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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 -
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 -
Arxiv:1505.07033V2 [Astro-Ph.IM] 4 Sep 2015
September 7, 2015 0:46 manuscript Journal of Astronomical Instrumentation c World Scientific Publishing Company A CUBESAT FOR CALIBRATING GROUND-BASED AND SUB-ORBITAL MILLIMETER-WAVE POLARIMETERS (CALSAT) Bradley R. Johnson1, Clement J. Vourch2, Timothy D. Drysdale2, Andrew Kalman3, Steve Fujikawa4, Brian Keating5 and Jon Kaufman5 1Department of Physics, Columbia University, New York, NY 10027, USA 2School of Engineering, University of Glasgow, Glasgow, Scotland G12 8QQ, UK 3Pumpkin, Inc., San Francisco, CA 94112, USA 4Maryland Aerospace Inc., Crofton, MD 21114, USA 5Department of Physics, University of California, San Diego, CA 92093-0424, USA Received (to be inserted by publisher); Revised (to be inserted by publisher); Accepted (to be inserted by publisher); We describe a low-cost, open-access, CubeSat-based calibration instrument that is designed to support ground- based and sub-orbital experiments searching for various polarization signals in the cosmic microwave background (CMB). All modern CMB polarization experiments require a robust calibration program that will allow the effects of instrument-induced signals to be mitigated during data analysis. A bright, compact, and linearly polarized astrophysical source with polarization properties known to adequate precision does not exist. Therefore, we designed a space-based millimeter-wave calibration instrument, called CalSat, to serve as an open-access calibrator, and this paper describes the results of our design study. The calibration source on board CalSat is composed of five \tones" with one each at 47.1, 80.0, 140, 249 and 309 GHz. The five tones we chose are well matched to (i) the observation windows in the atmospheric transmittance spectra, (ii) the spectral bands commonly used in polarimeters by the CMB community, and (iii) The Amateur Satellite Service bands in the Table of Frequency Allocations used by the Federal Communications Commission. -
Pointing Analysis and Design Drivers for Low Earth Orbit Satellite Quantum Key Distribution Jeremiah A
Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-24-2016 Pointing Analysis and Design Drivers for Low Earth Orbit Satellite Quantum Key Distribution Jeremiah A. Specht Follow this and additional works at: https://scholar.afit.edu/etd Part of the Information Security Commons, and the Space Vehicles Commons Recommended Citation Specht, Jeremiah A., "Pointing Analysis and Design Drivers for Low Earth Orbit Satellite Quantum Key Distribution" (2016). Theses and Dissertations. 451. https://scholar.afit.edu/etd/451 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. POINTING ANALYSIS AND DESIGN DRIVERS FOR LOW EARTH ORBIT SATELLITE QUANTUM KEY DISTRIBUTION THESIS Jeremiah A. Specht, 1st Lt, USAF AFIT-ENY-MS-16-M-241 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A. APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENY-MS-16-M-241 POINTING ANALYSIS AND DESIGN DRIVERS FOR LOW EARTH ORBIT SATELLITE QUANTUM KEY DISTRIBUTION THESIS Presented to the Faculty Department of Aeronautics and Astronautics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Master of Science in Space Systems Jeremiah A. -
Orbit and Spin
Orbit and Spin Overview: A whole-body activity that explores the relative sizes, distances, orbit, and spin of the Sun, Earth, and Moon. Target Grade Level: 3-5 Estimated Duration: 2 40-minute sessions Learning Goals: Students will be able to… • compare the relative sizes of the Earth, Moon, and Sun. • contrast the distance between the Earth and Moon to the distance between the Earth and Sun. • differentiate between the motions of orbit and spin. • demonstrate the spins of the Earth and the Moon, as well as the orbits of the Earth around the Sun, and the Moon around the Earth. Standards Addressed: Benchmarks (AAAS, 1993) The Physical Setting, 4A: The Universe, 4B: The Earth National Science Education Standards (NRC, 1996) Physical Science, Standard B: Position and motion of objects Earth and Space Science, Standard D: Objects in the sky, Changes in Earth and sky Table of Contents: Background Page 1 Materials and Procedure 5 What I Learned… Science Journal Page 14 Earth Picture 15 Sun Picture 16 Moon Picture 17 Earth Spin Demonstration 18 Moon Orbit Demonstration 19 Extensions and Adaptations 21 Standards Addressed, detailed 22 Background: Sun The Sun is the center of our Solar System, both literally—as all of the planets orbit around it, and figuratively—as its rays warm our planet and sustain life as we know it. The Sun is very hot compared to temperatures we usually encounter. Its mean surface temperature is about 9980° Fahrenheit (5800 Kelvin) and its interior temperature is as high as about 28 million° F (15,500,000 Kelvin). -
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. -
Mission Design for the Lunar Reconnaissance Orbiter
AAS 07-057 Mission Design for the Lunar Reconnaissance Orbiter Mark Beckman Goddard Space Flight Center, Code 595 29th ANNUAL AAS GUIDANCE AND CONTROL CONFERENCE February 4-8, 2006 Sponsored by Breckenridge, Colorado Rocky Mountain Section AAS Publications Office, P.O. Box 28130 - San Diego, California 92198 AAS-07-057 MISSION DESIGN FOR THE LUNAR RECONNAISSANCE ORBITER † Mark Beckman The Lunar Reconnaissance Orbiter (LRO) will be the first mission under NASA’s Vision for Space Exploration. LRO will fly in a low 50 km mean altitude lunar polar orbit. LRO will utilize a direct minimum energy lunar transfer and have a launch window of three days every two weeks. The launch window is defined by lunar orbit beta angle at times of extreme lighting conditions. This paper will define the LRO launch window and the science and engineering constraints that drive it. After lunar orbit insertion, LRO will be placed into a commissioning orbit for up to 60 days. This commissioning orbit will be a low altitude quasi-frozen orbit that minimizes stationkeeping costs during commissioning phase. LRO will use a repeating stationkeeping cycle with a pair of maneuvers every lunar sidereal period. The stationkeeping algorithm will bound LRO altitude, maintain ground station contact during maneuvers, and equally distribute periselene between northern and southern hemispheres. Orbit determination for LRO will be at the 50 m level with updated lunar gravity models. This paper will address the quasi-frozen orbit design, stationkeeping algorithms and low lunar orbit determination. INTRODUCTION The Lunar Reconnaissance Orbiter (LRO) is the first of the Lunar Precursor Robotic Program’s (LPRP) missions to the moon. -
Positioning: Drift Orbit and Station Acquisition
Orbits Supplement GEOSTATIONARY ORBIT PERTURBATIONS INFLUENCE OF ASPHERICITY OF THE EARTH: The gravitational potential of the Earth is no longer µ/r, but varies with longitude. A tangential acceleration is created, depending on the longitudinal location of the satellite, with four points of stable equilibrium: two stable equilibrium points (L 75° E, 105° W) two unstable equilibrium points ( 15° W, 162° E) This tangential acceleration causes a drift of the satellite longitude. Longitudinal drift d'/dt in terms of the longitude about a point of stable equilibrium expresses as: (d/dt)2 - k cos 2 = constant Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF EARTH ASPHERICITY VARIATION IN THE LONGITUDINAL ACCELERATION OF A GEOSTATIONARY SATELLITE: Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN & MOON ATTRACTION Gravitational attraction by the sun and moon causes the satellite orbital inclination to change with time. The evolution of the inclination vector is mainly a combination of variations: period 13.66 days with 0.0035° amplitude period 182.65 days with 0.023° amplitude long term drift The long term drift is given by: -4 dix/dt = H = (-3.6 sin M) 10 ° /day -4 diy/dt = K = (23.4 +.2.7 cos M) 10 °/day where M is the moon ascending node longitude: M = 12.111 -0.052954 T (T: days from 1/1/1950) 2 2 2 2 cos d = H / (H + K ); i/t = (H + K ) Depending on time within the 18 year period of M d varies from 81.1° to 98.9° i/t varies from 0.75°/year to 0.95°/year Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN RADIATION PRESSURE Due to sun radiation pressure, eccentricity arises: EFFECT OF NON-ZERO ECCENTRICITY L = difference between longitude of geostationary satellite and geosynchronous satellite (24 hour period orbit with e0) With non-zero eccentricity the satellite track undergoes a periodic motion about the subsatellite point at perigee. -
Cislunar Tether Transport System
FINAL REPORT on NIAC Phase I Contract 07600-011 with NASA Institute for Advanced Concepts, Universities Space Research Association CISLUNAR TETHER TRANSPORT SYSTEM Report submitted by: TETHERS UNLIMITED, INC. 8114 Pebble Ct., Clinton WA 98236-9240 Phone: (206) 306-0400 Fax: -0537 email: [email protected] www.tethers.com Report dated: May 30, 1999 Period of Performance: November 1, 1998 to April 30, 1999 PROJECT SUMMARY PHASE I CONTRACT NUMBER NIAC-07600-011 TITLE OF PROJECT CISLUNAR TETHER TRANSPORT SYSTEM NAME AND ADDRESS OF PERFORMING ORGANIZATION (Firm Name, Mail Address, City/State/Zip Tethers Unlimited, Inc. 8114 Pebble Ct., Clinton WA 98236-9240 [email protected] PRINCIPAL INVESTIGATOR Robert P. Hoyt, Ph.D. ABSTRACT The Phase I effort developed a design for a space systems architecture for repeatedly transporting payloads between low Earth orbit and the surface of the moon without significant use of propellant. This architecture consists of one rotating tether in elliptical, equatorial Earth orbit and a second rotating tether in a circular low lunar orbit. The Earth-orbit tether picks up a payload from a circular low Earth orbit and tosses it into a minimal-energy lunar transfer orbit. When the payload arrives at the Moon, the lunar tether catches it and deposits it on the surface of the Moon. Simultaneously, the lunar tether picks up a lunar payload to be sent down to the Earth orbit tether. By transporting equal masses to and from the Moon, the orbital energy and momentum of the system can be conserved, eliminating the need for transfer propellant. Using currently available high-strength tether materials, this system could be built with a total mass of less than 28 times the mass of the payloads it can transport. -
Analysis of Transfer Maneuvers from Initial
Revista Mexicana de Astronom´ıa y Astrof´ısica, 52, 283–295 (2016) ANALYSIS OF TRANSFER MANEUVERS FROM INITIAL CIRCULAR ORBIT TO A FINAL CIRCULAR OR ELLIPTIC ORBIT M. A. Sharaf1 and A. S. Saad2,3 Received March 14 2016; accepted May 16 2016 RESUMEN Presentamos un an´alisis de las maniobras de transferencia de una ´orbita circu- lar a una ´orbita final el´ıptica o circular. Desarrollamos este an´alisis para estudiar el problema de las transferencias impulsivas en las misiones espaciales. Consideramos maniobras planas usando ecuaciones reci´enobtenidas; con estas ecuaciones se com- paran las maniobras circulares y el´ıpticas. Esta comparaci´on es importante para el dise˜no´optimo de misiones espaciales, y permite obtener mapeos ´utiles para mostrar cu´al es la mejor maniobra. Al respecto, desarrollamos este tipo de comparaciones mediante 10 resultados, y los mostramos gr´aficamente. ABSTRACT In the present paper an analysis of the transfer maneuvers from initial circu- lar orbit to a final circular or elliptic orbit was developed to study the problem of impulsive transfers for space missions. It considers planar maneuvers using newly derived equations. With these equations, comparisons of circular and elliptic ma- neuvers are made. This comparison is important for the mission designers to obtain useful mappings showing where one maneuver is better than the other. In this as- pect, we developed this comparison throughout ten results, together with some graphs to show their meaning. Key Words: celestial mechanics — methods: analytical — space vehicles 1. INTRODUCTION The large amount of information from interplanetary missions, such as Pioneer (Dyer et al. -
GEO, MEO, and LEO How Orbital Altitude Impacts Network Performance in Satellite Data Services
GEO, MEO, AND LEO How orbital altitude impacts network performance in satellite data services COMMUNICATION OVER SATELLITE “An entire multi-orbit is now well accepted as a key enabler across the telecommunications industry. Satellite networks can supplement existing infrastructure by providing global reach satellite ecosystem is where terrestrial networks are unavailable or not feasible. opening up above us, But not all satellite networks are created equal. Providers offer different solutions driving new opportunities depending on the orbits available to them, and so understanding how the distance for high-performance from Earth affects performance is crucial for decision making when selecting a satellite service. The following pages give an overview of the three main orbit gigabit connectivity and classes, along with some of the principal trade-offs between them. broadband services.” Stewart Sanders Executive Vice President of Key terms Technology at SES GEO – Geostationary Earth Orbit. NGSO – Non-Geostationary Orbit. NGSO is divided into MEO and LEO. MEO – Medium Earth Orbit. LEO – Low Earth Orbit. HTS – High Throughput Satellites designed for communication. Latency – the delay in data transmission from one communication endpoint to another. Latency-critical applications include video conferencing, mobile data backhaul, and cloud-based business collaboration tools. SD-WAN – Software-Defined Wide Area Networking. Based on policies controlled by the user, SD-WAN optimises network performance by steering application traffic over the most suitable access technology and with the appropriate Quality of Service (QoS). Figure 1: Schematic of orbital altitudes and coverage areas GEOSTATIONARY EARTH ORBIT Altitude 36,000km GEO satellites match the rotation of the Earth as they travel, and so remain above the same point on the ground.