Interplanetary Rapid Transit to Mars
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Modelling and the Transit of Venus
Modelling and the transit of Venus Dave Quinn University of Queensland <[email protected]> Ron Berry University of Queensland <[email protected]> Introduction enior secondary mathematics students could justifiably question the rele- Svance of subject matter they are being required to understand. One response to this is to place the learning experience within a context that clearly demonstrates a non-trivial application of the material, and which thereby provides a definite purpose for the mathematical tools under consid- eration. This neatly complements a requirement of mathematics syllabi (for example, Queensland Board of Senior Secondary School Studies, 2001), which are placing increasing emphasis on the ability of students to apply mathematical thinking to the task of modelling real situations. Success in this endeavour requires that a process for developing a mathematical model be taught explicitly (Galbraith & Clatworthy, 1991), and that sufficient opportu- nities are provided to students to engage them in that process so that when they are confronted by an apparently complex situation they have the think- ing and operational skills, as well as the disposition, to enable them to proceed. The modelling process can be seen as an iterative sequence of stages (not ) necessarily distinctly delineated) that convert a physical situation into a math- 1 ( ematical formulation that allows relationships to be defined, variables to be 0 2 l manipulated, and results to be obtained, which can then be interpreted and a n r verified as to their accuracy (Galbraith & Clatworthy, 1991; Mason & Davis, u o J 1991). The process is iterative because often, at this point, limitations, inac- s c i t curacies and/or invalid assumptions are identified which necessitate a m refinement of the model, or perhaps even a reassessment of the question for e h t which we are seeking an answer. -
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 -
Asteroid Retrieval Mission
Where you can put your asteroid Nathan Strange, Damon Landau, and ARRM team NASA/JPL-CalTech © 2014 California Institute of Technology. Government sponsorship acknowledged. Distant Retrograde Orbits Works for Earth, Moon, Mars, Phobos, Deimos etc… very stable orbits Other Lunar Storage Orbit Options • Lagrange Points – Earth-Moon L1/L2 • Unstable; this instability enables many interesting low-energy transfers but vehicles require active station keeping to stay in vicinity of L1/L2 – Earth-Moon L4/L5 • Some orbits in this region is may be stable, but are difficult for MPCV to reach • Lunar Weakly Captured Orbits – These are the transition from high lunar orbits to Lagrange point orbits – They are a new and less well understood class of orbits that could be long term stable and could be easier for the MPCV to reach than DROs – More study is needed to determine if these are good options • Intermittent Capture – Weakly captured Earth orbit, escapes and is then recaptured a year later • Earth Orbit with Lunar Gravity Assists – Many options with Earth-Moon gravity assist tours Backflip Orbits • A backflip orbit is two flybys half a rev apart • Could be done with the Moon, Earth or Mars. Backflip orbit • Lunar backflips are nice plane because they could be used to “catch and release” asteroids • Earth backflips are nice orbits in which to construct things out of asteroids before sending them on to places like Earth- Earth or Moon orbit plane Mars cyclers 4 Example Mars Cyclers Two-Synodic-Period Cycler Three-Synodic-Period Cycler Possibly Ballistic Chen, et al., “Powered Earth-Mars Cycler with Three Synodic-Period Repeat Time,” Journal of Spacecraft and Rockets, Sept.-Oct. -
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. -
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 -
Predictable Patterns in Planetary Transit Timing Variations and Transit Duration Variations Due to Exomoons
Astronomy & Astrophysics manuscript no. ms c ESO 2016 June 21, 2016 Predictable patterns in planetary transit timing variations and transit duration variations due to exomoons René Heller1, Michael Hippke2, Ben Placek3, Daniel Angerhausen4, 5, and Eric Agol6, 7 1 Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany; [email protected] 2 Luiter Straße 21b, 47506 Neukirchen-Vluyn, Germany; [email protected] 3 Center for Science and Technology, Schenectady County Community College, Schenectady, NY 12305, USA; [email protected] 4 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; [email protected] 5 USRA NASA Postdoctoral Program Fellow, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA 6 Astronomy Department, University of Washington, Seattle, WA 98195, USA; [email protected] 7 NASA Astrobiology Institute’s Virtual Planetary Laboratory, Seattle, WA 98195, USA Received 22 March 2016; Accepted 12 April 2016 ABSTRACT We present new ways to identify single and multiple moons around extrasolar planets using planetary transit timing variations (TTVs) and transit duration variations (TDVs). For planets with one moon, measurements from successive transits exhibit a hitherto unde- scribed pattern in the TTV-TDV diagram, originating from the stroboscopic sampling of the planet’s orbit around the planet–moon barycenter. This pattern is fully determined and analytically predictable after three consecutive transits. The more measurements become available, the more the TTV-TDV diagram approaches an ellipse. For planets with multi-moons in orbital mean motion reso- nance (MMR), like the Galilean moon system, the pattern is much more complex and addressed numerically in this report. -
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 -
Low-Excess Speed Triple Cyclers of Venus, Earth, and Mars
AAS 17-577 LOW EXCESS SPEED TRIPLE CYCLERS OF VENUS, EARTH, AND MARS Drew Ryan Jones,∗ Sonia Hernandez,∗ and Mark Jesick∗ Ballistic cycler trajectories which repeatedly encounter Earth and Mars may be in- valuable to a future transportation architecture ferrying humans to and from Mars. Such trajectories which also involve at least one flyby of Venus are computed here for the first time. The so-called triple cyclers are constructed to exhibit low excess speed on Earth-Mars and Mars-Earth transit legs, and thereby reduce the cost of hyperbolic rendezvous. Thousands of previously undocumented two synodic pe- riod Earth-Mars-Venus triple cyclers are discovered. Many solutions are identified with average transit leg excess speed below 5 km/sec, independent of encounter epoch. The energy characteristics are lower than previously documented cyclers not involving Venus, but the repeat periods are generally longer. NOMENCLATURE ∆tH Earth-Mars Hohmann transfer flight time, days δ Hyperbolic flyby turning angle, degrees R;^ S;^ T^ B-plane unit vectors B B-plane vector, km µ Gravitational parameter, km3/sec2 θB B-plane angle between B and T^, degrees rp Periapsis radius, km T Cycler repeat period, days t0 Cycle starting epoch ∗ t0 Earth-Mars Hohmann transfer epoch tf Cycle ending epoch Tsyn Venus-Earth-Mars synodic period, days v1 Hyperbolic excess speed, km/sec INTRODUCTION Trajectories are computed which ballistically and periodically cycle between flybys of Venus, Earth, and Mars. Using only gravity assists, a cycling vehicle returns to the starting body after a flight time commensurate with the celestial bodies’ orbital periods, thereby permitting indefinite repetition. -
Martian Outpost the Challenges of Establishing a Human Settlement on Mars Erik Seedhouse
Martian Outpost The Challenges of Establishing a Human Settlement on Mars Erik Seedhouse Martian Outpost The Challenges of Establishing a Human Settlement on Mars Springer Published in association with ~ '· i €I Praxis Publishing PR i ~ . i •", . ~ Chichester, UK Dr Erik Seedhouse, F.B.I.S., As.M.A. Milton Ontario Canada SPRINGER±PRAXIS BOOKS IN SPACE EXPLORATION SUBJECT ADVISORY EDITOR: John Mason M.B.E., B.Sc., M.Sc., Ph.D. ISBN 978-0-387-98190-1 Springer Berlin Heidelberg New York Springer is a part of Springer Science + Business Media (springer.com) Library of Congress Control Number: 2009921645 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. # Copyright, 2009 Praxis Publishing Ltd. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Jim Wilkie Copy editor: Dr John Mason Typesetting: BookEns Ltd, Royston, Herts., UK Printed in Germany on acid-free paper Contents Preface ..................................................... xiii Acknowledgments................................................xv About the author .............................................. -
Download Paper
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.