Orbit Options for an Orion-Class Spacecraft Mission to a Near-Earth Object
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Low Thrust Manoeuvres to Perform Large Changes of RAAN Or Inclination in LEO
Facoltà di Ingegneria Corso di Laurea Magistrale in Ingegneria Aerospaziale Master Thesis Low Thrust Manoeuvres To Perform Large Changes of RAAN or Inclination in LEO Academic Tutor: Prof. Lorenzo CASALINO Candidate: Filippo GRISOT July 2018 “It is possible for ordinary people to choose to be extraordinary” E. Musk ii Filippo Grisot – Master Thesis iii Filippo Grisot – Master Thesis Acknowledgments I would like to address my sincere acknowledgments to my professor Lorenzo Casalino, for your huge help in these moths, for your willingness, for your professionalism and for your kindness. It was very stimulating, as well as fun, working with you. I would like to thank all my course-mates, for the time spent together inside and outside the “Poli”, for the help in passing the exams, for the fun and the desperation we shared throughout these years. I would like to especially express my gratitude to Emanuele, Gianluca, Giulia, Lorenzo and Fabio who, more than everyone, had to bear with me. I would like to also thank all my extra-Poli friends, especially Alberto, for your support and the long talks throughout these years, Zach, for being so close although the great distance between us, Bea’s family, for all the Sundays and summers spent together, and my soccer team Belfiga FC, for being the crazy lovable people you are. A huge acknowledgment needs to be address to my family: to my grandfather Luciano, for being a great friend; to my grandmother Bianca, for teaching me what “fighting” means; to my grandparents Beppe and Etta, for protecting me -
Osculating Orbit Elements and the Perturbed Kepler Problem
Osculating orbit elements and the perturbed Kepler problem Gmr a = 3 + f(r, v,t) Same − r x & v Define: r := rn ,r:= p/(1 + e cos f) ,p= a(1 e2) − osculating orbit he sin f h v := n + λ ,h:= Gmp p r n := cos ⌦cos(! + f) cos ◆ sinp ⌦sin(! + f) e − X +⇥ sin⌦cos(! + f) + cos ◆ cos ⌦sin(! + f⇤) eY actual orbit +sin⇥ ◆ sin(! + f) eZ ⇤ λ := cos ⌦sin(! + f) cos ◆ sin⌦cos(! + f) e − − X new osculating + sin ⌦sin(! + f) + cos ◆ cos ⌦cos(! + f) e orbit ⇥ − ⇤ Y +sin⇥ ◆ cos(! + f) eZ ⇤ hˆ := n λ =sin◆ sin ⌦ e sin ◆ cos ⌦ e + cos ◆ e ⇥ X − Y Z e, a, ω, Ω, i, T may be functions of time Perturbed Kepler problem Gmr a = + f(r, v,t) − r3 dh h = r v = = r f ⇥ ) dt ⇥ v h dA A = ⇥ n = Gm = f h + v (r f) Gm − ) dt ⇥ ⇥ ⇥ Decompose: f = n + λ + hˆ R S W dh = r λ + r hˆ dt − W S dA Gm =2h n h + rr˙ λ rr˙ hˆ. dt S − R S − W Example: h˙ = r S d (h cos ◆)=h˙ e dt · Z d◆ h˙ cos ◆ h sin ◆ = r cos(! + f)sin◆ + r cos ◆ − dt − W S Perturbed Kepler problem “Lagrange planetary equations” dp p3 1 =2 , dt rGm 1+e cos f S de p 2 cos f + e(1 + cos2 f) = sin f + , dt Gm R 1+e cos f S r d◆ p cos(! + f) = , dt Gm 1+e cos f W r d⌦ p sin(! + f) sin ◆ = , dt Gm 1+e cos f W r d! 1 p 2+e cos f sin(! + f) = cos f + sin f e cot ◆ dt e Gm − R 1+e cos f S− 1+e cos f W r An alternative pericenter angle: $ := ! +⌦cos ◆ d$ 1 p 2+e cos f = cos f + sin f dt e Gm − R 1+e cos f S r Perturbed Kepler problem Comments: § these six 1st-order ODEs are exactly equivalent to the original three 2nd-order ODEs § if f = 0, the orbit elements are constants § if f << Gm/r2, use perturbation theory -
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 -
Non-Principal Axis Rotation (Tumbling) Asteroids
NON-PRINCIPAL AXIS ROTATION (TUMBLING) ASTEROIDS Asteroid PAR Per1 Amp1 Per2 Amp2 Reference 244 Sita T0 129.51 0.82 0 129.51 0.82 Brinsfield, 09 253 Mathilde T 417.7 0.50 –3 417.7 0.45 250. Mottola, 95 –3 418. 0.5 250. Pravec, 05 288 Glauke T 1170. 0.9 –1 1200. 0.9 Harris, 99 0 Pravec, 14 –2 1170. 0.37 740. Pilcher, 15 299∗ Thora T– 272.9 0.50 0 274. 0.39 Pilcher, 14 +2 272.9 0.47 Pilcher, 17 319∗ Leona T 430. 0.5 –2 430. 0.5 1084. Pilcher, 17 341∗ California T 318. 0.92 –2 318. 0.9 250. Pilcher, 17 –2 317.0 0.54 Polakis, 17 –1 317.0 0.92 Polakis, 17 408 Fama T0 202.1 0.58 0 202.1 0.58 Stephens, 08 470 Kilia T0 290. 0.26 0 290. 0.26 Stephens, 09 0 Stephens, 09 496∗ Gryphia T 1072. 1.25 –2 1072. 1.25 Pilcher, 17 571 Dulcinea T 126.3 0.50 –2 126.3 0.50 Stephens, 11 630 Euphemia T0 350. 0.45 0 350. 0.45 Warner, 11 703∗ No¨emi T? 200. 0.78 –1 201.7 0.78 Noschese, 17 0 115.108 0.28 Sada, 17 –2 200. 0.62 Franco, 17 707 Ste¨ına T0 414. 1.00 0 Pravec, 14 763∗ Cupido T 151.5 0.45 –1 151.1 0.24 Polakis, 18 –2 151.5 0.45 101. Pilcher, 18 823 Sisigambis T0 146. -
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 -
Achievements of Hayabusa2: Unveiling the World of Asteroid by Interplanetary Round Trip Technology
Achievements of Hayabusa2: Unveiling the World of Asteroid by Interplanetary Round Trip Technology Yuichi Tsuda Project Manager, Hayabusa2 Japan Aerospace ExplorationAgency 58th COPUOS, April 23, 2021 Lunar and Planetary Science Missions of Japan 1980 1990 2000 2010 2020 Future Plan Moon 2007 Kaguya 1990 Hiten SLIM Lunar-A × Venus 2010 Akatsuki 2018 Mio 1998 Nozomi × Planets Mercury (Mars) 2010 IKAROS Venus MMX Phobos/Mars 1985 Suisei 2014 Hayabusa2 Small Bodies Asteroid Ryugu 2003 Hayabusa 1985 Sakigake Asteroid Itokawa Destiny+ Comet Halley Comet Pheton 2 Hayabusa2 Mission ✓ Sample return mission to a C-type asteroid “Ryugu” ✓ 5.2 billion km interplanetary journey. Launch Earth Gravity Assist Ryugu Arrival MINERVA-II-1 Deployment Dec.3, 2014 Sep.21, 2018 Dec.3, 2015 Jun.27, 2018 MASCOT Deployment Oct.3, 2018 Ryugu Departure Nov.13.2019 Kinetic Impact Earth Return Second Dec.6, 2020 Apr.5, 2019 Target Markers Orbiting Touchdown Sep.16, 2019 Jul,11, 2019 First Touchdown Feb.22, 2019 MINERVA-II-2 Orbiting MD [D VIp srvlxp #534<# Oct.2, 2019 Hayabusa2 Spacecraft Overview Deployable Xband Xband Camera (DCAM3) HGA LGA Xband Solar Array MGA Kaba nd Ion Engine HGA Panel RCS thrusters ×12 ONC‐T, ONC‐W1 Star Trackers Near Infrared DLR MASCOT Spectrometer (NIRS3) Lander Thermal Infrared +Z Imager (TIR) Reentry Capsule +X MINERVA‐II Small Carry‐on +Z LIDAR ONC‐W2 +Y Rovers Impactor (SCI) +X Sampler Horn Target +Y Markers ×5 Launch Mass: 609kg Ion Engine: Total ΔV=3.2km/s, Thrust=5-28mN (variable), Specific Impulse=2800- 3000sec. (4 thrusters, mounted on two-axis gimbal) Chemical RCS: Bi-prop. -
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. -
CURRICULUM VITAE, ALAN W. HARRIS Personal: Born
CURRICULUM VITAE, ALAN W. HARRIS Personal: Born: August 3, 1944, Portland, OR Married: August 22, 1970, Rose Marie Children: W. Donald (b. 1974), David (b. 1976), Catherine (b 1981) Education: B.S. (1966) Caltech, Geophysics M.S. (1967) UCLA, Earth and Space Science PhD. (1975) UCLA, Earth and Space Science Dissertation: Dynamical Studies of Satellite Origin. Advisor: W.M. Kaula Employment: 1966-1967 Graduate Research Assistant, UCLA 1968-1970 Member of Tech. Staff, Space Division Rockwell International 1970-1971 Physics instructor, Santa Monica College 1970-1973 Physics Teacher, Immaculate Heart High School, Hollywood, CA 1973-1975 Graduate Research Assistant, UCLA 1974-1991 Member of Technical Staff, Jet Propulsion Laboratory 1991-1998 Senior Member of Technical Staff, Jet Propulsion Laboratory 1998-2002 Senior Research Scientist, Jet Propulsion Laboratory 2002-present Senior Research Scientist, Space Science Institute Appointments: 1976 Member of Faculty of NATO Advanced Study Institute on Origin of the Solar System, Newcastle upon Tyne 1977-1978 Guest Investigator, Hale Observatories 1978 Visiting Assoc. Prof. of Physics, University of Calif. at Santa Barbara 1978-1980 Executive Committee, Division on Dynamical Astronomy of AAS 1979 Visiting Assoc. Prof. of Earth and Space Science, UCLA 1980 Guest Investigator, Hale Observatories 1983-1984 Guest Investigator, Lowell Observatory 1983-1985 Lunar and Planetary Review Panel (NASA) 1983-1992 Supervisor, Earth and Planetary Physics Group, JPL 1984 Science W.G. for Voyager II Uranus/Neptune Encounters (JPL/NASA) 1984-present Advisor of students in Caltech Summer Undergraduate Research Fellowship Program 1984-1985 ESA/NASA Science Advisory Group for Primitive Bodies Missions 1985-1993 ESA/NASA Comet Nucleus Sample Return Science Definition Team (Deputy Chairman, U.S. -
Five Special Types of Orbits Around Mars
JOURNAL OF GUIDANCE,CONTROL, AND DYNAMICS Vol. 33, No. 4, July–August 2010 Engineering Notes Five Special Types of Orbits sensing satellites. Lagrangian planetary equations, which give the mean precession rate of the line of node, provide the theoretical Around Mars foundation of sun-synchronous orbits. Boain described basic mechanical characteristics of Earth’s sun-synchronous orbits and ∗ † ‡ provided several design algorithms to satisfy practical mission Xiaodong Liu, Hexi Baoyin, and Xingrui Ma requirements [4]. Several Martian satellites have been placed into Tsinghua University, sun-synchronous orbits, such as MGS [1] and MRO [2]. 100084 Beijing, People’s Republic of China Orbits at the critical inclination can keep eccentricity and argument of perigee invariable on average. For example, the Molniya DOI: 10.2514/1.48706 and Tundra orbits applied such conditions to stop the rotation of argument of perigee. Orlov introduced the concept of the Earth Nomenclature critical inclination [5], and Brouwer eliminated short-period terms based on canonical transformations [6]. Later, Coffey et al. analyzed a = semimajor axis, km the averaged Hamilton system reduced by the Delaunay normal- e = orbital eccentricity ization and provided geometrical interpretation of the critical i = orbital inclination, deg. inclination for Earth’s artificial satellites [7]. Some research has J2 = second-order zonal harmonic regarded orbits at the critical inclination as types of frozen orbits J3 = third-order zonal harmonic [8,9]. J4 = fourth-order zonal harmonic Frozen orbits have always been an important focus of orbit design, J22 = second-degree and -order tesseral harmonic because their average eccentricity and argument of perigee remain M = mean anomaly, deg. -
Aas 12-269 Frozen Orbits for Scientific Missions Using
AAS 12-269 FROZEN ORBITS FOR SCIENTIFIC MISSIONS USING ROTATING TETHERS Hodei Urrutxua,∗ Jes ´usPelaez´ y and Martin Laraz We derive a semi-analytic formulation that permits to study the long-term dynam- ics of fast-rotating inert tethers around planetary satellites. Since space tethers are extensive bodies they generate non-keplerian gravitational forces which depend solely on their mass geometry and attitude, that can be exploited for controlling science orbits. We conclude that rotating tethers modify the geometry of frozen orbits, allowing for lower eccentricity frozen orbits for a wide range of orbital in- clination, where the length of the tether becomes a new parameter that the mission analyst may use to shape frozen orbits to tighter operational constraints. INTRODUCTION Science orbits for missions to planetary satellites have, in general, low altitudes and near-polar inclinations so that the entire surface can be mapped, and the science requirements of the mission can be accomplished.1,2 However, designing such an orbit can be difficult because the dynamical environment of many planetary satellites is highly perturbed due to their proximity to the central planet.3 One such example is the Moon, on which we focus on the current study. High-inclination orbits around the Moon are known to be unstable.4,5,6 However, the onset of instability can be delayed by a proper orbit design, hence maximizing the orbital lifetime.7 In this regard, the so called frozen orbits offer an interesting starting point for the design of science orbits,1,8,9 since all their orbital elements, with the only exception of the mean anomaly and the longitude of the ascending node, remain constant. -
Sun-Synchronous Satellites
Topic: Sun-synchronous Satellites Course: Remote Sensing and GIS (CC-11) M.A. Geography (Sem.-3) By Dr. Md. Nazim Professor, Department of Geography Patna College, Patna University Lecture-3 Concept: Orbits and their Types: Any object that moves around the Earth has an orbit. An orbit is the path that a satellite follows as it revolves round the Earth. The plane in which a satellite always moves is called the orbital plane and the time taken for completing one orbit is called orbital period. Orbit is defined by the following three factors: 1. Shape of the orbit, which can be either circular or elliptical depending upon the eccentricity that gives the shape of the orbit, 2. Altitude of the orbit which remains constant for a circular orbit but changes continuously for an elliptical orbit, and 3. Angle that an orbital plane makes with the equator. Depending upon the angle between the orbital plane and equator, orbits can be categorised into three types - equatorial, inclined and polar orbits. Different orbits serve different purposes. Each has its own advantages and disadvantages. There are several types of orbits: 1. Polar 2. Sunsynchronous and 3. Geosynchronous Field of View (FOV) is the total view angle of the camera, which defines the swath. When a satellite revolves around the Earth, the sensor observes a certain portion of the Earth’s surface. Swath or swath width is the area (strip of land of Earth surface) which a sensor observes during its orbital motion. Swaths vary from one sensor to another but are generally higher for space borne sensors (ranging between tens and hundreds of kilometers wide) in comparison to airborne sensors. -
Asteroid Touring Nanosatellite Fleet
Asteroid Touring Nanosatellite Fleet S Mihkel Pajusalu Postdoctoral fellow Massachusetts Institute of Technology (and Tartu Observatory) [email protected] + Pekka Janhunen, Andris Slavinskis, and the MAT collaboration Bio • 2010 MSc in Physics, University of Tartu, Estonia • 2010-2015 ESTCube-1 team, leader of Electrical Power Subsystem • 2014 PhD in Physics University of Tartu, Estonia • 2015 - 2019 Postdoc at MIT, Seager Group (astrobiology and instrumentation development for the MAT mission) Only 12 asteroids have been visited this far 1 Ceres Image Credit: NASA / 4 253 Mathilde 433 Eros JPL-Caltech / UCLA / Vesta NEAR /NASA NEAR Shoemaker MPS / DLR / IDA / Justin NASA/JPL/JHUAPL Cowart 951 Gaspra 243 Ida and 2867 Šteins 21 Lutetia Dactyl Galileo/NASA Rosetta ESA MPS ESA 2010 MPS for Galileo/NASA / JPL/USGS for OSIRIS Team OSIRIS Team MPS/UPD/LAM/IAA MPS/UPD/LAM/IAA/RSS D/INTA/UPM/DASP/IDA 9969 Braille 5535 Annefrank Deep Space 25143 Itokawa 4179 Toutatis Stardust/JPL/NASA 1/NASA/JPL/USGS Hayabusa/JAXA Chang’e/CNSA Multiple Asteroid Touring (MAT) mission See Slavinskis et al, “Nanospacecraft Fleet for Multi-asteroid Touring with Electric Solar Wind Sails”, IEEE Aerospace conference, 2018 Mission details • The reference mission contains 50 identical CubeSats • Estimated total cost <100 million USD • Each to visit 6 targets on average • 100 km – 1000 km flybys • Total of 300 visits during 3.2 years • Even if 50% are successful, number of visited asteroids would increase by a factor of 10 • First published concept from Finnish Meteorological