Section 9 Orbit Data - Launch Trajectory --~'- Section 9 Launch Trajectory
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AAS 13-250 Hohmann Spiral Transfer with Inclination Change Performed
AAS 13-250 Hohmann Spiral Transfer With Inclination Change Performed By Low-Thrust System Steven Owens1 and Malcolm Macdonald2 This paper investigates the Hohmann Spiral Transfer (HST), an orbit transfer method previously developed by the authors incorporating both high and low- thrust propulsion systems, using the low-thrust system to perform an inclination change as well as orbit transfer. The HST is similar to the bi-elliptic transfer as the high-thrust system is first used to propel the spacecraft beyond the target where it is used again to circularize at an intermediate orbit. The low-thrust system is then activated and, while maintaining this orbit altitude, used to change the orbit inclination to suit the mission specification. The low-thrust system is then used again to reduce the spacecraft altitude by spiraling in-toward the target orbit. An analytical analysis of the HST utilizing the low-thrust system for the inclination change is performed which allows a critical specific impulse ratio to be derived determining the point at which the HST consumes the same amount of fuel as the Hohmann transfer. A critical ratio is found for both a circular and elliptical initial orbit. These equations are validated by a numerical approach before being compared to the HST utilizing the high-thrust system to perform the inclination change. An additional critical ratio comparing the HST utilizing the low-thrust system for the inclination change with its high-thrust counterpart is derived and by using these three critical ratios together, it can be determined when each transfer offers the lowest fuel mass consumption. -
Low-Energy Lunar Trajectory Design
LOW-ENERGY LUNAR TRAJECTORY DESIGN Jeffrey S. Parker and Rodney L. Anderson Jet Propulsion Laboratory Pasadena, California July 2013 ii DEEP SPACE COMMUNICATIONS AND NAVIGATION SERIES Issued by the Deep Space Communications and Navigation Systems Center of Excellence Jet Propulsion Laboratory California Institute of Technology Joseph H. Yuen, Editor-in-Chief Published Titles in this Series Radiometric Tracking Techniques for Deep-Space Navigation Catherine L. Thornton and James S. Border Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation Theodore D. Moyer Bandwidth-Efficient Digital Modulation with Application to Deep-Space Communication Marvin K. Simon Large Antennas of the Deep Space Network William A. Imbriale Antenna Arraying Techniques in the Deep Space Network David H. Rogstad, Alexander Mileant, and Timothy T. Pham Radio Occultations Using Earth Satellites: A Wave Theory Treatment William G. Melbourne Deep Space Optical Communications Hamid Hemmati, Editor Spaceborne Antennas for Planetary Exploration William A. Imbriale, Editor Autonomous Software-Defined Radio Receivers for Deep Space Applications Jon Hamkins and Marvin K. Simon, Editors Low-Noise Systems in the Deep Space Network Macgregor S. Reid, Editor Coupled-Oscillator Based Active-Array Antennas Ronald J. Pogorzelski and Apostolos Georgiadis Low-Energy Lunar Trajectory Design Jeffrey S. Parker and Rodney L. Anderson LOW-ENERGY LUNAR TRAJECTORY DESIGN Jeffrey S. Parker and Rodney L. Anderson Jet Propulsion Laboratory Pasadena, California July 2013 iv Low-Energy Lunar Trajectory Design July 2013 Jeffrey Parker: I dedicate the majority of this book to my wife Jen, my best friend and greatest support throughout the development of this book and always. -
Appendix a Orbits
Appendix A Orbits As discussed in the Introduction, a good ¯rst approximation for satellite motion is obtained by assuming the spacecraft is a point mass or spherical body moving in the gravitational ¯eld of a spherical planet. This leads to the classical two-body problem. Since we use the term body to refer to a spacecraft of ¯nite size (as in rigid body), it may be more appropriate to call this the two-particle problem, but I will use the term two-body problem in its classical sense. The basic elements of orbital dynamics are captured in Kepler's three laws which he published in the 17th century. His laws were for the orbital motion of the planets about the Sun, but are also applicable to the motion of satellites about planets. The three laws are: 1. The orbit of each planet is an ellipse with the Sun at one focus. 2. The line joining the planet to the Sun sweeps out equal areas in equal times. 3. The square of the period of a planet is proportional to the cube of its mean distance to the sun. The ¯rst law applies to most spacecraft, but it is also possible for spacecraft to travel in parabolic and hyperbolic orbits, in which case the period is in¯nite and the 3rd law does not apply. However, the 2nd law applies to all two-body motion. Newton's 2nd law and his law of universal gravitation provide the tools for generalizing Kepler's laws to non-elliptical orbits, as well as for proving Kepler's laws. -
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 -
Ionizing Feedback from Massive Stars in Massive Clusters III: Disruption of Partially Unbound Clouds 3
Mon. Not. R. Astron. Soc. 000, 1–14 (2006) Printed 30 August 2021 (MN LATEX style file v2.2) Ionizing feedback from massive stars in massive clusters III: Disruption of partially unbound clouds J. E. Dale1⋆, B. Ercolano1, I. A. Bonnell2 1Excellence Cluster ‘Universe’, Boltzmannstr. 2, 85748 Garching, Germany. 2Department of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS 30 August 2021 ABSTRACT We extend our previous SPH parameter study of the effects of photoionization from O–stars on star–forming clouds to include initially unbound clouds. We generate a set 4 6 of model clouds in the mass range 10 -10 M⊙ with initial virial ratios Ekin/Epot=2.3, allow them to form stars, and study the impact of the photoionizing radiation pro- duced by the massive stars. We find that, on the 3Myr timescale before supernovae are expected to begin detonating, the fractions of mass expelled by ionizing feedback is a very strong function of the cloud escape velocities. High–mass clouds are largely unaf- fected dynamically, while lower–mass clouds have large fractions of their gas reserves expelled on this timescale. However, the fractions of stellar mass unbound are modest and significant portions of the unbound stars are so only because the clouds themselves are initially partially unbound. We find that ionization is much more able to create well–cleared bubbles in the unbound clouds, owing to their intrinsic expansion, but that the presence of such bubbles does not necessarily indicate that a given cloud has been strongly influenced by feedback. -
Optimisation of Propellant Consumption for Power Limited Rockets
Delft University of Technology Faculty Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics Optimisation of Propellant Consumption for Power Limited Rockets. What Role do Power Limited Rockets have in Future Spaceflight Missions? (Dutch title: Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten. De rol van deze raketten in toekomstige ruimtevlucht missies. ) A thesis submitted to the Delft Institute of Applied Mathematics as part to obtain the degree of BACHELOR OF SCIENCE in APPLIED MATHEMATICS by NATHALIE OUDHOF Delft, the Netherlands December 2017 Copyright c 2017 by Nathalie Oudhof. All rights reserved. BSc thesis APPLIED MATHEMATICS \ Optimisation of Propellant Consumption for Power Limited Rockets What Role do Power Limite Rockets have in Future Spaceflight Missions?" (Dutch title: \Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten De rol van deze raketten in toekomstige ruimtevlucht missies.)" NATHALIE OUDHOF Delft University of Technology Supervisor Dr. P.M. Visser Other members of the committee Dr.ir. W.G.M. Groenevelt Drs. E.M. van Elderen 21 December, 2017 Delft Abstract In this thesis we look at the most cost-effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the Hohmann Transfer Orbit, will be explained. Using Optimal Control Theory, the optimal trajectory for power limited rockets can be found. Three trajectories will be discussed: Low Earth Orbit to Geostationary Earth Orbit, Earth to Mars and Earth to Saturn. After this we compare the propellant use of the thrust limited rockets for these trajectories with the power limited rockets. -
An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies
2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies The National Academies—comprising the National Academy of Sciences, the National Academy of Engineering, the Institute of Medicine, and the National Research Council—work together to enlist the nation’s top scientists, engineers, health professionals, and other experts to study specific issues in science, technology, and medicine that underlie many questions of national importance. The results of their deliberations have inspired some of the nation’s most significant and lasting efforts to improve the health, education, and welfare of the United States and have provided independent advice on issues that affect people’s lives worldwide. To learn more about the Academies’ activities, check the website at www.nationalacademies.org. Copyright 2011 by the National Academy of Sciences. All rights reserved. Printed in the United States of America This study was supported by Contract NNX08AN97G between the National Academy of Sciences and the National Aeronautics and Space Administration, Contract AST-0743899 between the National Academy of Sciences and the National Science Foundation, and Contract DE-FG02-08ER41542 between the National Academy of Sciences and the U.S. Department of Energy. Support for this study was also provided by the Vesto Slipher Fund. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the agencies that provided support for the project. 2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics Committee for a Decadal Survey of Astronomy and Astrophysics ROGER D. -
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. -
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 . -
Interplanetary Trajectories in STK in a Few Hundred Easy Steps*
Interplanetary Trajectories in STK in a Few Hundred Easy Steps* (*and to think that last year’s students thought some guidance would be helpful!) Satellite ToolKit Interplanetary Tutorial STK Version 9 INITIAL SETUP 1) Open STK. Choose the “Create a New Scenario” button. 2) Name your scenario and, if you would like, enter a description for it. The scenario time is not too critical – it will be updated automatically as we add segments to our mission. 3) STK will give you the opportunity to insert a satellite. (If it does not, or you would like to add another satellite later, you can click on the Insert menu at the top and choose New…) The Orbit Wizard is an easy way to add satellites, but we will choose Define Properties instead. We choose Define Properties directly because we want to use a maneuver-based tool called the Astrogator, which will undo any initial orbit set using the Orbit Wizard. Make sure Satellite is selected in the left pane of the Insert window, then choose Define Properties in the right-hand pane and click the Insert…button. 4) The Properties window for the Satellite appears. You can access this window later by right-clicking or double-clicking on the satellite’s name in the Object Browser (the left side of the STK window). When you open the Properties window, it will default to the Basic Orbit screen, which happens to be where we want to be. The Basic Orbit screen allows you to choose what kind of numerical propagator STK should use to move the satellite. -
Positional Astronomy Coordinate Systems
Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. -
Spacex Rocket Data Satisfies Elementary Hohmann Transfer Formula E-Mail: [email protected] and [email protected]
IOP Physics Education Phys. Educ. 55 P A P ER Phys. Educ. 55 (2020) 025011 (9pp) iopscience.org/ped 2020 SpaceX rocket data satisfies © 2020 IOP Publishing Ltd elementary Hohmann transfer PHEDA7 formula 025011 Michael J Ruiz and James Perkins M J Ruiz and J Perkins Department of Physics and Astronomy, University of North Carolina at Asheville, Asheville, NC 28804, United States of America SpaceX rocket data satisfies elementary Hohmann transfer formula E-mail: [email protected] and [email protected] Printed in the UK Abstract The private company SpaceX regularly launches satellites into geostationary PED orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper 10.1088/1361-6552/ab5f4c this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit around the Earth to enter a Hohmann transfer orbit, an elliptical orbit on which the spacecraft reaches 1361-6552 a high altitude. A simple derivation is given for the Hohmann transfer velocity boost that introductory students can derive on their own with a little teacher guidance. They can then use the SpaceX telemetry data to verify the Published theoretical results, finding the discrepancy between observation and theory to be 3% or less. The students will love the rocket videos as the launches and 3 transfer burns are very exciting to watch. 2 Introduction Complex 39A at the NASA Kennedy Space Center in Cape Canaveral, Florida. This launch SpaceX is a company that ‘designs, manufactures and launches advanced rockets and spacecraft.