DOCSLIB.ORG

Orbit Determination Issues for Libration Point Orbits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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every libration point mission except the recent Genesis mission out of JPL • This presentation presents published and unpublished orbit determination results from 4 previous LPO missions • ISEE-3 • SOHO • ACE • MAP • The use of advanced technology can improve accuracy and reduce tracking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 tracking data to 37 min/day 5 Advanced Composition Explorer (ACE) • Launched in 1997 into small Lissajous orbit about Earth-Sun L1 • Tracking: DSN 26-m & 34-m, 3.5 hr/day, 4 to 14 day batch arcs (HGA pointing requirements require attitude maneuvers every 4 to 14 days) RSS Radial Along-trk Cross-trk Definitive Point Overlap Pos (km) 10 4 5 8 Vel 1.2 0.9 0.1 0.9 (mm/s) 2-Week Predictive Overlap Pos (km) 23 8 6 21 Vel 1.2 0.9 0.1 0.9 6 (mm/s) Maneuver Modeling • Covariance analysis was performed to determine OD accuracy with modeled maneuvers in the batch data arc • 4 mm/sec maneuvers performed every day over 21 day arc • Thrust modeled with 3% or 5% uncertainty in dV magnitude Delta-V Pos Error Vel Error Error (km) (cm/sec) 3% 12-47 3.5-4.0 5% 16-78 5.8-6.5 7 Microwave Anisotropy Probe (MAP) • Launched in 2001 into small Lissajous orbit about Earth- Sun L2 • Tracking: S-band DSN 34-m & 70-m, 45 min/day tracking, 14 to 72 day batch arc • Fixed spacecraft area WRT Sun enables consistent estimation of solar pressure forces and allows extension of data arc 8 Additional MAP Results • Cr estimated to ± 0.005 • Predictive overlaps below from period of low solar activity RSS Radial Along- Cross- track track 5-Week Predictive Overlap Pos (km) 2.0 0.3 1.4 2.0 Vel 0.83 0.36 0.40 0.79 (mm/s) 9-Week Predictive Overlap Pos (km) 6.7 6.2 2.3 1.8 Vel 3.9 3.8 0.4 0.6 9 (mm/s) Celestial Navigator (CelNav) • GNCC flight algorithms for onboard navigation • Uses standard spacecraft attitude sensors (e.g. DSS, star tracker, Earth sensor, visible camera) and communication components (to extract 1-way forward Doppler) Autonomous Navigation Scenario • Real-time accuracies to 10 km RMS S/C to Sun directional for LPO are achievable using high- measurement Ground Station S/C to Earth to S/C Doppler directional accuracy attitude sensors and one- measurement measurement way Doppler measurements Earth 10 CelNav Results _ Addition of more realistic parameters degraded solution accuracy to a range of 14 to 22 km _ noisy USO (10 times the noise sigma) _ reduced Doppler tracking data _ directional measurement biases _ elimination of Earth directional measurements 160 100 160 100 RMS Maximum RMS Maximum 90 140 80 120 70 100 60 80 50 57 40 30 (Kilometers) (Kilometers) 60 46 30 31 40 (Millimeters per Second) (Millimeters per Second) 20 10 4 5 Total Position Error After 7 weeks 9 Total Velocity Error After 7 weeks Total Position Error After 7 weeks 20 7 Total Velocity Error After 7 weeks 10 2 0 0 Optimistic Realistic with Sun, Realistic with Sun Optimistic Realistic with Sun, Realistic with Sun Earth, and and Earth Earth, and Doppler and Earth 11 Doppler Delta-Differential One-Way Range (DDOR) • All previous LPO missions have used ground based tracking using range and Doppler measurement types • Both of these measurements give information only along the spacecraft line- of-sight • The radial component of the orbital uncertainty is considerably more accurate than the plane-of-the- sky components. • DDOR is a true VLBI measurement type that is being implemented at the DSN 34-m and 70-m (X- band only) sites as a nominal measurement type by May 2003 • DDOR is obtained by double differencing simultaneous observations of the spacecraft from two widely separated ground sites followed immediately by observations from an angularly 12 nearby quasar DDOR Analysis • Used operationally before on Voyager, Galileo, and Magellan, and tested on Mars Global Surveyor and Mars Odyssey • DDOR provides relative angular measurement accurate to 5 nrad • Covariance analysis on DDOR for LPOs shows improved accuracy with decreased tracking times R&D Sch* DDOR Baseline Def Pos Tot DSN Acc (km) Trk Time (hrs/wk) 2 hrs/day None NA 3.8 14 1 hr/3 days None NA 6.5 2.5 1 hr/3 days Once 50% Gds-Mad 2.8 2.5 /day 12% Can-Mad 38% Gds-Can * Rotating stations each day including both northern/southern hemisphere 13 DDOR Drawbacks _ For each acquisition during Voyager, 109 bits were reduced to obtain one measurement _ Extensive post-processing typically took up to 24 hrs _ DDOR has been used as a supplemental measurement source with independent solutions obtained from standard measurement types used as references; an increased reliance on DDOR and large reductions in standard tracking would reduce the quality assurance of DDOR 14 Conclusions • Actual OD results from previous LPO missions indicate a total position uncertainty of 2 km (MAP) to 10 km (ACE) • Accuracy is dependent upon: • Amount and quality of the tracking data • Accurate modeling of solar pressure forces • No spacecraft perturbations within minimum 21 day data arc • CelNav technology can provide real-time onboard OD accurate to 10-22 km depending on attitude sensor quality • DDOR measurement type can improve any tracking scenario while reducing tracking times 15.
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
    [Show full text]
  • Orbit Determination Methods and Techniques
    PROJECTE FINAL DE CARRERA (PFC) GEOSAR Mission: Orbit Determination Methods and Techniques Marc Fernàndez Uson PFC Advisor: Prof. Antoni Broquetas Ibars May 2016 PROJECTE FINAL DE CARRERA (PFC) GEOSAR Mission: Orbit Determination Methods and Techniques Marc Fernàndez Uson ABSTRACT ABSTRACT Multiple applications such as land stability control, natural risks prevention or accurate numerical weather prediction models from water vapour atmospheric mapping would substantially benefit from permanent radar monitoring given their fast evolution is not observable with present Low Earth Orbit based systems. In order to overcome this drawback, GEOstationary Synthetic Aperture Radar missions (GEOSAR) are presently being studied. GEOSAR missions are based on operating a radar payload hosted by a communication satellite in a geostationary orbit. Due to orbital perturbations, the satellite does not follow a perfectly circular orbit, but has a slight eccentricity and inclination that can be used to form the synthetic aperture required to obtain images. Several sources affect the along-track phase history in GEOSAR missions causing unwanted fluctuations which may result in image defocusing. The main expected contributors to azimuth phase noise are orbit determination errors, radar carrier frequency drifts, the Atmospheric Phase Screen (APS), and satellite attitude instabilities and structural vibration. In order to obtain an accurate image of the scene after SAR processing, the range history of every point of the scene must be known. This fact requires a high precision orbit modeling and the use of suitable techniques for atmospheric phase screen compensation, which are well beyond the usual orbit determination requirement of satellites in GEO orbits. The other influencing factors like oscillator drift and attitude instability, vibration, etc., must be controlled or compensated.
    [Show full text]
  • 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 ...............................................................................................
    [Show full text]
  • 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.
    [Show full text]
  • Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling
    Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik B.S. Computer Science Michigan Technological University, 2000 SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2008 © 2008 Massachusetts Institute of Technology. All rights reserved. Signature of Author:_______________________________________________________ Department of Aeronautics and Astronautics May 23, 2008 Certified by:_____________________________________________________________ Dr. Paul J. Cefola Lecturer, Department of Aeronautics and Astronautics Thesis Supervisor Certified by:_____________________________________________________________ Professor Jonathan P. How Professor, Department of Aeronautics and Astronautics Thesis Advisor Accepted by:_____________________________________________________________ Professor David L. Darmofal Associate Department Head Chair, Committee on Graduate Students 1 [This page intentionally left blank.] 2 Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik Submitted to the Department of Aeronautics and Astronautics on May 23, 2008 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics ABSTRACT The development of electric propulsion technology for spacecraft has led to reduced costs and longer lifespans for certain
    [Show full text]
  • 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.
    [Show full text]
  • Libration Orbit Mission Design: Applications of Numerical and Dynamical Methods
    Libration Orbit Mission Design: Applications Of Numerical And Dynamical Methods David Folta and Mark Beckman NASA - Goddard Space Flight Center Libration Point Orbits and Applications June 10-14, 2002, Girona, Spain Agenda • NASA Enterprises • Challenges • Historical and future missions • Libration mission design via numerical and dynamical methods • Applications ¾Direct transfer ¾Low thrust ¾Servicing ¾Formations: Constellation-X and Stellar Imager ¾Conceptual studies • Improved tools • Conclusions NASA Themes and Libration Orbits NASA Enterprises of Space Sciences (SSE) and Earth Sciences (ESE) are a combination of several programs and themes SSE ESE SEU SEC Origins • Recent SEC missions include ACE, SOHO, and the L1/L2 WIND mission. The Living With a Star (LWS) portion of SEC may require libration orbits at the L1 and L3 Sun-Earth libration points. • Structure and Evolution of the Universe (SEU) currently has MAP and the future Micro Arc-second X-ray Imaging Mission (MAXIM) and Constellation-X missions. •Space Sciences’ Origins libration missions are the Next Generation Space Telescope (NGST) and The Terrestrial Planet Finder (TPF). • The Triana mission is the lone ESE mission not orbiting the Earth. • A major challenge is formation flying components of Constellation-X, MAXIM, TPF, and Stellar Imager. Future Libration Mission SSE and ESE Challenges ¾ Orbit ¾Biased orbits when using large sun shades ¾Shadow restrictions ¾Very small amplitudes ¾Reorientation to different planes and Lissajous classes ¾Rendezvous and formation flying ¾Low
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • Statistical Orbit Determination
    Preface The modem field of orbit determination (OD) originated with Kepler's inter­ pretations of the observations made by Tycho Brahe of the planetary motions. Based on the work of Kepler, Newton was able to establish the mathematical foundation of celestial mechanics. During the ensuing centuries, the efforts to im­ prove the understanding of the motion of celestial bodies and artificial satellites in the modem era have been a major stimulus in areas of mathematics, astronomy, computational methodology and physics. Based on Newton's foundations, early efforts to determine the orbit were focused on a deterministic approach in which a few observations, distributed across the sky during a single arc, were used to find the position and velocity vector of a celestial body at some epoch. This uniquely categorized the orbit. Such problems are deterministic in the sense that they use the same number of independent observations as there are unknowns. With the advent of daily observing programs and the realization that the or­ bits evolve continuously, the foundation of modem precision orbit determination evolved from the attempts to use a large number of observations to determine the orbit. Such problems are over-determined in that they utilize far more observa­ tions than the number required by the deterministic approach. The development of the digital computer in the decade of the 1960s allowed numerical approaches to supplement the essentially analytical basis for describing the satellite motion and allowed a far more rigorous representation of the force models that affect the motion. This book is based on four decades of classroom instmction and graduate- level research.
    [Show full text]
  • 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.
    [Show full text]
  • Multiple Solutions for Asteroid Orbits: Computational Procedure and Applications
    A&A 431, 729–746 (2005) Astronomy DOI: 10.1051/0004-6361:20041737 & c ESO 2005 Astrophysics Multiple solutions for asteroid orbits: Computational procedure and applications A. Milani1,M.E.Sansaturio2,G.Tommei1, O. Arratia2, and S. R. Chesley3 1 Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy e-mail: [milani;tommei]@mail.dm.unipi.it 2 E.T.S. de Ingenieros Industriales, University of Valladolid Paseo del Cauce 47011 Valladolid, Spain e-mail: [meusan;oscarr]@eis.uva.es 3 Jet Propulsion Laboratory, 4800 Oak Grove Drive, CA-91109 Pasadena, USA e-mail: [email protected] Received 27 July 2004 / Accepted 20 October 2004 Abstract. We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a “weak” direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method.
    [Show full text]