Positioning: Drift Orbit and Station Acquisition
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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 -
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 -
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Ever Wonder What’s in Molniya? We Do. John T. McGraw J. T. McGraw and Associates, LLC and University of New Mexico Peter C. Zimmer J. T. McGraw and Associates, LLC Mark R. Ackermann J. T. McGraw and Associates, LLC ABSTRACT Molniya orbits are high inclination, high eccentricity orbits which provide the utility of long apogee dwell time over northern continents, with the additional benefit of obviating the largest orbital perturbation introduced by the Earth’s nonspherical (oblate) gravitational potential. We review the few earlier surveys of the Molniya domain and evaluate results from a new, large area unbiased survey of the northern Molniya domain. We detect 120 Molniya objects in a three hour survey of ~ 1300 square degrees of the sky to a limiting magnitude of about 16.5. Future Molniya surveys will discover a significant number of objects, including debris, and monitoring these objects might provide useful data with respect to orbital perturbations including solar radiation and Earth atmosphere drag effects. 1. SPECIALIZED ORBITS Earth Orbital Space (EOS) supports many versions of specialized satellite orbits defined by a combination of satellite mission and orbital dynamics. Surely the most well-known family of specialized orbits is the geostationary orbits proposed by science fiction author Arthur C. Clarke in 1945 [1] that lie sensibly in the plane of Earth’s equator, with orbital period that matches the Earth’s rotation period. Satellites in these orbits, and the closely related geosynchronous orbits, appear from Earth to remain constantly overhead, allowing continuous communication with the majority of the hemisphere below. Constellations of three geostationary satellites equally spaced in orbit (~ 120° separation) can maintain near-global communication and terrestrial surveillance. -
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. -
Molniya" Type Orbits
EXAMINATION OF THE LIFETIME, EVOLUTION AND RE-ENTRY FEATURES FOR THE "MOLNIYA" TYPE ORBITS Yu.F. Kolyuka, N.M. Ivanov, T.I. Afanasieva, T.A. Gridchina Mission Control Center, 4, Pionerskaya str., Korolev, Moscow Region, 141070, Russia, [email protected] ABSTRACT Space vehicles of the "Molniya" series, launched into the special highly elliptical orbits with a period of ~ 12 hours, are intended for solution of telecommunication problems in stretched territories of the former USSR and nowadays − Russia, and also for providing the connectivity between Russia and other countries. The inclination of standard orbits of such a kind of satellites is near to the critical value i ≈ 63.4 deg and their initial minimal altitude normally has a value Hmin ~ 500 km. As a rule, the “Molniya" satellites of a concrete series form the groups with determined disposition of orbital planes on an ascending node longitude that allows to ensure requirements of the continuous link between any points in northern hemisphere. The first satellite of the "Molniya" series has been inserted into designed orbit in 1964. Up to now it is launched over 160 space vehicles of such a kind. As well as all artificial satellites, space vehicles "Molniya" undergo the action of various perturbing forces influencing a change of their orbital parameters. However in case of space vehicles "Molniya" these changes of parameters have a specific character and in many things they differ from the perturbations which are taking place for the majority of standard orbits of the artificial satellites with rather small eccentricity. In particular, to strong enough variations (first of all, at the expense of the luni-solar attraction) it is subjected the orbit perigee distance rπ that can lead to such reduction Hmin when further flight of the satellite on its orbit becomes impossible, it re-entries and falls to the Earth. -
An Introduction to Rockets -Or- Never Leave Geeks Unsupervised
An Introduction to Rockets -or- Never Leave Geeks Unsupervised Kevin Mellett 27 Apr 2006 2 What is a Rocket? • A propulsion system that contains both oxidizer and fuel • NOT a jet, which requires air for O2 3 A Brief History • 400 BC – Steam Bird • 100 BC – Hero Engine • 100 AD – Gunpowder Invented in China – Celebrations – Religious Ceremonies – Bamboo Misfires? 4 A Brief History • Chinese Invent Fire Arrows 13th c – First True Rockets •16th c Wan-Hu – 47 Rockets 5 A Brief History •13th –16th c Improvements in Technology – English Improved Gunpowder – French Improved Guidance by Shooting Through a Tube “Bazooka Style” – Germans Invented “Step Rockets” (Staging) 6 A Brief History • 1687 Newton Publishes Principia Mathematica 7 Newton’s Third Law MOMENTUM is the key concept of rocketry 8 A Brief History • 1903 KonstantineTsiolkovsky Publishes the “Rocket Equation” – Proposes Liquid Fuel ⎛ Mi ⎞ V = Ve*ln⎜ ⎟ ⎝ Mf ⎠ 9 A Brief History • Goddard Flies the First Liquid Fueled Rocket on 16 Mar 1926 – Theorized Rockets Would Work in a Vacuum – NY Times: Goddard “…lacks the basic physics ladeled out in our high schools…” 10 A Brief History • Germans at Peenemunde – Oberth and von Braun lead development of the V-2 – Amazing achievement, but too late to change the tide of WWII – After WWII, USSR and USA took German Engineers and Hardware 11 Mission Requirements • Launch On Need – No Time for Complex Pre-Launch Preps – Long Shelf Life • Commercial / Government – Risk Tolerance –R&D Costs 12 Mission Requirements • Payload Mass and Orbital Objectives – How much do you need, and where do you want it? Both drive energy requirements. -
Richard Dalbello Vice President, Legal and Government Affairs Intelsat General
Commercial Management of the Space Environment Richard DalBello Vice President, Legal and Government Affairs Intelsat General The commercial satellite industry has billions of dollars of assets in space and relies on this unique environment for the development and growth of its business. As a result, safety and the sustainment of the space environment are two of the satellite industry‘s highest priorities. In this paper I would like to provide a quick survey of past and current industry space traffic control practices and to discuss a few key initiatives that the industry is developing in this area. Background The commercial satellite industry has been providing essential space services for almost as long as humans have been exploring space. Over the decades, this industry has played an active role in developing technology, worked collaboratively to set standards, and partnered with government to develop successful international regulatory regimes. Success in both commercial and government space programs has meant that new demands are being placed on the space environment. This has resulted in orbital crowding, an increase in space debris, and greater demand for limited frequency resources. The successful management of these issues will require a strong partnership between government and industry and the careful, experience-based expansion of international law and diplomacy. Throughout the years, the satellite industry has never taken for granted the remarkable environment in which it works. Industry has invested heavily in technology and sought out the best and brightest minds to allow the full, but sustainable exploitation of the space environment. Where problems have arisen, such as space debris or electronic interference, industry has taken 1 the initiative to deploy new technologies and adopt new practices to minimize negative consequences. -
Open Rosen Thesis.Pdf
THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF AEROSPACE ENGINEERING END OF LIFE DISPOSAL OF SATELLITES IN HIGHLY ELLIPTICAL ORBITS MITCHELL ROSEN SPRING 2019 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Aerospace Engineering with honors in Aerospace Engineering Reviewed and approved* by the following: Dr. David Spencer Professor of Aerospace Engineering Thesis Supervisor Dr. Mark Maughmer Professor of Aerospace Engineering Honors Adviser * Signatures are on file in the Schreyer Honors College. i ABSTRACT Highly elliptical orbits allow for coverage of large parts of the Earth through a single satellite, simplifying communications in the globe’s northern reaches. These orbits are able to avoid drastic changes to the argument of periapse by using a critical inclination (63.4°) that cancels out the first level of the geopotential forces. However, this allows the next level of geopotential forces to take over, quickly de-orbiting satellites. Thus, a balance between the rate of change of the argument of periapse and the lifetime of the orbit is necessitated. This thesis sets out to find that balance. It is determined that an orbit with an inclination of 62.5° strikes that balance best. While this orbit is optimal off of the critical inclination, it is still near enough that to allow for potential use of inclination changes as a deorbiting method. Satellites are deorbited when the propellant remaining is enough to perform such a maneuver, and nothing more; therefore, the less change in velocity necessary for to deorbit, the better. Following the determination of an ideal highly elliptical orbit, the different methods of inclination change is tested against the usual method for deorbiting a satellite, an apoapse burn to lower the periapse, to find the most propellant- efficient method. -
Satellite Orbits
Course Notes for Ocean Colour Remote Sensing Course Erdemli, Turkey September 11 - 22, 2000 Module 1: Satellite Orbits prepared by Assoc Professor Mervyn J Lynch Remote Sensing and Satellite Research Group School of Applied Science Curtin University of Technology PO Box U1987 Perth Western Australia 6845 AUSTRALIA tel +618-9266-7540 fax +618-9266-2377 email <[email protected]> Module 1: Satellite Orbits 1.0 Artificial Earth Orbiting Satellites The early research on orbital mechanics arose through the efforts of people such as Tyco Brahe, Copernicus, Kepler and Galileo who were clearly concerned with some of the fundamental questions about the motions of celestial objects. Their efforts led to the establishment by Keppler of the three laws of planetary motion and these, in turn, prepared the foundation for the work of Isaac Newton who formulated the Universal Law of Gravitation in 1666: namely, that F = GmM/r2 , (1) Where F = attractive force (N), r = distance separating the two masses (m), M = a mass (kg), m = a second mass (kg), G = gravitational constant. It was in the very next year, namely 1667, that Newton raised the possibility of artificial Earth orbiting satellites. A further 300 years lapsed until 1957 when the USSR achieved the first launch into earth orbit of an artificial satellite - Sputnik - occurred. Returning to Newton's equation (1), it would predict correctly (relativity aside) the motion of an artificial Earth satellite if the Earth was a perfect sphere of uniform density, there was no atmosphere or ocean or other external perturbing forces. However, in practice the situation is more complicated and prediction is a less precise science because not all the effects of relevance are accurately known or predictable. -
Orbital Inclination and Eccentricity Oscillations in Our Solar
Long term orbital inclination and eccentricity oscillations of the planets in our solar system Abstract The orbits of the planets in our solar system are not in the same plane, therefore natural torques stemming from Newton’s gravitational forces exist to pull them all back to the same plane. This causes the inclinations of the planet orbits to oscillate with potentially long periods and very small damping, because the friction in space is very small. Orbital inclination changes are known for some planets in terms of current rates of change, but the oscillation periods are not well published. They can however be predicted with proper dynamic simulations of the solar system. A three-dimensional dynamic simulation was developed for our solar system capable of handling 12 objects, where all objects affect all other objects. Each object was considered to be a point mass which proved to be an adequate approximation for this study. Initial orbital radii, eccentricities and speeds were set according to known values. The validity of the simulation was demonstrated in terms of short term characteristics such as sidereal periods of planets as well as long term characteristics such as the orbital inclination and eccentricity oscillation periods of Jupiter and Saturn. A significantly more accurate result, than given on approximate analytical grounds in a well-known solar system dynamics textbook, was found for the latter period. Empirical formulas were developed from the simulation results for both these periods for three-object solar type systems. They are very accurate for the Sun, Jupiter and Saturn as well as for some other comparable systems. -
A Decade of Growth
A publication of The Orbital Debris Program Office NASA Johnson Space Center Houston, Texas 77058 October 2000 Volume 5, Issue 4. NEWS A Decade of Growth P. Anz-Meador and Globalstar commercial communication of the population. For example, consider the This article will examine changes in the spacecraft constellations, respectively. Given peak between 840-850 km (Figure 1’s peak low Earth orbit (LEO) environment over the the uncertain future of the Iridium constellation, “B”). This volume is populated by the period 1990-2000. Two US Space Surveillance the spike between 770 and 780 km may change Commonwealth of Independent State’s Tselina- Network (SSN) catalogs form the basis of our drastically or even disappear over the next 2 spacecraft constellation, several US Defense comparison. Included are all unclassified several years. Less prominent is the Orbcomm Meteorological Support Program (DMSP) cataloged and uncataloged objects in both data commercial constellation, with a primary spacecraft, and their associated rocket bodies sets, but objects whose epoch times are “older” concentration between 810 and 820 km altitude and debris. While the region is traversed by than 30 days were excluded from further (peak “A” in Figure 1). Smaller series of many other space objects, including debris, consideration. Moreover, the components of satellites may also result in local enhancements these satellites and rocket boosters are in near the Mir orbital station are 3.0E-08 circular orbits. Thus, any “collectivized” into one group of spacecraft whose object so as not to depict a orbits are tightly January 1990 plethora of independently- 2.5E-08 maintained are capable of orbiting objects at Mir’s A January 2000 producing a spike similar altitude; the International B to that observed with the Space Station (ISS) is 2.0E-08 commercial constellations.