Low-Thrust Control of a Lunar Mapping Orbit
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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 -
Electric Propulsion System Scaling for Asteroid Capture-And-Return Missions
Electric propulsion system scaling for asteroid capture-and-return missions Justin M. Little⇤ and Edgar Y. Choueiri† Electric Propulsion and Plasma Dynamics Laboratory, Princeton University, Princeton, NJ, 08544 The requirements for an electric propulsion system needed to maximize the return mass of asteroid capture-and-return (ACR) missions are investigated in detail. An analytical model is presented for the mission time and mass balance of an ACR mission based on the propellant requirements of each mission phase. Edelbaum’s approximation is used for the Earth-escape phase. The asteroid rendezvous and return phases of the mission are modeled as a low-thrust optimal control problem with a lunar assist. The numerical solution to this problem is used to derive scaling laws for the propellant requirements based on the maneuver time, asteroid orbit, and propulsion system parameters. Constraining the rendezvous and return phases by the synodic period of the target asteroid, a semi- empirical equation is obtained for the optimum specific impulse and power supply. It was found analytically that the optimum power supply is one such that the mass of the propulsion system and power supply are approximately equal to the total mass of propellant used during the entire mission. Finally, it is shown that ACR missions, in general, are optimized using propulsion systems capable of processing 100 kW – 1 MW of power with specific impulses in the range 5,000 – 10,000 s, and have the potential to return asteroids on the order of 103 104 tons. − Nomenclature -
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. -
Arxiv:1505.07033V2 [Astro-Ph.IM] 4 Sep 2015
September 7, 2015 0:46 manuscript Journal of Astronomical Instrumentation c World Scientific Publishing Company A CUBESAT FOR CALIBRATING GROUND-BASED AND SUB-ORBITAL MILLIMETER-WAVE POLARIMETERS (CALSAT) Bradley R. Johnson1, Clement J. Vourch2, Timothy D. Drysdale2, Andrew Kalman3, Steve Fujikawa4, Brian Keating5 and Jon Kaufman5 1Department of Physics, Columbia University, New York, NY 10027, USA 2School of Engineering, University of Glasgow, Glasgow, Scotland G12 8QQ, UK 3Pumpkin, Inc., San Francisco, CA 94112, USA 4Maryland Aerospace Inc., Crofton, MD 21114, USA 5Department of Physics, University of California, San Diego, CA 92093-0424, USA Received (to be inserted by publisher); Revised (to be inserted by publisher); Accepted (to be inserted by publisher); We describe a low-cost, open-access, CubeSat-based calibration instrument that is designed to support ground- based and sub-orbital experiments searching for various polarization signals in the cosmic microwave background (CMB). All modern CMB polarization experiments require a robust calibration program that will allow the effects of instrument-induced signals to be mitigated during data analysis. A bright, compact, and linearly polarized astrophysical source with polarization properties known to adequate precision does not exist. Therefore, we designed a space-based millimeter-wave calibration instrument, called CalSat, to serve as an open-access calibrator, and this paper describes the results of our design study. The calibration source on board CalSat is composed of five \tones" with one each at 47.1, 80.0, 140, 249 and 309 GHz. The five tones we chose are well matched to (i) the observation windows in the atmospheric transmittance spectra, (ii) the spectral bands commonly used in polarimeters by the CMB community, and (iii) The Amateur Satellite Service bands in the Table of Frequency Allocations used by the Federal Communications Commission. -
Dynamical Analysis of Rendezvous and Docking with Very Large Space Infrastructures in Non-Keplerian Orbits
DYNAMICAL ANALYSIS OF RENDEZVOUS AND DOCKING WITH VERY LARGE SPACE INFRASTRUCTURES IN NON-KEPLERIAN ORBITS Andrea Colagrossi ∗, Michele` Lavagna y, Simone Flavio Rafano Carna` z Politecnico di Milano Department of Aerospace Science and Technology Via La Masa 34 – 20156 Milan (MI) – Italy ABSTRACT the whole mission scenario is the so called Evolvable Deep Space Habitat: a modular space station in lunar vicinity. A space station in the vicinity of the Moon can be exploited At the current level of study, the optimum location for as a gateway for future human and robotic exploration of the space infrastructure of this kind has not yet been determined, Solar System. The natural location for a space system of this but a favorable solution can be about one of the Earth-Moon kind is about one of the Earth-Moon libration points. libration points, such as in a EML2 (Earth-Moon Lagrangian The study addresses the dynamics during rendezvous and Point no 2) Halo orbit. Moreover, the final configuration of docking operations with a very large space infrastructure in a the entire system is still to be defined, but it is already clear EML2 Halo orbit. The model takes into account the coupling that in order to assemble the structure several rendezvous and effects between the orbital and the attitude motion in a Circular docking activities will be carried out, many of which to be Restricted Three-Body Problem environment. The flexibility completely automated. of the system is included, and the interaction between the Unfortunately, the current knowledge about rendezvous in modes of the structure and those related with the orbital motion cis-lunar orbits is minimal and it is usually limited to point- is investigated. -
What Is the Interplanetary Superhighway?
What is the InterPlanetary Suppgyerhighway? Kathleen Howell Purdue University Lo and Ross Trajectory Key Space Technology Mission-Enabling Technology Not All Technology is hardware! The InterPlanetary Superhighway (IPS) • LELow Energy ObitfSOrbits for Space Mi Miissions • InterPlanetary Superhighway—“a vast network of winding tunnels in space” that connects the Sun , the planets, their moons, AND many other destinations • Systematic mapping properly known as InterPlanetary Transport Network Simó, Gómez, Masdemont / Lo, Howell, Barden / Howell, Folta / Lo, Ross / Koon, Lo, Marsden, Ross / Marchand, Howell, Lo / Scheeres, Villac/ ……. Originates with Poincaré (1892) Applications to wide range of fields Different View of Problems in N-Bodies • Much more than Kepler and Newton imagined • Computationally challenging Poincaré (1854-1912) “Mathematics is the art of giving the same name to different things” Jules Henri Poincaré NBP Play 3BP Wang 2BP New Era in Celestial Mechanics Pioneering Work: Numerical Exploration by Hand (Breakwell, Farquhar and Dunham) Current Libration Point Missions Goddard Space Flight Center • z WIND SOHO ACE MAPGENESIS NGST Courtesy of D. Folta, GSFC Multi-Body Problem Orbit propagated for 4 conic periods: • Change our perspective 4*19 days = 75.7 days Earth Earth Sun To Sun Inertial View RotatingRotating View View Inertial View (Ro ta tes w ith two b odi es) Aeronautics and Astronautics Multi-Body Problem • Change our perspective • Effects of added gravity fields Earth Earth TSTo Sun Rotating View Inertial View Equilibrium -
Up, Up, and Away by James J
www.astrosociety.org/uitc No. 34 - Spring 1996 © 1996, Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, CA 94112. Up, Up, and Away by James J. Secosky, Bloomfield Central School and George Musser, Astronomical Society of the Pacific Want to take a tour of space? Then just flip around the channels on cable TV. Weather Channel forecasts, CNN newscasts, ESPN sportscasts: They all depend on satellites in Earth orbit. Or call your friends on Mauritius, Madagascar, or Maui: A satellite will relay your voice. Worried about the ozone hole over Antarctica or mass graves in Bosnia? Orbital outposts are keeping watch. The challenge these days is finding something that doesn't involve satellites in one way or other. And satellites are just one perk of the Space Age. Farther afield, robotic space probes have examined all the planets except Pluto, leading to a revolution in the Earth sciences -- from studies of plate tectonics to models of global warming -- now that scientists can compare our world to its planetary siblings. Over 300 people from 26 countries have gone into space, including the 24 astronauts who went on or near the Moon. Who knows how many will go in the next hundred years? In short, space travel has become a part of our lives. But what goes on behind the scenes? It turns out that satellites and spaceships depend on some of the most basic concepts of physics. So space travel isn't just fun to think about; it is a firm grounding in many of the principles that govern our world and our universe. -
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. -
Positioning: Drift Orbit and Station Acquisition
Orbits Supplement GEOSTATIONARY ORBIT PERTURBATIONS INFLUENCE OF ASPHERICITY OF THE EARTH: The gravitational potential of the Earth is no longer µ/r, but varies with longitude. A tangential acceleration is created, depending on the longitudinal location of the satellite, with four points of stable equilibrium: two stable equilibrium points (L 75° E, 105° W) two unstable equilibrium points ( 15° W, 162° E) This tangential acceleration causes a drift of the satellite longitude. Longitudinal drift d'/dt in terms of the longitude about a point of stable equilibrium expresses as: (d/dt)2 - k cos 2 = constant Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF EARTH ASPHERICITY VARIATION IN THE LONGITUDINAL ACCELERATION OF A GEOSTATIONARY SATELLITE: Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN & MOON ATTRACTION Gravitational attraction by the sun and moon causes the satellite orbital inclination to change with time. The evolution of the inclination vector is mainly a combination of variations: period 13.66 days with 0.0035° amplitude period 182.65 days with 0.023° amplitude long term drift The long term drift is given by: -4 dix/dt = H = (-3.6 sin M) 10 ° /day -4 diy/dt = K = (23.4 +.2.7 cos M) 10 °/day where M is the moon ascending node longitude: M = 12.111 -0.052954 T (T: days from 1/1/1950) 2 2 2 2 cos d = H / (H + K ); i/t = (H + K ) Depending on time within the 18 year period of M d varies from 81.1° to 98.9° i/t varies from 0.75°/year to 0.95°/year Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN RADIATION PRESSURE Due to sun radiation pressure, eccentricity arises: EFFECT OF NON-ZERO ECCENTRICITY L = difference between longitude of geostationary satellite and geosynchronous satellite (24 hour period orbit with e0) With non-zero eccentricity the satellite track undergoes a periodic motion about the subsatellite point at perigee. -
Spacecraft Trajectories in a Sun, Earth, and Moon Ephemeris Model
SPACECRAFT TRAJECTORIES IN A SUN, EARTH, AND MOON EPHEMERIS MODEL A Project Presented to The Faculty of the Department of Aerospace Engineering San José State University In Partial Fulfillment of the Requirements for the Degree Master of Science in Aerospace Engineering by Romalyn Mirador i ABSTRACT SPACECRAFT TRAJECTORIES IN A SUN, EARTH, AND MOON EPHEMERIS MODEL by Romalyn Mirador This project details the process of building, testing, and comparing a tool to simulate spacecraft trajectories using an ephemeris N-Body model. Different trajectory models and methods of solving are reviewed. Using the Ephemeris positions of the Earth, Moon and Sun, a code for higher-fidelity numerical modeling is built and tested using MATLAB. Resulting trajectories are compared to NASA’s GMAT for accuracy. Results reveal that the N-Body model can be used to find complex trajectories but would need to include other perturbations like gravity harmonics to model more accurate trajectories. i ACKNOWLEDGEMENTS I would like to thank my family and friends for their continuous encouragement and support throughout all these years. A special thank you to my advisor, Dr. Capdevila, and my friend, Dhathri, for mentoring me as I work on this project. The knowledge and guidance from the both of you has helped me tremendously and I appreciate everything you both have done to help me get here. ii Table of Contents List of Symbols ............................................................................................................................... v 1.0 INTRODUCTION -
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Cis-Lunar Autonomous Navigation via Implementation of Optical Asteroid Angle-Only Measurements Mark B. Hinga, Ph.D., P.E. ∗ Autonomous cis- or trans-Lunar spacecraft navigation is critical to mission success as communication to ground stations and access to GPS signals could be lost. However, if the satellite has a camera of sufficient qual- ity, line of sight (unit vector) measurements can be made to known solar system bodies to provide observations which enable autonomous estimation of position and velocity of the spacecraft, that can be telemetered to those interested space based or ground based consumers. An improved Gaussian-Initial Orbit Determination (IOD) algorithm, based on the exact values of the f and g series (free of the 8th order polynomial and range guessing), for spacecraft state estimation, is presented here and exercised in the inertial coordinate frame (2-Body Prob- lem) to provide an initial guess for the Batch IOD that is performed in the Circular Restricted Three Body Problem (CRTBP) reference frame, which ultimately serves to initialize a CRTBP Extended Kalman Filter (EKF) navigator that collects angle only measurements to a known Asteroid 2014 EC (flying by the Earth) to sequentially estimate position and velocity of an observer spacecraft flying on an APOLLO-like trajectory to the Moon. With the addition of simulating/expressing the accelerations that would be sensed in the IMU plat- form frame due to delta velocities caused by either perturbations or corrective guidance maneuvers, this three phase algorithm is able to autonomously track the spacecraft state on its journey to the Moon while observing the motion of the Asteroid. -
Cislunar Tether Transport System
FINAL REPORT on NIAC Phase I Contract 07600-011 with NASA Institute for Advanced Concepts, Universities Space Research Association CISLUNAR TETHER TRANSPORT SYSTEM Report submitted by: TETHERS UNLIMITED, INC. 8114 Pebble Ct., Clinton WA 98236-9240 Phone: (206) 306-0400 Fax: -0537 email: [email protected] www.tethers.com Report dated: May 30, 1999 Period of Performance: November 1, 1998 to April 30, 1999 PROJECT SUMMARY PHASE I CONTRACT NUMBER NIAC-07600-011 TITLE OF PROJECT CISLUNAR TETHER TRANSPORT SYSTEM NAME AND ADDRESS OF PERFORMING ORGANIZATION (Firm Name, Mail Address, City/State/Zip Tethers Unlimited, Inc. 8114 Pebble Ct., Clinton WA 98236-9240 [email protected] PRINCIPAL INVESTIGATOR Robert P. Hoyt, Ph.D. ABSTRACT The Phase I effort developed a design for a space systems architecture for repeatedly transporting payloads between low Earth orbit and the surface of the moon without significant use of propellant. This architecture consists of one rotating tether in elliptical, equatorial Earth orbit and a second rotating tether in a circular low lunar orbit. The Earth-orbit tether picks up a payload from a circular low Earth orbit and tosses it into a minimal-energy lunar transfer orbit. When the payload arrives at the Moon, the lunar tether catches it and deposits it on the surface of the Moon. Simultaneously, the lunar tether picks up a lunar payload to be sent down to the Earth orbit tether. By transporting equal masses to and from the Moon, the orbital energy and momentum of the system can be conserved, eliminating the need for transfer propellant. Using currently available high-strength tether materials, this system could be built with a total mass of less than 28 times the mass of the payloads it can transport.