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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 -
NASA's Curiosity Rover Maximizes Data Sent to Earth by Using International Space Data Communication Standards
Press Release For immediate release NASA's Curiosity Rover Maximizes Data Sent to Earth by Using International Space Data Communication Standards WASHINGTON, 22 August 2012 (CCSDS) – NASA’s Mars Science Laboratory (MSL) mission began its planned 2-year Mars surface exploration mission on August 6 after landing its large, mobile laboratory called Curiosity. The goal of the mission is to assess whether Mars has ever had, or still has, environmental conditions favorable to microbial life. Curiosity, with its one-ton payload carrying capacity carries 10 science instruments that will gather samples of rocks and soil, and process and distribute them to onboard test chambers inside analytical instruments. Some of the rover’s scientific data, including images of the surface of Mars collected by Curiosity’s 17 onboard cameras, are sent directly to and from Earth via NASA’s Deep Space Network (DSN) of large ground antennas. However, once Curiosity becomes fully operational most of the scientific and engineering data will be transferred via relay satellites that are in orbit around Mars. These are primarily the Mars Reconnaissance Orbiter (MRO) and the Mars Odyssey (ODY) spacecraft. The MSL Mars-Earth communications systems are using internationally-agreed space data communications standards to enable reliable transmission of the expected rich data sets to be gathered by Curiosity. These standards were developed by a team of international space data communication specialists collaborating within the Consultative Committee for Space Data Systems (CCSDS). Use of internationally-agreed upon standards reduce cost and risk to space missions, and also offer rich “cross-support” capabilities to collaborate since key data interfaces are inherently interoperable. -
Mars Reconnaissance Orbiter
Chapter 6 Mars Reconnaissance Orbiter Jim Taylor, Dennis K. Lee, and Shervin Shambayati 6.1 Mission Overview The Mars Reconnaissance Orbiter (MRO) [1, 2] has a suite of instruments making observations at Mars, and it provides data-relay services for Mars landers and rovers. MRO was launched on August 12, 2005. The orbiter successfully went into orbit around Mars on March 10, 2006 and began reducing its orbit altitude and circularizing the orbit in preparation for the science mission. The orbit changing was accomplished through a process called aerobraking, in preparation for the “science mission” starting in November 2006, followed by the “relay mission” starting in November 2008. MRO participated in the Mars Science Laboratory touchdown and surface mission that began in August 2012 (Chapter 7). MRO communications has operated in three different frequency bands: 1) Most telecom in both directions has been with the Deep Space Network (DSN) at X-band (~8 GHz), and this band will continue to provide operational commanding, telemetry transmission, and radiometric tracking. 2) During cruise, the functional characteristics of a separate Ka-band (~32 GHz) downlink system were verified in preparation for an operational demonstration during orbit operations. After a Ka-band hardware anomaly in cruise, the project has elected not to initiate the originally planned operational demonstration (with yet-to-be used redundant Ka-band hardware). 201 202 Chapter 6 3) A new-generation ultra-high frequency (UHF) (~400 MHz) system was verified with the Mars Exploration Rovers in preparation for the successful relay communications with the Phoenix lander in 2008 and the later Mars Science Laboratory relay operations. -
Orbit Options for an Orion-Class Spacecraft Mission to a Near-Earth Object
Orbit Options for an Orion-Class Spacecraft Mission to a Near-Earth Object by Nathan C. Shupe B.A., Swarthmore College, 2005 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Department of Aerospace Engineering Sciences 2010 This thesis entitled: Orbit Options for an Orion-Class Spacecraft Mission to a Near-Earth Object written by Nathan C. Shupe has been approved for the Department of Aerospace Engineering Sciences Daniel Scheeres Prof. George Born Assoc. Prof. Hanspeter Schaub Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Shupe, Nathan C. (M.S., Aerospace Engineering Sciences) Orbit Options for an Orion-Class Spacecraft Mission to a Near-Earth Object Thesis directed by Prof. Daniel Scheeres Based on the recommendations of the Augustine Commission, President Obama has pro- posed a vision for U.S. human spaceflight in the post-Shuttle era which includes a manned mission to a Near-Earth Object (NEO). A 2006-2007 study commissioned by the Constellation Program Advanced Projects Office investigated the feasibility of sending a crewed Orion spacecraft to a NEO using different combinations of elements from the latest launch system architecture at that time. The study found a number of suitable mission targets in the database of known NEOs, and pre- dicted that the number of candidate NEOs will continue to increase as more advanced observatories come online and execute more detailed surveys of the NEO population. -
Use of MESSENGER Radioscience Data to Improve Planetary Ephemeris and to Test General Relativity
A&A 561, A115 (2014) Astronomy DOI: 10.1051/0004-6361/201322124 & © ESO 2014 Astrophysics Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity A. K. Verma1;2, A. Fienga3;4, J. Laskar4, H. Manche4, and M. Gastineau4 1 Observatoire de Besançon, UTINAM-CNRS UMR6213, 41bis avenue de l’Observatoire, 25000 Besançon, France e-mail: [email protected] 2 Centre National d’Études Spatiales, 18 avenue Édouard Belin, 31400 Toulouse, France 3 Observatoire de la Côte d’Azur, GéoAzur-CNRS UMR7329, 250 avenue Albert Einstein, 06560 Valbonne, France 4 Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR8028, 77 Av. Denfert-Rochereau, 75014 Paris, France Received 24 June 2013 / Accepted 7 November 2013 ABSTRACT The current knowledge of Mercury’s orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform general relativity tests of the parametrized post-Newtonian (PPN) formalism. -
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. -
GRAIL Twins Toast New Year from Lunar Orbit
Jet JANUARY Propulsion 2012 Laboratory VOLUME 42 NUMBER 1 GRAIL twins toast new year from Three-month ‘formation flying’ mission will By Mark Whalen lunar orbit study the moon from crust to core Above: The GRAIL team celebrates with cake and apple cider. Right: Celebrating said. “So it does take a lot of planning, a lot of test- the other spacecraft will accelerate towards that moun- GRAIL-A’s Jan. 1 lunar orbit insertion are, from left, Maria Zuber, GRAIL principal ing and then a lot of small maneuvers in order to get tain to measure it. The change in the distance between investigator, Massachusetts Institute of Technology; Charles Elachi, JPL director; ready to set up to get into this big maneuver when we the two is noted, from which gravity can be inferred. Jim Green, NASA director of planetary science. go into orbit around the moon.” One of the things that make GRAIL unique, Hoffman JPL’s Gravity Recovery and Interior Laboratory (GRAIL) A series of engine burns is planned to circularize said, is that it’s the first formation flying of two spacecraft mission celebrated the new year with successful main the twins’ orbit, reducing their orbital period to a little around any body other than Earth. “That’s one of the engine burns to place its twin spacecraft in a perfectly more than two hours before beginning the mission’s biggest challenges we have, and it’s what makes this an synchronized orbit around the moon. 82-day science phase. “If these all go as planned, we exciting mission,” he said. -
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. -
Mars Science Laboratory: Curiosity Rover Curiosity’S Mission: Was Mars Ever Habitable? Acquires Rock, Soil, and Air Samples for Onboard Analysis
National Aeronautics and Space Administration Mars Science Laboratory: Curiosity Rover www.nasa.gov Curiosity’s Mission: Was Mars Ever Habitable? acquires rock, soil, and air samples for onboard analysis. Quick Facts Curiosity is about the size of a small car and about as Part of NASA’s Mars Science Laboratory mission, Launch — Nov. 26, 2011 from Cape Canaveral, tall as a basketball player. Its large size allows the rover Curiosity is the largest and most capable rover ever Florida, on an Atlas V-541 to carry an advanced kit of 10 science instruments. sent to Mars. Curiosity’s mission is to answer the Arrival — Aug. 6, 2012 (UTC) Among Curiosity’s tools are 17 cameras, a laser to question: did Mars ever have the right environmental Prime Mission — One Mars year, or about 687 Earth zap rocks, and a drill to collect rock samples. These all conditions to support small life forms called microbes? days (~98 weeks) help in the hunt for special rocks that formed in water Taking the next steps to understand Mars as a possible and/or have signs of organics. The rover also has Main Objectives place for life, Curiosity builds on an earlier “follow the three communications antennas. • Search for organics and determine if this area of Mars was water” strategy that guided Mars missions in NASA’s ever habitable for microbial life Mars Exploration Program. Besides looking for signs of • Characterize the chemical and mineral composition of Ultra-High-Frequency wet climate conditions and for rocks and minerals that ChemCam Antenna rocks and soil formed in water, Curiosity also seeks signs of carbon- Mastcam MMRTG • Study the role of water and changes in the Martian climate over time based molecules called organics. -
Navigation Challenges During Exomars Trace Gas Orbiter Aerobraking Campaign
NON-PEER REVIEW Please select category below: Normal Paper Student Paper Young Engineer Paper Navigation Challenges during ExoMars Trace Gas Orbiter Aerobraking Campaign Gabriele Bellei 1, Francesco Castellini 2, Frank Budnik 3 and Robert Guilanyà Jané 4 1 DEIMOS Space located at ESA/ESOC, Robert-Bosch-Str. 5, Darmstadt, 64293, Germany 2 Telespazio VEGA located at ESA/ESOC, Robert-Bosch-Str. 5, Darmstadt, 64293, Germany 3 ESA/ESOC, Robert-Bosch-Str. 5, Darmstadt, 64293, Germany 4 GMV INSYEN located at ESA/ESOC, Robert-Bosch-Str. 5, Darmstadt, 64293, Germany Abstract The ExoMars Trace Gas Orbiter satellite spent one year in aerobraking operations at Mars, lowering its orbit period from one sol to about two hours. This delicate phase challenged the operations team and in particular the navigation system due to the highly unpredictable Mars atmosphere, which imposed almost continuous monitoring, navigation and re-planning activities. An aerobraking navigation concept was, for the first time at ESA, designed, implemented and validated on-ground and in-flight, based on radiometric tracking data and complemented by information extracted from spacecraft telemetry. The aerobraking operations were successfully completed, on time and without major difficulties, thanks to the simplicity and robustness of the selected approach. This paper describes the navigation concept, presents a recollection of the main in-flight results and gives a retrospective of the main lessons learnt during this activity. Keywords: ExoMars, Trace Gas Orbiter, aerobraking, navigation, orbit determination, Mars atmosphere, accelerometer Introduction The ExoMars program is a cooperation between the European Space Agency (ESA) and Roscosmos for the robotic exploration of the red planet. -
What's Mars Solar Conjunction, and Why Does It Matter? 24 August 2019, by Andrew Good
What's Mars solar conjunction, and why does it matter? 24 August 2019, by Andrew Good spacecraft for conjunction for months. They'll still be collecting science data at Mars, and some will attempt to send that data home. But we won't be commanding the spacecraft out of concern that they could act on a corrupted command." When is this taking place? Solar conjunction occurs every two years. This time, the hold on issuing commands—called a "command moratorium"—will run from Aug. 28 to Sept. 7, 2019. Some missions will have stopped commanding their spacecraft earlier in preparation This animation illustrates Mars solar conjunction, a for the moratorium. period when Mars is on the opposite side of the Sun from Earth. During this time, the Sun can interrupt radio What happens to the spacecraft? transmissions to spacecraft on and around the Red Planet. Credit: NASA/JPL-Caltech Although some instruments aboard spacecraft—especially cameras that generate large amounts of data—will be inactive, all of NASA's Mars spacecraft will continue their science; they'll The daily chatter between antennas here on Earth just have much simpler "to-do" lists than they and those on NASA spacecraft at Mars is about to normally would carry out. get much quieter for a few weeks. On the surface of Mars, the Curiosity rover will stop That's because Mars and Earth will be on opposite driving, while the InSight lander won't move its sides of the Sun, a period known as Mars solar robotic arm. Above Mars, both the Odyssey orbiter conjunction. -
Initial Maven Observations of Ion Cyclotron Waves and Pickup Protons: a Measurement of Hydrogen Loss in the Upper Martian Exosphere F
46th Lunar and Planetary Science Conference (2015) 2628.pdf INITIAL MAVEN OBSERVATIONS OF ION CYCLOTRON WAVES AND PICKUP PROTONS: A MEASUREMENT OF HYDROGEN LOSS IN THE UPPER MARTIAN EXOSPHERE F. J. Crary1, J. E. P. Connerney2, J. R. Espley3 and J. P. McFadden4, 1Laboratory for Space and Atmospheric Physics, University of Col- orado, Boulder, 1234 Innovation Dr., Boulder, CO, 80303, [email protected] 2Goddard Space Flight Center, Mail Code 695, Greenbelt, MD, 20771, [email protected] 3Goddard Space Flight Center, Mail Code 695, Greenbelt, MD, 20771, [email protected], 4Space Science Laboratory, University of California, Berkeley, 7 Gauss Way, Berkeley, CA 94720-7450, [email protected]. Introduction: Observations by the Mars Global Surveyor, Mars Express and Phobos 2 spacecraft [1],[2],[3] have shown that Mars has a hydrogen exo- sphere which extends as much as ten Martian radii from the planet. These hydrogen atoms ionize and are “picked up” in the solar wind flow. Neither the associ- ated hydrogen loss rate nor the structure of this extend- ed exosphere, have previously been well determined. The resulting pickup protons have a distinctive veloci- ty distribution and generate low frequency electromag- netic waves near the ion cyclotron frequency. Proton pickup ions have been observed by Mars Express [4] and proton cyclotron waves have been observed by Mars Global Surveyor [2]. The MAVEN spacecraft is the first Mars orbiter able to simultane- ously measure both ion cyclotron waves. Data from the spacecraft’s magnetometer [5], providing the vector magnetic field at a rate of 32 samples per second, is Fourier transformed to produce dynamic spectra of right-circularly polarized (whistler mode) and left- circularly polarized (ion cyclotron mode) ultralow fre- quency electromagnetic waves.