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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 -
Call for M5 Missions
ESA UNCLASSIFIED - For Official Use M5 Call - Technical Annex Prepared by SCI-F Reference ESA-SCI-F-ESTEC-TN-2016-002 Issue 1 Revision 0 Date of Issue 25/04/2016 Status Issued Document Type Distribution ESA UNCLASSIFIED - For Official Use Table of contents: 1 Introduction .......................................................................................................................... 3 1.1 Scope of document ................................................................................................................................................................ 3 1.2 Reference documents .......................................................................................................................................................... 3 1.3 List of acronyms ..................................................................................................................................................................... 3 2 General Guidelines ................................................................................................................ 6 3 Analysis of some potential mission profiles ........................................................................... 7 3.1 Introduction ............................................................................................................................................................................. 7 3.2 Current European launchers ........................................................................................................................................... -
Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite
46th AIAA Aerospace Sciences Meeting and Exhibit AIAA 2008-1131 7 – 10 January 20006, Reno, Nevada Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite Stephen A. Whitmore* and Tyson K. Smith† Utah State University, Logan, UT, 84322-4130 A trade study investigating the economics, mass budget, and concept of operations for delivery of a small technology-demonstration satellite to a medium-altitude earth orbit is presented. The mission requires payload deployment at a 19,000 km orbit altitude and an inclination of 55o. Because the payload is a technology demonstrator and not part of an operational mission, launch and deployment costs are a paramount consideration. The payload includes classified technologies; consequently a USA licensed launch system is mandated. A preliminary trade analysis is performed where all available options for FAA-licensed US launch systems are considered. The preliminary trade study selects the Orbital Sciences Minotaur V launch vehicle, derived from the decommissioned Peacekeeper missile system, as the most favorable option for payload delivery. To meet mission objectives the Minotaur V configuration is modified, replacing the baseline 5th stage ATK-37FM motor with the significantly smaller ATK Star 27. The proposed design change enables payload delivery to the required orbit without using a 6th stage kick motor. End-to-end mass budgets are calculated, and a concept of operations is presented. Monte-Carlo simulations are used to characterize the expected accuracy of the final orbit. -
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. -
Design of the Trajectory of a Tether Mission to Saturn
DOI: 10.13009/EUCASS2019-510 8TH EUROPEAN CONFERENCE FOR AERONAUTICS AND AEROSPACE SCIENCES (EUCASS) DOI: Design of the trajectory of a tether mission to Saturn ⋆ Riccardo Calaon , Elena Fantino§, Roberto Flores ‡ and Jesús Peláez† ⋆Dept. of Industrial Engineering, University of Padova Via Gradenigio G/a -35131- Padova, Italy §Dept. of Aerospace Engineering, Khalifa University Abu Dhabi, Unites Arab Emirates ‡Inter. Center for Numerical Methods in Engineering Campus Norte UPC, Gran Capitán s/n, Barcelona, Spain †Space Dynamics Group, UPM School of Aeronautical and Space Engineering, Pz. Cardenal Cisneros 3, Madrid, Spain [email protected], [email protected], rfl[email protected], [email protected] †Corresponding author Abstract This paper faces the design of the trajectory of a tether mission to Saturn. To reduce the hyperbolic excess velocity at arrival to the planet, a gravity assist at Jupiter is included. The Earth-to-Jupiter portion of the transfer is unpropelled. The Jupiter-to-Saturn trajectory has two parts: a first coasting arc followed by a second arc where a low thrust engine is switched on. An optimization process provides the law of thrust control that minimizes the velocity relative to Saturn at arrival, thus facilitating the tethered orbit insertion. 1. Introduction The outer planets are of particular interest in terms of what they can reveal about the origin and evolution of our solar system. They are also local analogues for the many extra-solar planets that have been detected over the past twenty years. The study of these planets furthers our comprehension of our neighbourhood and provides the foundations to understand distant planetary systems. -
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. -
Utilizing Deep Reinforcement Learning to Effect Autonomous Orbit Transfers and Intercepts Via Electromagnetic Propulsion
Problem Utilizing Deep Reinforcement Learning to Effect Autonomous Results The growth in space-capable entities has caused a rapid rise in Orbit Transfers and Intercepts via Electromagnetic Propulsion ➢ Analysis the number of derelict satellites and space debris in orbit Gabriel Sutherland ([email protected]), Oregon State University, Corvallis, OR, USA ❖ The data suggests spacecraft highly capable of around Earth, which pose a significant navigation hazard. Frank Soboczenski ([email protected]), King’s College London, London, UK neutralizing/capturing small to intermediate debris Athanasios Vlontzos ([email protected]), Imperial College London, London, UK ❖ In simulations, spacecraft was able to capture and/or Objectives neutralize debris ranging in mass from 1g to 100g ❖ Satellites suffered damage in some Develop a system that is capable of autonomously neutralizing simulations multiple pieces of space debris in various orbits. Software & Simulations ❖ Simulations show that damaged segments of satellite were vaporized, which means Background that no additional debris was added to orbit ➢ Dangerous amounts of space debris in orbit, estimates vary ❖ Neural Network based on Deep Deterministic Policy ➢20,000+ tracked objects larger Gradient (DDPG) effective at low-thrust orbit transfers in than 10 cm diameter 2D Hohmann transfer problem ➢Est 500,000 objects larger ❖ Using ASTOS simulation software, mission-representative than 1 cm in diameter model of spacecraft and experimental propulsion system ➢Est 100 million objects ❖ Interfaced with DRL to train the Neural smaller than 1cm in diameter ➢ Orbital speeds of these objects Network with realistic data vary from 100+ kph to 28,100 kph ➢ Future Studies ➢ Spacecraft collisions due to space ❖ Train DDPG for 3 dimensional orbit transfer problems debris have been sparse so far Tracked spacecraft in Earth orbit. -
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 -
VASIMR VX-200 Performance and Near-Term SEP Capability for Unmanned Mars Flight
VASIMR VX-200 Performance and Near-term SEP Capability for Unmanned Mars Flight Future In-Space Operations Seminar January 19, 2011 presented by Tim Glover Director of Development [email protected] Ad Astra Rocket Company www.adastrarocket.com 1 Ad Astra Rocket Company Notes and Acronyms Notes: - solar array power values are for 1 AU - a number of publications on VASIMR R&D are available on the company’s website: http://www.adastrarocket.com Acronyms: SEP solar electric propulsion NTR nuclear thermal rocket VASIMR Variable Specific Impulse Magnetoplasma Rocket TMI Trans-Mars Insertion MOI Mars Orbit Insertion SOI sphere of influence IMLEO initial mass in low Earth orbit 2 Ad Astra Rocket Company Outline 1. VASIMR Prototype Performance 2. Simplified Earth‐Mars Trajectories 3. Chemical and NTR Hohmann Transfers 4. SEP: Initial Mass‐to‐Power Ratio and Payload Fraction 5. Near‐term SEP Mars Capabilities 6. Backup slides: • Propellant and transit time variation for actual orbits of Earth and Mars •Atlas V 551 performance curve 3 Ad Astra Rocket Company My Background • B.S., Physics, New Mexico State U. • M.S., Aerospace Engineering (Orbital Mechanics), UT-Austin • M.S., Physics, University of Pittsburgh • five years teaching high school physics, Ethical Culture Schools, New York • Ph.D., Applied Physics, Rice University, 2002 − thesis research at Johnson Space Center: designed and built plasma diagnostics to measure exhaust velocity in early VASIMR prototypes • Research Scientist, MEI Technologies 2003-2005 − continued experimental work on VASIMR up to 50 kW • Director of Development, Ad Astra Rocket Company 2005 – present − business development, external relations 4 Ad Astra Rocket Company VASIMR Operating Principles Superconducting Magnets typical path of an ion Helicon coupler (30 kW) through the rocket Ion cyclotron (170 kW) coupler i gas cold accelerated plasma plasma POWER 1. -
Magnetoshell Aerocapture: Advances Toward Concept Feasibility
Magnetoshell Aerocapture: Advances Toward Concept Feasibility Charles L. Kelly A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics & Astronautics University of Washington 2018 Committee: Uri Shumlak, Chair Justin Little Program Authorized to Offer Degree: Aeronautics & Astronautics c Copyright 2018 Charles L. Kelly University of Washington Abstract Magnetoshell Aerocapture: Advances Toward Concept Feasibility Charles L. Kelly Chair of the Supervisory Committee: Professor Uri Shumlak Aeronautics & Astronautics Magnetoshell Aerocapture (MAC) is a novel technology that proposes to use drag on a dipole plasma in planetary atmospheres as an orbit insertion technique. It aims to augment the benefits of traditional aerocapture by trapping particles over a much larger area than physical structures can reach. This enables aerocapture at higher altitudes, greatly reducing the heat load and dynamic pressure on spacecraft surfaces. The technology is in its early stages of development, and has yet to demonstrate feasibility in an orbit-representative envi- ronment. The lack of a proof-of-concept stems mainly from the unavailability of large-scale, high-velocity test facilities that can accurately simulate the aerocapture environment. In this thesis, several avenues are identified that can bring MAC closer to a successful demonstration of concept feasibility. A custom orbit code that dynamically couples magnetoshell physics with trajectory prop- agation is developed and benchmarked. The code is used to simulate MAC maneuvers for a 60 ton payload at Mars and a 1 ton payload at Neptune, both proposed NASA mis- sions that are not possible with modern flight-ready technology. In both simulations, MAC successfully completes the maneuver and is shown to produce low dynamic pressures and continuously-variable drag characteristics. -
Go, No-Go for Apollo Based on Orbital Life Time
https://ntrs.nasa.gov/search.jsp?R=19660014325 2020-03-24T02:45:56+00:00Z I L GO, NO-GO FOR APOLLO BASED ON ORBITAL LIFE TIME I hi 01 GPO PRICE $ Q N66(ACCESSION -2361 NUMBER1 4 ITHRU) Pf - CFSTI PRICE(S) $ > /7 (CODE) IPAGES) 'I 2 < -55494 (CATEGORY) f' (NASA CR OR rwx OR AD NUMBER) Hard copy (HC) /# d-a I Microfiche (M F) I By ff653 Julv65 F. 0. VONBUN NOVEMBER 1965 t GODDARD SPACE FLIGHT CENTER GREENBELT, MARYLAND ABSTRACT A simple expression for the go, no-go criterion is derived in analytical form. This provides a better understanding of the prob- lems involved which is lacking when large computer programs are used. A comparison between "slide rule" results and computer re- sults is indicated on Figure 2. An example is given using a 185 km near circular parking or- bit. It is shown that a 3a speed error of 6 m/s and a 3c~flight path angle error of 4.5 mrad result in a 3c~perigee error of 30 km which is tolerable when a 5 day orbital life time of the Apollo (SIVB + Service + Command Module) is required. iii CONTENTS Page INTRODUCTION ...................................... 1 I. VARLATIONAL EQUATION FOR THE PERIGEE HEIGHT h,. 1 11. THE ERROR IN THE ORBITAL PERIGEE HEIGHT ah,. 5 III. CRITERION FOR GO, NO-GO IN SIMPLE FORM . 5 REFERENCES ....................................... 10 LIST OF ILLUSTRATIONS Figure Page 1 Orbital Insertion Geometry . 2 2 Perigee Error for Apollo Parking Orbits (e 0, h, = 185 km) . 6 3 Height of the Apollo Parking Orbit After Insertion .