A Delta-V Map of the Known Main Belt Asteroids
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Low Thrust Manoeuvres to Perform Large Changes of RAAN Or Inclination in LEO
Facoltà di Ingegneria Corso di Laurea Magistrale in Ingegneria Aerospaziale Master Thesis Low Thrust Manoeuvres To Perform Large Changes of RAAN or Inclination in LEO Academic Tutor: Prof. Lorenzo CASALINO Candidate: Filippo GRISOT July 2018 “It is possible for ordinary people to choose to be extraordinary” E. Musk ii Filippo Grisot – Master Thesis iii Filippo Grisot – Master Thesis Acknowledgments I would like to address my sincere acknowledgments to my professor Lorenzo Casalino, for your huge help in these moths, for your willingness, for your professionalism and for your kindness. It was very stimulating, as well as fun, working with you. I would like to thank all my course-mates, for the time spent together inside and outside the “Poli”, for the help in passing the exams, for the fun and the desperation we shared throughout these years. I would like to especially express my gratitude to Emanuele, Gianluca, Giulia, Lorenzo and Fabio who, more than everyone, had to bear with me. I would like to also thank all my extra-Poli friends, especially Alberto, for your support and the long talks throughout these years, Zach, for being so close although the great distance between us, Bea’s family, for all the Sundays and summers spent together, and my soccer team Belfiga FC, for being the crazy lovable people you are. A huge acknowledgment needs to be address to my family: to my grandfather Luciano, for being a great friend; to my grandmother Bianca, for teaching me what “fighting” means; to my grandparents Beppe and Etta, for protecting me -
Osculating Orbit Elements and the Perturbed Kepler Problem
Osculating orbit elements and the perturbed Kepler problem Gmr a = 3 + f(r, v,t) Same − r x & v Define: r := rn ,r:= p/(1 + e cos f) ,p= a(1 e2) − osculating orbit he sin f h v := n + λ ,h:= Gmp p r n := cos ⌦cos(! + f) cos ◆ sinp ⌦sin(! + f) e − X +⇥ sin⌦cos(! + f) + cos ◆ cos ⌦sin(! + f⇤) eY actual orbit +sin⇥ ◆ sin(! + f) eZ ⇤ λ := cos ⌦sin(! + f) cos ◆ sin⌦cos(! + f) e − − X new osculating + sin ⌦sin(! + f) + cos ◆ cos ⌦cos(! + f) e orbit ⇥ − ⇤ Y +sin⇥ ◆ cos(! + f) eZ ⇤ hˆ := n λ =sin◆ sin ⌦ e sin ◆ cos ⌦ e + cos ◆ e ⇥ X − Y Z e, a, ω, Ω, i, T may be functions of time Perturbed Kepler problem Gmr a = + f(r, v,t) − r3 dh h = r v = = r f ⇥ ) dt ⇥ v h dA A = ⇥ n = Gm = f h + v (r f) Gm − ) dt ⇥ ⇥ ⇥ Decompose: f = n + λ + hˆ R S W dh = r λ + r hˆ dt − W S dA Gm =2h n h + rr˙ λ rr˙ hˆ. dt S − R S − W Example: h˙ = r S d (h cos ◆)=h˙ e dt · Z d◆ h˙ cos ◆ h sin ◆ = r cos(! + f)sin◆ + r cos ◆ − dt − W S Perturbed Kepler problem “Lagrange planetary equations” dp p3 1 =2 , dt rGm 1+e cos f S de p 2 cos f + e(1 + cos2 f) = sin f + , dt Gm R 1+e cos f S r d◆ p cos(! + f) = , dt Gm 1+e cos f W r d⌦ p sin(! + f) sin ◆ = , dt Gm 1+e cos f W r d! 1 p 2+e cos f sin(! + f) = cos f + sin f e cot ◆ dt e Gm − R 1+e cos f S− 1+e cos f W r An alternative pericenter angle: $ := ! +⌦cos ◆ d$ 1 p 2+e cos f = cos f + sin f dt e Gm − R 1+e cos f S r Perturbed Kepler problem Comments: § these six 1st-order ODEs are exactly equivalent to the original three 2nd-order ODEs § if f = 0, the orbit elements are constants § if f << Gm/r2, use perturbation theory -
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 -
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. -
Orbital Mechanics
Orbital Mechanics These notes provide an alternative and elegant derivation of Kepler's three laws for the motion of two bodies resulting from their gravitational force on each other. Orbit Equation and Kepler I Consider the equation of motion of one of the particles (say, the one with mass m) with respect to the other (with mass M), i.e. the relative motion of m with respect to M: r r = −µ ; (1) r3 with µ given by µ = G(M + m): (2) Let h be the specific angular momentum (i.e. the angular momentum per unit mass) of m, h = r × r:_ (3) The × sign indicates the cross product. Taking the derivative of h with respect to time, t, we can write d (r × r_) = r_ × r_ + r × ¨r dt = 0 + 0 = 0 (4) The first term of the right hand side is zero for obvious reasons; the second term is zero because of Eqn. 1: the vectors r and ¨r are antiparallel. We conclude that h is a constant vector, and its magnitude, h, is constant as well. The vector h is perpendicular to both r and the velocity r_, hence to the plane defined by these two vectors. This plane is the orbital plane. Let us now carry out the cross product of ¨r, given by Eqn. 1, and h, and make use of the vector algebra identity A × (B × C) = (A · C)B − (A · B)C (5) to write µ ¨r × h = − (r · r_)r − r2r_ : (6) r3 { 2 { The r · r_ in this equation can be replaced by rr_ since r · r = r2; and after taking the time derivative of both sides, d d (r · r) = (r2); dt dt 2r · r_ = 2rr;_ r · r_ = rr:_ (7) Substituting Eqn. -
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. -
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 -
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 -
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.