trajectory Design
Paper ID: 7461 61st International Astronautical Congress 2010 Applications of Multi-Body Dynamical Environments: The ARTEMIS Transfer Trajectory Design ASTRODYNAMICS SYMPOSIUM (CI) Mission Design, Operations and Optimization (2) (9) Mr. David C. Folta and Mr. Mark Woodard National Aeronautics and Space Administration (NASA)/Goddard Space Flight Center, Greenbelt, MD, United States, david.c.folta<@nasa.gov Prof. Kathleen Howell, Chris Patterson, Wayne Schlei Purdue University, West Lafayette, IN, United States, [email protected] Abstract The application of forces in multi-body dynamical environments to pennit the transfer of spacecraft from Earth orbit to Sun-Earth weak stability regions and then return to the Earth-Moon libration (L1 and L2) orbits has been successfully accomplished for the first time. This demonstrated transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecraft into Earth Moon libration orbits by means of these applications. INTRODUCTION The exploitation of multi-body dynamical environments to pennit the transfer of spacecraft from Earth to Sun-Earth weak stability regions and then return to the Earth-Moon libration (L 1 and L2) orbits has been successfully accomplished. This demonstrated transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-Velocity (L.\V) expenditure. Initialized using gravity assists to overcome fuel constraints, the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission design has successfully placed two spacecraft into Earth-Moon libration orbits by means of this application of forces from multiple gravity fields. -
Stationkeeping in and Design of Transfer Between Earth-Moon L1,2 Orbits: ARTEMIS Mission Results
Goddard Space Flight Center Stationkeeping in and Design of Transfer Between Earth-Moon L1,2 Orbits: ARTEMIS Mission Results Future In-Space Operations (FISO) Dave Folta Goddard Space Flight Center February, 23, 2011 Agenda Goddard Space Flight Center • General Libration Orbit Background • Stationkeeping Methods • The ARTEMIS Mission Results and Operations • Stationkeeping Observations • Comparison to Other Lunar Orbits • Summary Libration Orbit Dynamics Goddard Space Flight Center Where Are They? What Are They?? Collinear Points: L1, L2, L3 (unstable) Equilibrium or libration points represent Triangular Points: L4, L5 (stable) singularities in the equations of motion where velocity and acceleration components are zero and the forces are balanced Viewed in the rotating frame: centrifugal L4 (Coriolis-Type) force balances with gravitational forces of the two primaries 1 a.u. 1 a.u. Libration points are in plane with no Z component. Orbits are mapped to a rotating L3 Sun L1 L2 frame where there are no time dependent forces 0.01 a.u. A system of interest involves the Sun (m1), Earth/Moon System the Earth-Moon system (m2) and the spacecraft m3 L1 and L2 At a distance of 1.5 million km L5 L4 and L5 At a distance of 150. million km Solar Rotating Coordinates Ecliptic Plane Projection Rotating Coordinate Frames Goddard Space Flight Center Sun-Earth & Earth-Moon • X is towards smaller body (sun to Earth) • Y is along smaller body velocity • Z is out of Ecliptic plane • Co-linear Unstable locations at L1, L2, and ‘L3’ • Stable locations -
SERVICING and DEPLOYMENT of NATIONAL RESOURCES in SUN-EARTH LIBRATION POINT ORBITS 53Th International Astronautical Congress
SERVICING AND DEPLOYMENT OF NATIONAL RESOURCES IN SUN-EARTH LIBRATION POINT ORBITS D. C. Folta, M. Beckman, S. J. Leete, G. C. Marr, M. Mesarch, and S. Cooley NASA Goddard Space Flight Center Greenbelt, MD, USA 53th International Astronautical Congress The World Space Congress - 2002 10-3 9 Oct 2002 I Houston, Texas For permission to copy or republish, contact the International Astronautical Federation, 3-5 Rue Mario-Nikis, 75015 Paris, France SERVICING AND DEPLOYMENT OF NATIONAL RESOURCES IN SUN-EARTH LIBRATION POINT ORBITS D. C. Folta, M. Beckman, G. C. Marr, M. Mesarch, S. Cooley Flight Dynamics Analysis Branch NASA Goddard Space Flight Center, Greenbelt, MD, USA dfolta@;gsfc.nasa.gov S. J. Leete Space Science Missions Branch, NASA Goddard Space Flight Center, Greenbelt, MD, USA Abstract Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refbeling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the AV costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. -
Analysis of the Gaia Orbit Around L2
TREBALL DE FI DE CARRERA TÍTOL DEL TFC: Analysis of the Gaia orbit around L2 TITULACIÓ: Enginyeria Tècnica Aeronàutica, especialitat Aeronavegació AUTOR: Jordi Carlos García García DIRECTORS: Santiago Torres Gil, Enrique García-Berro Montilla 2 Analysis of the Gaia orbit around L2 DATA: 27 de juliol de 2009 Títol: Analysis of the Gaia orbit around L2 Autor: Jordi Carlos García García Directors: Santiago Torres Gil, Enrique García-Berro Montilla Data: 27 de juliol de 2009 Resum Gaia és una missió astromètrica de l'Agència Espacial Europea (ESA) amb l'ambiciós objectiu de fer el mapa en tres dimensions de la nostra Galàxia més gran i precís fet fins ara. Per aconseguir-ho Gaia escanejarà l'espai contínuament i proporcionarà informació molt precisa sobre la posició, velocitat i espectre d'aproximadament mil milions d'estrelles de la Via Làctia. Això proporcionarà una informació molt valuosa sobre la composició, formació i evolució de la nostra Galàxia. Gaia també detectarà milers de petits objectes del sistema solar, planetes extra-solars, galàxies llunyanes, etc. Per tal de fer les observacions el més precises possibles Gaia descriurà una òrbita de tipus Lissajous al voltant del punt Lagrangià L2 del sistema Sol-Terra. Aquesta és una òrbita molt adequada ja es molt estable. Així mateix, aquesta òrbita té una gran estabilitat tèrmica. A més té unes característiques d'observació molt bones ja que el Sol, la Terra, la Lluna i els planetes interiors estan sempre per darrere del camp d'observació. En aquest treball final de carrera, en un primer lloc, estudiarem les òrbites de Lissajous, simularem l'orbita de Lissajous prevista per la missió Gaia i analitzarem les seves característiques. -
Eight-Shaped Lissajous Orbits in the Earth-Moon System Grégory Archambeau, Philippe Augros, Emmanuel Trélat
Eight-shaped Lissajous orbits in the Earth-Moon system Grégory Archambeau, Philippe Augros, Emmanuel Trélat To cite this version: Grégory Archambeau, Philippe Augros, Emmanuel Trélat. Eight-shaped Lissajous orbits in the Earth- Moon system. MathematicS In Action, Société de Mathématiques Appliquées et Industrielles, 2011, 4 (1), pp.1–23. hal-00312910v2 HAL Id: hal-00312910 https://hal.archives-ouvertes.fr/hal-00312910v2 Submitted on 23 Jan 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. MathematicS In Action Version de travail Eight-shaped Lissajous orbits in the Earth-Moon system Gregory´ Archambeau Philippe Augros Emmanuel Trelat´ ∗ EADS SPACE Transportation SAS, Flight Control Group, 66 route de Verneuil, BP 3002, 78133 Les Mureaux Cedex, France E-mail address: [email protected] y EADS SPACE Transportation SAS, Flight Control Group, 66 route de Verneuil, BP 3002, 78133 Les Mureaux Cedex, France E-mail address: [email protected] z Universit´ed'Orl´eans,Laboratoire MAPMO, CNRS, UMR 6628, F´ed´erationDenis Poisson, FR 2964, Bat. Math., BP 6759, 45067 Orl´eanscedex 2, France E-mail address: [email protected]. Abstract. Euler and Lagrange proved the existence of five equilibrium points in the circular restricted three-body problem. -
Trajectory Sensitivities for Sun-Mars Libration Point Missions
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Calhoun, Institutional Archive of the Naval Postgraduate School Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications Collection 2016 Trajectory Sensitivities for Sun-Mars Libration Point Missions Kutrieb, Joshua M. http://hdl.handle.net/10945/48886 AAS 01-327 TRAJECTORY SENSITIVITIES FOR SUN-MARS LIBRATION POINT MISSIONS John P. Carrico*, Jon D. Strizzi‡, Joshua M. Kutrieb‡, and Paul E. Damphousse‡ Previous research has analyzed proposed missions utilizing spacecraft in Lissajous orbits about each of the co-linear, near-Mars, Sun-Mars libration points to form a communication relay with Earth. This current effort focuses on 2016 Earth-Mars transfers to these mission orbits with their trajectory characteristics and sensitivities. This includes further analysis of using a mid-course correction as well as a braking maneuver at close approach to Mars to control Lissajous orbit insertion and the critical parameter of the phasing of the two-vehicle relay system, with one spacecraft each in orbit about L1 and L2. Stationkeeping sensitivities are investigated via a monte carlo technique. Commercial, desktop simulation and analysis tools are used to provide numerical data; and on-going, successful collaboration between military and industry researchers in a virtual environment is demonstrated. The resulting data should provide new information on these trajectory sensitivities to future researchers and mission planners. INTRODUCTION “NASA is seeking innovation to attack the diversity of Mars…to change the vantage point from which we explore…” - CNN, 25 June 2001 The concept of using communication relay vehicles in orbit about colinear Lagrange points to support exploration of the secondary body is not entirely new, being first conceptualized in the case of the Earth-Moon system by R. -
ARTEMIS: the First Mission to the Lunar Libration Orbits
ARTEMIS: The First Mission to the Lunar Libration Orbits (1) (2) (3) Mark Woodard , David Folta , Dennis Woodfork (1) NASA/GSFC, Greenbelt, MD 20771 USA, +1 301.286.9611, [email protected] (2) NASA/GSFC, Greenbelt, MD 20771 USA, +1 301.286.6082, [email protected] (3) NASA/GSFC, Greenbelt, MD 20771 USA, +1 301.286.6009, [email protected] ABSTRACT The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. -
Long Term Missions at the Sun-Earth Libration Point L1: Ace, Soho, and Wind Aas 11
AAS 11- 485 LONG TERM MISSIONS AT THE SUN-EARTH LIBRATION POINT L1: ACE, SOHO, AND WIND Craig E. Roberts* Three heliophysics missionsthe Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience WINDhave been orbiting the Sun-Earth interior libration point L1 conti- nuously since 1996, 1997, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center Flight Dynamics Facility. While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND prior to 2004 flew a remarkable 10-year deep-space trajectory that featured 38 targeted lunar flybys. The L1 orbits and the mission histories of the three spacecraft are briefly reviewed, and the station-keeping techniques and orbit maneuver experience are discussed. INTRODUCTION Three heliophysics missionsthe Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience International Physics Laboratory (un- iversally referred to by its nickname, WIND)have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively.† ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) all have their maneuver operations con- ducted from the NASA Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 38 targeted lunar flybys during an initial Double-Lunar-Swingby (DLS) phase, a Distant Prograde Orbit (DPO) phase, and looping excursions to both the Sun- Earth L1 and L2 collinear points before its final insertion into an L1 orbit. -
Orbit Determination Issues for Libration Point Orbits
Orbit Determination Issues for Libration Point Orbits Mark Beckman [email protected] 301-286-8866 Agenda • Goddard Space Flight Center has designed and supported every libration point mission except the recent Genesis mission out of JPL • This presentation presents published and unpublished orbit determination results from 4 previous LPO missions • ISEE-3 • SOHO • ACE • MAP • The use of advanced technology can improve accuracy and reduce tracking times • CelNav • DDOR 2 International Sun-Earth Explorer-3 (ISEE-3) • Launched in 1978 into large halo orbit about Earth-Sun L1 • Tracking: S-band STDN, 9 x 5 min tracking passes per day, 21 day batch arc Period Overlap Covariance Compare Analysis (km) (km) A 8.1 6.0 B 9.0 5.5 C 3.6 5.4 3 Solar & Heliospheric Observatory (SOHO) • Launched in 1995 into large halo orbit about Earth-Sun L1 • Tracking: S-band DSN 26-m with some 34-m & 70-m, 5 hrs/day tracking, up to 21 day batch arcs Data Axis Covariance Maximum Total Error Span Def Period 60d Pred (d) Pos Vel Pos Vel (km) (cm/s) (km) (cm/s) 14 Y 10.1 0.42 17.4 0.79 21 Y 8.6 0.19 8.4 0.34 14 Z 6.6 0.39 20.1 1.05 21 Z 5.7 0.26 11.3 0.06 4 Additional SOHO Results • Actual definitive overlap comparisons showed 7 km accuracy (14 km after 44 day prediction) DEF RSS Radial Along- Cross- 44d RSS Radial Along- Cross- track track PRED track track Pos 7 1 2 7 Pos 14 9 2 11 (km) (km) Vel 0.4 0.1 0.2 0.3 Vel 0.7 0.2 0.3 0.6 (mm/s) (mm/s) • Analysis for MAP using real SOHO tracking data showed a degradation of accuracy of less than 2 km when reducing