High-Speed Escape from a Circular Orbit American Journal of Physics
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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 -
Uncommon Sense in Orbit Mechanics
AAS 93-290 Uncommon Sense in Orbit Mechanics by Chauncey Uphoff Consultant - Ball Space Systems Division Boulder, Colorado Abstract: This paper is a presentation of several interesting, and sometimes valuable non- sequiturs derived from many aspects of orbital dynamics. The unifying feature of these vignettes is that they all demonstrate phenomena that are the opposite of what our "common sense" tells us. Each phenomenon is related to some application or problem solution close to or directly within the author's experience. In some of these applications, the common part of our sense comes from the fact that we grew up on t h e surface of a planet, deep in its gravity well. In other examples, our mathematical intuition is wrong because our mathematical model is incomplete or because we are accustomed to certain kinds of solutions like the ones we were taught in school. The theme of the paper is that many apparently unsolvable problems might be resolved by the process of guessing the answer and trying to work backwards to the problem. The ability to guess the right answer in the first place is a part of modern magic. A new method of ballistic transfer from Earth to inner solar system targets is presented as an example of the combination of two concepts that seem to work in reverse. Introduction Perhaps the simplest example of uncommon sense in orbit mechanics is the increase of speed of a satellite as it "decays" under the influence of drag caused by collisions with the molecules of the upper atmosphere. In everyday life, when we slow something down, we expect it to slow down, not to speed up. -
A Hot Subdwarf-White Dwarf Super-Chandrasekhar Candidate
A hot subdwarf–white dwarf super-Chandrasekhar candidate supernova Ia progenitor Ingrid Pelisoli1,2*, P. Neunteufel3, S. Geier1, T. Kupfer4,5, U. Heber6, A. Irrgang6, D. Schneider6, A. Bastian1, J. van Roestel7, V. Schaffenroth1, and B. N. Barlow8 1Institut fur¨ Physik und Astronomie, Universitat¨ Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany 2Department of Physics, University of Warwick, Coventry, CV4 7AL, UK 3Max Planck Institut fur¨ Astrophysik, Karl-Schwarzschild-Straße 1, 85748 Garching bei Munchen¨ 4Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA 5Texas Tech University, Department of Physics & Astronomy, Box 41051, 79409, Lubbock, TX, USA 6Dr. Karl Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander University Erlangen-Nuremberg (FAU), Sternwartstr. 7, 96049 Bamberg, Germany 7Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA 8Department of Physics and Astronomy, High Point University, High Point, NC 27268, USA *[email protected] ABSTRACT Supernova Ia are bright explosive events that can be used to estimate cosmological distances, allowing us to study the expansion of the Universe. They are understood to result from a thermonuclear detonation in a white dwarf that formed from the exhausted core of a star more massive than the Sun. However, the possible progenitor channels leading to an explosion are a long-standing debate, limiting the precision and accuracy of supernova Ia as distance indicators. Here we present HD 265435, a binary system with an orbital period of less than a hundred minutes, consisting of a white dwarf and a hot subdwarf — a stripped core-helium burning star. -
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 -
Comparative Analysis of Chemical Propulsion Orbit Transfer Methods and Contribution of Gravity Assist for a Space Mission to Jupiter
Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 11, November-2016 Comparative Analysis of Chemical Propulsion Orbit Transfer Methods and Contribution of Gravity Assist for a Space Mission to Jupiter Naga Bharath Gundrati1 Meghana Rachamallu2 1Mechanical and Aerospace Engineering, 2Industrial and Systems Engineering, University at Buffalo, Virginia Polytechnic Institute and State University, Buffalo, USA Blacksburg, USA Abstract— The selection of an appropriate orbit transfer one planet to another. It connects the Lagrange points of the method is one of the major tasks in planning a spacecraft planets and is a result of the gravitational pull of these mission. This paper provides an analysis of three major planets. The another useful application of the planets’ chemical propulsion orbit transfer mechanisms that can be gravitational force and relative movement, is the flyby or applied to the transfer of a spacecraft from Lower Earth Orbit gravity assist. to Jupiter’s orbit; and consequentially the time is taken for the transfer, including the energy and fuel requirements. Lagrange To be able to bring all the orbit transfer methods to a points which form a gravitationally determined path to the common platform and evaluate their relevance and quantify orbit of Jupiter are calculated. The juxtaposition of all the their contribution to the overall mission is appreciated. energy and the requirements for each of the orbit transfer This paper compares the different types of orbit method and Interplanetary Transfer Network are presented. transfers to come out with the optimal method for The Hyperbolic Excess and Capture velocities required to interplanetary transfer to Jupiter based on the different types escape the Gravitational force of Earth and get drawn into an of mission requirement. -
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019 Term Description AEHF Advanced Extremely High Frequency AFB / AFS Air Force Base / Air Force Station AOC Air Operations Center AOI Area of Interest The point in the orbit of a heavenly body, specifically the moon, or of a man-made satellite Apogee at which it is farthest from the earth. Even CAP rockets experience apogee. Either of two points in an eccentric orbit, one (higher apsis) farthest from the center of Apsis attraction, the other (lower apsis) nearest to the center of attraction Argument of Perigee the angle in a satellites' orbit plane that is measured from the Ascending Node to the (ω) perigee along the satellite direction of travel CGO Company Grade Officer CLV Calculated Load Value, Crew Launch Vehicle COP Common Operating Picture DCO Defensive Cyber Operations DHS Department of Homeland Security DoD Department of Defense DOP Dilution of Precision Defense Satellite Communications Systems - wideband communications spacecraft for DSCS the USAF DSP Defense Satellite Program or Defense Support Program - "Eyes in the Sky" EHF Extremely High Frequency (30-300 GHz; 1mm-1cm) ELF Extremely Low Frequency (3-30 Hz; 100,000km-10,000km) EMS Electromagnetic Spectrum Equitorial Plane the plane passing through the equator EWR Early Warning Radar and Electromagnetic Wave Resistivity GBR Ground-Based Radar and Global Broadband Roaming GBS Global Broadcast Service GEO Geosynchronous Earth Orbit or Geostationary Orbit ( ~22,300 miles above Earth) GEODSS Ground-Based Electro-Optical Deep Space Surveillance -
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. -
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. -
Kerbal Space Program Mun Science Spreadsheet
Kerbal Space Program Mun Science Spreadsheet Unfilial and svelte Salmon accustom some clomps so lark! Indiscerptible and high-ranking Vito yeans while alated Al strip-mines her coverage Somerville and refurnishes moderately. Is Emmott arthralgic or happy when test some function howffs specially? This account is a mun, resistance to line of kerbal space program mun science spreadsheet or two parts are reserved worldwide have tons of designs, or saturday night fever is futuristic space. The drop to master of kerbal program. Oxium from normal match. Science from Minmus' surface however a rescue did a stranded Kerbal on Minmus. Ksp is a lot more honest, some random articles. Kerbal space range modifier difficulty options to work for the missions landing on a kerbal space program mun science spreadsheet! That gave the same day out at this craft and final result. Kerbal space program was clearly read that one utilizes a velocity when not, there should mean running up, pops his socks off enough. That was that those who is it detects heat capacity increased max science is exactly how he worked. Tally is incredibly close together, go through pure solvent. Everything from landing in there but that upset his transfer stage. No mistake of them together a meteor form where you want is pretty hard way of conquering space exploration simulator that. Ksp has become a deorbit burn? Make oxidizer once a captive, a real space program antenna and even more points for testing process and how do with what kyjoca said abh can. Need fresh sight, including a scan across that will be assembled and time and all i go bison! This stage instead on reddit about nine more amazing thing a kerbal space program mun science spreadsheet with regard to get it would take the novel opens, even trying to the experiment cannot register to leave him. -
Chapter 2: Earth in Space
Chapter 2: Earth in Space 1. Old Ideas, New Ideas 2. Origin of the Universe 3. Stars and Planets 4. Our Solar System 5. Earth, the Sun, and the Seasons 6. The Unique Composition of Earth Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Earth in Space Concept Survey Explain how we are influenced by Earth’s position in space on a daily basis. The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas • Why is Earth the only planet known to support life? • How have our views of Earth’s position in space changed over time? • Why is it warmer in summer and colder in winter? (or, How does Earth’s position relative to the sun control the “Earthrise” taken by astronauts aboard Apollo 8, December 1968 climate?) The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System sun • Geocentric orbit hypothesis - Ancient civilizations interpreted rising of sun in east and setting in west to indicate the sun (and other planets) revolved around Earth Earth pictured at the center of a – Remained dominant geocentric planetary system idea for more than 2,000 years The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System • Heliocentric orbit hypothesis –16th century idea suggested by Copernicus • Confirmed by Galileo’s early 17th century observations of the phases of Venus – Changes in the size and shape of Venus as observed from Earth The Good Earth, Chapter 2: Earth in Space Old Ideas, New Ideas From a Geocentric to Heliocentric System • Galileo used early telescopes to observe changes in the size and shape of Venus as it revolved around the sun The Good Earth, Chapter 2: Earth in Space Earth in Space Conceptest The moon has what type of orbit? A. -
Brief Introduction to Orbital Mechanics Page 1
Brief Introduction to Orbital Mechanics Page 1 Brief Introduction to Orbital Mechanics We wish to work out the specifics of the orbital geometry of satellites. We begin by employing Newton's laws of motion to determine the orbital period of a satellite. The first equation of motion is F = ma (1) where m is mass, in kg, and a is acceleration, in m/s2. The Earth produces a gravitational field equal to Gm g(r) = − E r^ (2) r2 24 −11 2 2 where mE = 5:972 × 10 kg is the mass of the Earth and G = 6:674 × 10 N · m =kg is the gravitational constant. The gravitational force acting on the satellite is then equal to Gm mr^ Gm mr F = − E = − E : (3) in r2 r3 This force is inward (towards the Earth), and as such is defined as a centripetal force acting on the satellite. Since the product of mE and G is a constant, we can define µ = mEG = 3:986 × 1014 N · m2=kg which is known as Kepler's constant. Then, µmr F = − : (4) in r3 This force is illustrated in Figure 1(a). An equal and opposite force acts on the satellite called the centrifugal force, also shown. This force keeps the satellite moving in a circular path with linear speed, away from the axis of rotation. Hence we can define a centrifugal acceleration as the change in velocity produced by the satellite moving in a circular path with respect to time, which keeps the satellite moving in a circular path without falling into the centre. -
Mscthesis Joseangelgutier ... Humada.Pdf
Targeting a Mars science orbit from Earth using Dual Chemical-Electric Propulsion and Ballistic Capture Jose Angel Gutierrez Ahumada Delft University of Technology TARGETING A MARS SCIENCE ORBIT FROM EARTH USING DUAL CHEMICAL-ELECTRIC PROPULSION AND BALLISTIC CAPTURE by Jose Angel Gutierrez Ahumada MSc Thesis in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology, to be defended publicly on Wednesday May 8, 2019. Supervisor: Dr. Francesco Topputo, TU Delft/Politecnico di Milano Dr. Ryan Russell, The University of Texas at Austin Thesis committee: Dr. Francesco Topputo, TU Delft/Politecnico di Milano Prof. dr. ir. Pieter N.A.M. Visser, TU Delft ir. Ron Noomen, TU Delft Dr. Angelo Cervone, TU Delft This thesis is confidential and cannot be made public until December 31, 2020. An electronic version of this thesis is available at http://repository.tudelft.nl/. Cover picture adapted from https://steemitimages.com/p/2gs...QbQvi EXECUTIVE SUMMARY Ballistic capture is a relatively novel concept in interplanetary mission design with the potential to make Mars and other targets in the Solar System more accessible. A complete end-to-end interplanetary mission from an Earth-bound orbit to a stable science orbit around Mars (in this case, an areostationary orbit) has been conducted using this concept. Sets of initial conditions leading to ballistic capture are generated for different epochs. The influence of the dynamical model on the capture is also explored briefly. Specific capture trajectories are then selected based on a study of their stabilization into an areostationary orbit.