Evolution of the Rendezvous-Maneuver Plan for Lunar-Landing Missions
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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 -
The Following Are Edited Excerpts from Two Interviews Conducted with Dr
Interviews with Dr. Wernher von Braun Editor's note: The following are edited excerpts from two interviews conducted with Dr. Wernher von Braun. Interview #1 was conducted on August 25, 1970, by Robert Sherrod while Dr. von Braun was deputy associate administrator for planning at NASA Headquarters. Interview #2 was conducted on November 17, 1971, by Roger Bilstein and John Beltz. These interviews are among those published in Before This Decade is Out: Personal Reflections on the Apollo Program, (SP-4223, 1999) edited by Glen E. Swanson, whick is vailable on-line at http://history.nasa.gov/SP-4223/sp4223.htm on the Web. Interview #1 In the Apollo Spacecraft Chronology, you are quoted as saying "It is true that for a long time we were not in favor of lunar orbit rendezvous. We favored Earth orbit rendezvous." Well, actually even that is not quite correct, because at the outset we just didn't know which route [for Apollo to travel to the Moon] was the most promising. We made an agreement with Houston that we at Marshall would concentrate on the study of Earth orbit rendezvous, but that did not mean we wanted to sell it as our preferred scheme. We weren't ready to vote for it yet; our study was meant to merely identify the problems involved. The agreement also said that Houston would concentrate on studying the lunar rendezvous mode. Only after both groups had done their homework would we compare notes. This agreement was based on common sense. You don't start selling your scheme until you are convinced that it is superior. -
Space Almanac 2007
2007 Space Almanac The US military space operation in facts and figures. Compiled by Tamar A. Mehuron, Associate Editor, and the staff of Air Force Magazine 74 AIR FORCE Magazine / August 2007 Space 0.05g 60,000 miles Geosynchronous Earth Orbit 22,300 miles Hard vacuum 1,000 miles Medium Earth Orbit begins 300 miles 0.95g 100 miles Low Earth Orbit begins 60 miles Astronaut wings awarded 50 miles Limit for ramjet engines 28 miles Limit for turbojet engines 20 miles Stratosphere begins 10 miles Illustration not to scale Artist’s conception by Erik Simonsen AIR FORCE Magazine / August 2007 75 US Military Missions in Space Space Support Space Force Enhancement Space Control Space Force Application Launch of satellites and other Provide satellite communica- Ensure freedom of action in space Provide capabilities for the ap- high-value payloads into space tions, navigation, weather infor- for the US and its allies and, plication of combat operations and operation of those satellites mation, missile warning, com- when directed, deny an adversary in, through, and from space to through a worldwide network of mand and control, and intel- freedom of action in space. influence the course and outcome ground stations. ligence to the warfighter. of conflict. US Space Funding Millions of constant Fiscal 2007 dollars 60,000 50,000 40,000 30,000 20,000 10,000 0 Fiscal Year 59 62 65 68 71 74 77 80 83 86 89 92 95 98 01 04 Fiscal Year NASA DOD Other Total Fiscal Year NASA DOD Other Total 1959 1,841 3,457 240 5,538 1983 13,051 18,601 675 32,327 1960 3,205 3,892 -
Low Earth Orbit Slotting for Space Traffic Management Using Flower
Low Earth Orbit Slotting for Space Traffic Management Using Flower Constellation Theory David Arnas∗, Miles Lifson†, and Richard Linares‡ Massachusetts Institute of Technology, Cambridge, MA, 02139, USA Martín E. Avendaño§ CUD-AGM (Zaragoza), Crtra Huesca s / n, Zaragoza, 50090, Spain This paper proposes the use of Flower Constellation (FC) theory to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and optimize the available space. Specifically, it proposes the use of concentric orbital shells of admissible “slots” with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D Lattice Flower Constellations (2D-LFCs), and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. In particular, capacity is evaluated for various inclinations and other parameters. Next, a rough estimate for the capacity of LEO is generated subject to certain minimum separation and station-keeping assumptions and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management. I. Introduction SpaceX, OneWeb, Telesat and other companies are currently planning mega-constellations for space-based internet connectivity and other applications that would significantly increase the number of on-orbit active satellites across a variety of altitudes [1–5]. As these and other actors seek to make more intensive use of the global space commons, there is growing need to characterize the fundamental limits to the capacity of Low Earth Orbit (LEO), particularly in high-demand orbits and altitudes, and minimize the extent to which use by one space actor hampers use by other actors. -
The Great Game in Space China’S Evolving ASAT Weapons Programs and Their Implications for Future U.S
The Great Game in Space China’s Evolving ASAT Weapons Programs and Their Implications for Future U.S. Strategy Ian Easton The Project 2049 Institute seeks If there is a great power war in this century, it will not begin to guide decision makers toward with the sound of explosions on the ground and in the sky, but a more secure Asia by the rather with the bursting of kinetic energy and the flashing of century’s mid-point. The laser light in the silence of outer space. China is engaged in an anti-satellite (ASAT) weapons drive that has profound organization fills a gap in the implications for future U.S. military strategy in the Pacific. This public policy realm through Chinese ASAT build-up, notable for its assertive testing regime forward-looking, region-specific and unexpectedly rapid development as well as its broad scale, research on alternative security has already triggered a cascade of events in terms of U.S. and policy solutions. Its strategic recalibration and weapons acquisition plans. The interdisciplinary approach draws notion that the U.S. could be caught off-guard in a “space on rigorous analysis of Pearl Harbor” and quickly reduced from an information-age socioeconomic, governance, military juggernaut into a disadvantaged industrial-age power in any conflict with China is being taken very seriously military, environmental, by U.S. war planners. As a result, while China’s already technological and political impressive ASAT program continues to mature and expand, trends, and input from key the U.S. is evolving its own counter-ASAT deterrent as well as players in the region, with an eye its next generation space technology to meet the challenge, toward educating the public and and this is leading to a “great game” style competition in informing policy debate. -
America's Greatest Projects and Their Engineers - VII
America's Greatest Projects and Their Engineers - VII Course No: B05-005 Credit: 5 PDH Dominic Perrotta, P.E. Continuing Education and Development, Inc. 22 Stonewall Court Woodcliff Lake, NJ 076 77 P: (877) 322-5800 [email protected] America’s Greatest Projects & Their Engineers-Vol. VII The Apollo Project-Part 1 Preparing for Space Travel to the Moon Table of Contents I. Tragedy and Death Before the First Apollo Flight A. The Three Lives that Were Lost B. Investigation, Findings & Recommendations II. Beginning of the Man on the Moon Concept A. Plans to Land on the Moon B. Design Considerations and Decisions 1. Rockets – Launch Vehicles 2. Command/Service Module 3. Lunar Module III. NASA’s Objectives A. Unmanned Missions B. Manned Missions IV. Early Missions V. Apollo 7 Ready – First Manned Apollo Mission VI. Apollo 8 - Orbiting the Moon 1 I. Tragedy and Death Before the First Apollo Flight Everything seemed to be going well for the Apollo Project, the third in a series of space projects by the United States intended to place an American astronaut on the Moon before the end of the 1960’s decade. Apollo 1, known at that time as AS (Apollo Saturn)-204 would be the first manned spaceflight of the Apollo program, and would launch a few months after the flight of Gemini 12, which had occurred on 11 November 1966. Although Gemini 12 was a short duration flight, Pilot Buzz Aldrin had performed three extensive EVA’s (Extra Vehicular Activities), proving that Astronauts could work for long periods of time outside the spacecraft. -
Intelligence for the Space Race
APPROVED fOR RELEASE 1994 CIA HISTORICAL REVIEVI PROGRAM /F§£~r9r TITLE: Intelligence For The Space Race -'\:~--<::~~~~:~1~~rv;~,*: -'· ;'. - ~~~-- ._ ·:·.1t-:~;'\:>,1M~?J%$' ,'~/;.- · >~?!~i'4:r~:-.:-:~~~t~~*i-:·;~'f-:t.;: ·-~::~:~:~?:J-::' :~ ."~.?t~f;:'-'fH(,: :;~;~{~_Vi;~~r~·~~:.-~:~~~~~~,}~';tf!f'tu~i:t:,~:.;;, AUTHOR: Albert D. Wheelon and Sidney N. Graybeal .._ ..,.··:.,.'. VOLUME: 5 ISSUE: Fall YEAR: 1961 .. -;·' All statements of fact, opinion or analysis expressed in Studies in Intelligence are those of the authors. They do not necessarily reflect official positions or views of the Central Intelligence Agency or any other US Government entity, past or present. Nothing in the contents should be construed as asserting or implying US Government endorsement of an article's factual statements and interpretations. ·. r Prospects and methodology for supporting a symbolic Olympian technological duel. INTELLIGENCE FOR THE SPACE RACE Albert D. Wbeelon and . Sidney N. Gra,1beal i ~~·.:?;~~~{ .~s~:~~~~::>.~~ ~~~t-~~~0i~~::~ .... ::.~.~if;~~-·. _·._ .;.:f~~?;;~?t~{;~Jilif~~:r::~lff:! · ,;~:,;·~~~(~i~~rMJT%*!t::;:r~~1~~~~~f,~"t'*~~~~jl;t19:~?i~~ . · ~;,~~·}§.~~~: ' A college football coach, spurred by &;-·Vigilant body of alumni to maintain a winning team, is expected to devote a great deal. of energy to what in a more deadly competition .. ' ·- . ;r • . ' .• ,.. ,.•.. , '· ·•• ·-\- ~ . ,. would be ca.ned iritelligence activity. ·He must scout the oppo- sition before game time and plan his own defense and offense in the· light of what he learns. During a game he must diag nose plays as they occur in order to adjust his team's tactics and give it flexible direction in action. After the game he should be prepared with an appropriate analysis of what hap pened, both in order that his team may benefit from seeing its experience in clear focus and in order to placate or mod erate the Monday-morning quarterbacks. -
COMPARISON of DIRECT and INDIRECT ASCENT MODES for the 1966-1967 MARS OPPORTUNITY with an ATLAS-CENTAUR LAUNCH VEHICLE by Tim J
NASA TECHNICAL NOTE NASA TN D-2739 ._e-- e# / o* cr) h n7 z c 4 r/l 4 z COMPARISON OF DIRECT AND INDIRECT ASCENT MODES FOR THE 1966-1967 MARS OPPORTUNITY WITH AN ATLAS-CENTAUR LAUNCH VEHICLE by Tim J. Kreiter Lewis Researcb Center Cleveland, Ohio NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. 0 MARCH 1965 Ii 1 I TECH LIBRARY KAFB, "I I111111 11111 11111 Ill11 IIIII 11111 Ill11 1111 Ill 0079730 NASA TN D-2739 COMPARISON OF DIRECT AND INDIRECT ASCENT MODES FOR THE 1966-1967 MARS OPPORTUNITY WITH AN ATLAS-CENTAUR LAUNCH VEHICLE By Tim J. Kreiter Lewis Research Center Cleveland, Ohio NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by the Office of Technical Services, Department of Commerce, . Washington, D.C. 20230 -- Price $1.00 COMPARISON OF DIRECT AND INDIRECT ASCENT MODES FOR THE 1966-1967 MARS OPPORTUNITY WITH AN ATLAS-CENTAUR LAUNCH VEHICLE by Tim J. Kreiter Lewis Research Center 1 SUMMARY A study has been made to determine the feasibility of using a direct ascent Atlas- Centaur booster to launch a flyby spacecraft to Mars during the 1966-1967 period. In order to evaluate the effectiveness of the direct ascent launching mode, daily launch windows and payloads were computed for both direct and indirect ascent trajectories and the two modes were compared on the basis of total number of launch opportunities and payload capability. In this study, type I interplanetary transfer conics (heliocentric angles less than 180') were investigated over a three-month firing interval. A launch azimuth envelope of 90' to 114' was assumed, and a minimum daily launch window requirement of 60 min- utes was imposed. -
Closed-Form Optimal Impulsive Control of Spacecraft Relative Motion Using Reachable Set Theory
Closed-Form Optimal Impulsive Control of Spacecraft Relative Motion Using Reachable Set Theory Michelle Chernick ∗ and Simone D’Amico † Stanford University, Stanford, California, 94305 This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta-v cost of impulsive control actions while achieving a desired state in fixed time. The problem is posed in relative orbit element (ROE) space, which yields insight into relative motion geometry and allows for the straightforward inclusion of perturbations in linear time- variant form. Reachable set theory is used to translate the cost-minimization problem into a geometric path-planning problem and formulate the reachable delta-v minimum, a new metric to assess optimality and quantify reachability of a maneuver scheme. Next, this paper presents a methodology to compute maneuver schemes that meet this new optimality criteria and achieve a prescribed reconfiguration. Though the methodology is applicable to any linear time-variant system, this paper leverages a state representation in ROE to derive new globally optimal maneuver schemes in orbits of arbitrary eccentricity. The methodology is also used to generate quantifiably sub-optimal solutions when the optimal solutions are unreachable. Further, this paper determines the mathematical impact of uncertainties on achieving the desired end state and provides a geometric visualization of those effects on the reachable set. The proposed algorithms are tested in realistic reconfiguration scenarios and validated in a high-fidelity simulation environment. I. Introduction istributed space systems enable advanced missions in fields such as astronomy and astrophysics, planetary science, Dand space infrastructure by employing the collective usage of two or more cooperative spacecraft. -
Lunar Orbiting Cubesat Sensor Transport System Mike Seibert, Alejandro Levi, and Mitchell Paradis Graduate Students, Colorado School of Mines
Lunar Orbiting CubeSat Sensor Transport System Mike Seibert, Alejandro Levi, and Mitchell Paradis Graduate Students, Colorado School of Mines Concept Origin Notional Mission Evaluated Carrier Spacecraft Conceptual Design The 2018 Lunar Polar Prospecting (LPP) Workshop Objective: • Structure: Based on EELV Secondary generated a series of recommendations for Deploy a constellation of 6 sensor spacecraft in single Payload Adapter (ESPA) Grande. prospecting of lunar water. Recommendation 3 was polar low lunar orbit plane. • Propulsion: Monoprop system with 2.5 km/s for swarms CubeSats overflying polar regions at delta-V capability. altitudes below 20 km. Recommendation 3 also Cruise Phase: Includes 179 m/s for 110 days of recommended “a swarm of hundreds of low cost LOCuST is released from the launch vehicle in a GTO. orbit eccentricity control impactors instrumented for volatile detection and A series of perigee maneuvers using carrier spacecraft • Earth Telecom: Optical derived from LADEE or quantification.” [1] propulsion are used to raise apogee to lunar distance. IRIS Version 2.0 radio • Relay Telecom: IRIS Version 2.0 (multiple if all RF) The graduate student team developed both mission Lunar Orbit Insertion/Optimization • Thermal control:Accounts for challenges of low and vehicle designs that address the LPP Lunar orbit capture into an initial 200km altitude orbit over lunar day side. recommendation during the Space Resources Design I polar orbit. Orbit is lowered to 10km altitude Main Propulsion course at the Colorado School of Mines in Spring perilune, 100km apolune. All capture and initial 2019. CubeSat optimization maneuvers use carrier spacecraft Deployers propulsion. The CubeSat swarm concept was interpreted to mean a constellation of small short mission duration Deployments spacecraft with sensors optimized for localizing After each deployment orbit phasing maneuvers to Solar Array surface water ice. -
The Apollo Lunar Orbit Rendezvous Architecture Decision Revisited
Student Session II Paper No. GT-SSEC.E.2 The Apollo Lunar Orbit Rendezvous Architecture Decision Revisited David M. Reeves1 Georgia Institute of Technology National Institute of Aerospace, Hampton, VA, 23666 Michael D. Scher2 University of Maryland National Institute of Aerospace, Hampton, VA, 23666 Dr. Alan W. Wilhite3 Georgia Institute of Technology National Institute of Aerospace, Hampton, VA, 23666 Dr. Douglas O. Stanley4 Georgia Institute of Technology National Institute of Aerospace, Hampton, VA, ABSTRACT The 1962 Apollo architecture mode decision process was revisited with modern analysis and systems engineer tools to determine driving selection criteria and technology/operational mode design decisions that may be used for NASA’s current Space Exploration program. Results of the study agreed with the Apollo selection of the Lunar Orbit Rendezvous mode based on the technology maturity and politics in 1962. Using today’s greater emphasis on human safety and improvements in technology and design maturity, a slight edge may be given to the direct lunar mode over lunar orbit rendezvous. Also, the NOVA direct mode and Earth orbit rendezvous mode are not competitive based any selection criteria. Finally, reliability and development, operations, and production costs are major drivers in today’s decision process. 1Graduate Research Assistant, Georgia Institute of Technology, 100 Exploration Way, AIAA Student Member. 2 Graduate Research Assistant, University of Maryland, 100 Exploration Way, AIAA Student Member. 3 Langley Professor, Georgia Institute of Technology, 100 Exploration Way, AIAA Associate Fellow. 4 Langley Professor, Georgia Institute of Technology, 100 Exploration Way, AIAA Member. Page 1 of 12 Pages Student Session II Paper No. -
Simulation Framework for Orbit Propagation and Space Trajectory Visualization
Simulation Framework for Orbit Propagation and Space Trajectory Visualization 1 Abolfazl Shirazi Basque Center for Applied Mathematics BCAM, Bilbao, 48009, Spain University of the Basque Country UPV/EHU, Donostia, 20018, Spain 2 Josu Ceberio Intelligent Systems Group, University of the Basque Country UPV/EHU, Donostia, 20018, Spain 3 Jose A. Lozano Basque Center for Applied Mathematics BCAM, Bilbao, 48009, Spain University of the Basque Country UPV/EHU, Donostia, 20018, Spain Abstract In this paper, an interactive tool for simulation of satellites dynamics and autonomous spacecraft guidance is presented. Different geopotential models for orbit propagation of Earth-orbiting satellites are provided, which consider Earth’s gravitational field with var- ious accuracies. The presented software is a 3D visualization platform for space orbit simulation with analytical capabilities through various modules. Taking advantage of a graphical user interface, it can evaluate, analyze and illustrate the motion of satellite based on different orbit propagation schemes. Several cases of satellites and autonomous space- craft in the space rendezvous mission are simulated regarding different propagation models to demonstrate the performance of the application in space mission analysis, ground track visualization and trajectory optimization. Results are validated by comparing with other state-of-the-art tools, such as AGI System Toolkit (STK). Keywords: Orbit Simulation, Software Development, Visualization, Modeling, Spacecraft Dynamics 1. Introduction Modeling and simulation of autonomous spacecraft have made momentous strides in recent years, and the space industry, and other aerospace professions are on the verge of being able to use computing power. The aim of this usage is to simulate reality for all kinds of applications in space engineering such as autonomy of nanosatellites [1], flight simulation [2], space object registration [3], and orbit propagation [4].