Pegasus: a Geosynchronous Launch Profile*
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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 -
NTI Day 9 Astronomy Michael Feeback Go To: Teachastronomy
NTI Day 9 Astronomy Michael Feeback Go to: teachastronomy.com textbook (chapter layout) Chapter 3 The Copernican Revolution Orbits Read the article and answer the following questions. Orbits You can use Newton's laws to calculate the speed that an object must reach to go into a circular orbit around a planet. The answer depends only on the mass of the planet and the distance from the planet to the desired orbit. The more massive the planet, the faster the speed. The higher above the surface, the lower the speed. For Earth, at a height just above the atmosphere, the answer is 7.8 kilometers per second, or 17,500 mph, which is why it takes a big rocket to launch a satellite! This speed is the minimum needed to keep an object in space near Earth, and is called the circular velocity. An object with a lower velocity will fall back to the surface under Earth's gravity. The same idea applies to any object in orbit around a larger object. The circular velocity of the Moon around the Earth is 1 kilometer per second. The Earth orbits the Sun at an average circular velocity of 30 kilometers per second (the Earth's orbit is an ellipse, not a circle, but it's close enough to circular that this is a good approximation). At further distances from the Sun, planets have lower orbital velocities. Pluto only has an average circular velocity of about 5 kilometers per second. To launch a satellite, all you have to do is raise it above the Earth's atmosphere with a rocket and then accelerate it until it reaches a speed of 7.8 kilometers per second. -
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. -
Multisatellite Determination of the Relativistic Electron Phase Space Density at Geosynchronous Orbit: Methodology and Results During Geomagnetically Quiet Times Y
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, A10210, doi:10.1029/2004JA010895, 2005 Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: Methodology and results during geomagnetically quiet times Y. Chen, R. H. W. Friedel, and G. D. Reeves Los Alamos National Laboratory, Los Alamos, New Mexico, USA T. G. Onsager NOAA, Boulder, Colorado, USA M. F. Thomsen Los Alamos National Laboratory, Los Alamos, New Mexico, USA Received 10 November 2004; revised 20 May 2005; accepted 8 July 2005; published 20 October 2005. [1] We develop and test a methodology to determine the relativistic electron phase space density distribution in the vicinity of geostationary orbit by making use of the pitch-angle resolved energetic electron data from three Los Alamos National Laboratory geosynchronous Synchronous Orbit Particle Analyzer instruments and magnetic field measurements from two GOES satellites. Owing to the Earth’s dipole tilt and drift shell splitting for different pitch angles, each satellite samples a different range of Roederer L* throughout its orbit. We use existing empirical magnetic field models and the measured pitch-angle resolved electron spectra to determine the phase space density as a function of the three adiabatic invariants at each spacecraft. Comparing all satellite measurements provides a determination of the global phase space density gradient over the range L* 6–7. We investigate the sensitivity of this method to the choice of the magnetic field model and the fidelity of the instrument intercalibration in order to both understand and mitigate possible error sources. Results for magnetically quiet periods show that the radial slopes of the density distribution at low energy are positive, while at high energy the slopes are negative, which confirms the results from some earlier studies of this type. -
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 . -
Geosynchronous Orbit Determination Using Space Surveillance Network Observations and Improved Radiative Force Modeling
Geosynchronous Orbit Determination Using Space Surveillance Network Observations and Improved Radiative Force Modeling by Richard Harry Lyon B.S., Astronautical Engineering United States Air Force Academy, 2002 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 2004 0 2004 Massachusetts Institute of Technology. All rights reserved. Signature of Author: Department of Aeronautics and Astronautics May 14, 2004 Certified by: Dr. Pa1 J. Cefola Technical Staff, the MIT Lincoln Laboratory Lecturer, Department of Aeronautics and Astronautics Thesis Supervisor Accepted by: Edward M. Greitzer H.N. Slater Professor of Aeronautics and Astronautics MASSACHUSETTS INS E OF TECHNOLOGY Chair, Committee on Graduate Students JUL 0 1 2004 AERO LBRARIES [This page intentionally left blank.] 2 Geosynchronous Orbit Determination Using Space Surveillance Network Observations and Improved Radiative Force Modeling by Richard Harry Lyon Submitted to the Department of Aeronautics and Astronautics on May 14, 2004 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics ABSTRACT Correct modeling of the space environment, including radiative forces, is an important aspect of space situational awareness for geostationary (GEO) spacecraft. Solar radiation pressure has traditionally been modeled using a rotationally-invariant sphere with uniform optical properties. This study is intended to improve orbit determination accuracy for 3-axis stabilized GEO spacecraft via an improved radiative force model. The macro-model approach, developed earlier at NASA GSFC for the Tracking and Data Relay Satellites (TDRSS), models the spacecraft area and reflectivity properties using an assembly of flat plates to represent the spacecraft components. -
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. -
Interplanetary Trajectory Design Using Dynamical Systems Theory THESIS REPORT by Linda Van Der Ham
Interplanetary Trajectory Design using Dynamical Systems Theory THESIS REPORT by Linda van der Ham 8 February 2012 The image on the front is an artist impression of the Interplanetary Super- highway [NASA, 2002]. Preface This MSc. thesis forms the last part of the curriculum of Aerospace Engineering at Delft University of Technology in the Netherlands. It covers subjects from the MSc. track Space Exploration, focusing on astrodynamics and space missions, as well as new theory as studied in the literature study performed previously. Dynamical Systems Theory was one of those new subjects, I had never heard of before. The existence of a so-called Interplanetary Transport Network intrigued me and its use for space exploration would mean a total new way of transfer. During the literature study I did not find any practical application of the the- ory to interplanetary flight, while it was stated as a possibility. This made me wonder whether it was even an option, a question that could not be answered until the end of my thesis work. I would like to thank my supervisor Ron Noomen, for his help and enthusi- asm during this period; prof. Wakker for his inspirational lectures about the wonders of astrodynamics; the Tudat group, making research easier for a lot of students in the future. My parents for their unlimited support in every way. And Wouter, for being there. Thank you all and enjoy! i ii Abstract In this thesis, manifolds in the coupled planar circular restricted three-body problem (CR3BP) as means of interplanetary transfer are examined. The equa- tions of motion or differential equations of the CR3BP are studied according to Dynamical Systems Theory (DST). -
Analysis of Space Elevator Technology
Analysis of Space Elevator Technology SPRING 2014, ASEN 5053 FINAL PROJECT TYSON SPARKS Contents Figures .......................................................................................................................................................................... 1 Tables ............................................................................................................................................................................ 1 Analysis of Space Elevator Technology ........................................................................................................................ 2 Nomenclature ................................................................................................................................................................ 2 I. Introduction and Theory ....................................................................................................................................... 2 A. Modern Elevator Concept ................................................................................................................................. 2 B. Climber Concept ............................................................................................................................................... 3 C. Base Station Concept ........................................................................................................................................ 4 D. Space Elevator Astrodynamics ........................................................................................................................ -
Trajectory Design Tools for Libration and Cis-Lunar Environments
Trajectory Design Tools for Libration and Cis-Lunar Environments David C. Folta, Cassandra M. Webster, Natasha Bosanac, Andrew Cox, Davide Guzzetti, and Kathleen C. Howell National Aeronautics and Space Administration/ Goddard Space Flight Center, Greenbelt, MD, 20771 [email protected], [email protected] School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907 {nbosanac,cox50,dguzzett,howell}@purdue.edu ABSTRACT science orbit. WFIRST trajectory design is based on an optimal direct-transfer trajectory to a specific Sun- Innovative trajectory design tools are required to Earth L2 quasi-halo orbit. support challenging multi-body regimes with complex dynamics, uncertain perturbations, and the integration Trajectory design in support of lunar and libration of propulsion influences. Two distinctive tools, point missions is becoming more challenging as more Adaptive Trajectory Design and the General Mission complex mission designs are envisioned. To meet Analysis Tool have been developed and certified to these greater challenges, trajectory design software provide the astrodynamics community with the ability must be developed or enhanced to incorporate to design multi-body trajectories. In this paper we improved understanding of the Sun-Earth/Moon discuss the multi-body design process and the dynamical solution space and to encompass new capabilities of both tools. Demonstrable applications to optimal methods. Thus the support community needs confirmed missions, the Lunar IceCube Cubesat lunar to improve the efficiency and expand the capabilities mission and the Wide-Field Infrared Survey Telescope of current trajectory design approaches. For example, (WFIRST) Sun-Earth L2 mission, are presented. invariant manifolds, derived from dynamical systems theory, have been applied to the trajectory design of 1. -
Exergy Efficiency of Interplanetary Transfer Vehicles
2018 Conference on Systems Engineering Research Exergy Efficiency of Interplanetary Transfer Vehicles Sean T. Owena, Michael D. Watsonb*, Mitchell A. Rodriguezc aUniversity of Alabama in Huntsville, Huntsville, AL 35899, USA bNASA Marshall Space Flight Center, Huntsville, AL 35812 cJacobs Space Exploration Group, Huntsville, AL 35806, USA Abstract In order to optimize systems, systems engineers require some sort of measure with which to compare vastly different system components. One such measure is system exergy, or the usable system work. Exergy balance analysis models provide a comparison of different system configurations, allowing systems engineers to compare different systems configuration options. This paper presents the exergy efficiency of several Mars transportation system configurations, using data on the interplanetary trajectory, engine performance, and vehicle mass. The importance of the starting and final parking orbits is addressed in the analysis, as well as intermediate hyperbolic escape and entry orbits within Earth and Mars’ spheres of influence (SOIs). Propulsion systems analyzed include low-enriched uranium (LEU) nuclear thermal propulsion (NTP), high-enriched uranium (HEU) NTP, LEU methane (CH4) NTP, and liquid oxygen (LOX)/liquid hydrogen (LH2) chemical propulsion. © 2018 The Authors. Keywords: Interplanetary; Propulsion System; Sphere of Influence; Systems Engineering; System Exergy; Trajectory 1. Introduction everal space agencies, including NASA, are planning manned exploration of Mars in the upcoming decades. Many different mission S architectures have been proposed for accomplishing this. It is the role of systems engineers to compare and optimize different space transportation systems and components, up to and including full mission architectures. To do this, some measure is needed that applies * Corresponding author. -
Gateway Globe Lesson Plan: Understanding Orbits
Gateway Globe Lesson Plan: Understanding Orbits Location of Gateway Globe Gateway to Space Overview of Gateway Globe The Gateway Globe is a 36-inch wide spherical projection system which shows two different movies on it. One movie shows examples of parabolic flight paths of future space planes, and one shows examples of existing satellite orbits around the Earth. This lesson will allow students to learn how to describe the different kinds of satellite orbits. Lesson Background Information This lesson plan/unit could be used independently or to prepare for (or to extend the learning after) a visit to Spaceport America. It can be used by teachers or parents wishing to make the Spaceport visit a richer learning experience (for everyone!). An object that orbits the Earth is essentially falling around the Earth, but because of its horizontal velocity it never hits the ground. To understand this concept, you have to first understand a few of the basic laws of physics. You can do some simple experiments outdoors with your students that will help them grasp these basics. For both experiments, you will need two identical baseballs. Ask two students to throw the baseballs (forward) into the air while your other students watch. Then ask your class what they notice about the path of the balls. (The paths are curved.) This is because the force of the throw is causing the balls to go forward, but the force of gravity is also pulling the balls “down” toward the center of the Earth. This makes the paths curved. The faster they throw the ball, the farther it seems to go.