Orbit Estimation of Geosynchronous Objects Via Ground-Based and Space-Based Optical Tracking
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A Study of Ancient Khmer Ephemerides
A study of ancient Khmer ephemerides François Vernotte∗ and Satyanad Kichenassamy** November 5, 2018 Abstract – We study ancient Khmer ephemerides described in 1910 by the French engineer Faraut, in order to determine whether they rely on observations carried out in Cambodia. These ephemerides were found to be of Indian origin and have been adapted for another longitude, most likely in Burma. A method for estimating the date and place where the ephemerides were developed or adapted is described and applied. 1 Introduction Our colleague Prof. Olivier de Bernon, from the École Française d’Extrême Orient in Paris, pointed out to us the need to understand astronomical systems in Cambo- dia, as he surmised that astronomical and mathematical ideas from India may have developed there in unexpected ways.1 A proper discussion of this problem requires an interdisciplinary approach where history, philology and archeology must be sup- plemented, as we shall see, by an understanding of the evolution of Astronomy and Mathematics up to modern times. This line of thought meets other recent lines of research, on the conceptual evolution of Mathematics, and on the definition and measurement of time, the latter being the main motivation of Indian Astronomy. In 1910 [1], the French engineer Félix Gaspard Faraut (1846–1911) described with great care the method of computing ephemerides in Cambodia used by the horas, i.e., the Khmer astronomers/astrologers.2 The names for the astronomical luminaries as well as the astronomical quantities [1] clearly show the Indian origin ∗F. Vernotte is with UTINAM, Observatory THETA of Franche Comté-Bourgogne, University of Franche Comté/UBFC/CNRS, 41 bis avenue de l’observatoire - B.P. -
The Modern Broadcaster's Journey from Satellite to Ip
A CONCISE GUIDE TO… THE MODERN BROADCASTER’S JOURNEY FROM SATELLITE TO IP DELIVERY The commercial communication satellite will celebrate its 60th birthday next year but the concept is far from entering retirement. Nonetheless, as it moves into its seventh decade, the use of the satellite is rapidly evolving. As of 2020, approximately 1,400 communications satellites are orbiting the earth, delivering tens of thousands of TV channels and, increasingly, internet connectivity. Satellite communication is also a vital asset for the TV production industry, allowing live reportage to and from anywhere in the world – almost instantly. 1 Its place in the TV ecosystem is changing, much higher value. It was also well before the however, as it plays a reduced role in the on-demand content revolution. This trend delivery of video – a shift that several has led to the last major shift: the emergence underlying trends have accelerated. The first of multiplatform, over-the-top streaming is a massive proliferation of video content. over the last 15 years, which has eroded the dominance of the linear broadcaster. The Although satellite use in TV production rise of the streaming giants and specialist has been integral to high-profile live news platforms has forced broadcasters to increase and sports coverage, its role is waning. The their overall distribution capacity using last couple of decades has seen a massive Internet Protocol (IP)-centric methods. increase in live content from a broader range of leagues, niche sports, performance The trends impacting satellite’s role in events and 24-hour news networks. This the television landscape are forcing many expansion of content leads to the second broadcasters to look to their future and factor. -
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. -
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 -
Low-Cost Wireless Internet System for Rural India Using Geosynchronous Satellite in an Inclined Orbit
Low-cost Wireless Internet System for Rural India using Geosynchronous Satellite in an Inclined Orbit Karan Desai Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science In Electrical Engineering Timothy Pratt, Chair Jeffrey H. Reed J. Michael Ruohoniemi April 28, 2011 Blacksburg, Virginia Keywords: Internet, Low-cost, Rural Communication, Wireless, Geostationary Satellite, Inclined Orbit Copyright 2011, Karan Desai Low-cost Wireless Internet System for Rural India using Geosynchronous Satellite in an Inclined Orbit Karan Desai ABSTRACT Providing affordable Internet access to rural populations in large developing countries to aid economic and social progress, using various non-conventional techniques has been a topic of active research recently. The main obstacle in providing fiber-optic based terrestrial Internet links to remote villages is the cost involved in laying the cable network and disproportionately low rate of return on investment due to low density of paid users. The conventional alternative to this is providing Internet access using geostationary satellite links, which can prove commercially infeasible in predominantly cost-driven rural markets in developing economies like India or China due to high access cost per user. A low-cost derivative of the conventional satellite-based Internet access system can be developed by utilizing an aging geostationary satellite nearing the end of its active life, allowing it to enter an inclined geosynchronous orbit by limiting station keeping to only east-west maneuvers to save fuel. Eliminating the need for individual satellite receiver modules by using one centrally located earth station per village and providing last mile connectivity using Wi-Fi can further reduce the access cost per user. -
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. -
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. -
Highlights in Space 2010
International Astronautical Federation Committee on Space Research International Institute of Space Law 94 bis, Avenue de Suffren c/o CNES 94 bis, Avenue de Suffren UNITED NATIONS 75015 Paris, France 2 place Maurice Quentin 75015 Paris, France Tel: +33 1 45 67 42 60 Fax: +33 1 42 73 21 20 Tel. + 33 1 44 76 75 10 E-mail: : [email protected] E-mail: [email protected] Fax. + 33 1 44 76 74 37 URL: www.iislweb.com OFFICE FOR OUTER SPACE AFFAIRS URL: www.iafastro.com E-mail: [email protected] URL : http://cosparhq.cnes.fr Highlights in Space 2010 Prepared in cooperation with the International Astronautical Federation, the Committee on Space Research and the International Institute of Space Law The United Nations Office for Outer Space Affairs is responsible for promoting international cooperation in the peaceful uses of outer space and assisting developing countries in using space science and technology. United Nations Office for Outer Space Affairs P. O. Box 500, 1400 Vienna, Austria Tel: (+43-1) 26060-4950 Fax: (+43-1) 26060-5830 E-mail: [email protected] URL: www.unoosa.org United Nations publication Printed in Austria USD 15 Sales No. E.11.I.3 ISBN 978-92-1-101236-1 ST/SPACE/57 *1180239* V.11-80239—January 2011—775 UNITED NATIONS OFFICE FOR OUTER SPACE AFFAIRS UNITED NATIONS OFFICE AT VIENNA Highlights in Space 2010 Prepared in cooperation with the International Astronautical Federation, the Committee on Space Research and the International Institute of Space Law Progress in space science, technology and applications, international cooperation and space law UNITED NATIONS New York, 2011 UniTEd NationS PUblication Sales no. -
Elliptical Orbits
1 Ellipse-geometry 1.1 Parameterization • Functional characterization:(a: semi major axis, b ≤ a: semi minor axis) x2 y 2 b p + = 1 ⇐⇒ y(x) = · ± a2 − x2 (1) a b a • Parameterization in cartesian coordinates, which follows directly from Eq. (1): x a · cos t = with 0 ≤ t < 2π (2) y b · sin t – The origin (0, 0) is the center of the ellipse and the auxilliary circle with radius a. √ – The focal points are located at (±a · e, 0) with the eccentricity e = a2 − b2/a. • Parameterization in polar coordinates:(p: parameter, 0 ≤ < 1: eccentricity) p r(ϕ) = (3) 1 + e cos ϕ – The origin (0, 0) is the right focal point of the ellipse. – The major axis is given by 2a = r(0) − r(π), thus a = p/(1 − e2), the center is therefore at − pe/(1 − e2), 0. – ϕ = 0 corresponds to the periapsis (the point closest to the focal point; which is also called perigee/perihelion/periastron in case of an orbit around the Earth/sun/star). The relation between t and ϕ of the parameterizations in Eqs. (2) and (3) is the following: t r1 − e ϕ tan = · tan (4) 2 1 + e 2 1.2 Area of an elliptic sector As an ellipse is a circle with radius a scaled by a factor b/a in y-direction (Eq. 1), the area of an elliptic sector PFS (Fig. ??) is just this fraction of the area PFQ in the auxiliary circle. b t 2 1 APFS = · · πa − · ae · a sin t a 2π 2 (5) 1 = (t − e sin t) · a b 2 The area of the full ellipse (t = 2π) is then, of course, Aellipse = π a b (6) Figure 1: Ellipse and auxilliary circle. -
Probability of Collision in the Geostationary Orbit*
PROBABILITY OF COLLISION IN THE GEOSTATIONARY ORBIT* Raymond A. LeClair and Ramaswamy Sridharan MIT Lincoln Laboratory, 244 Wood Street, Lexington, Massachusetts 02420 USA, Email: [email protected] ABSTRACT/RESUME The initial Geosynchronous Encounter Analysis (GEA) CRDA spanned two years beginning in mid 1997. The advent of geostationary satellite communication During this period, Lincoln Laboratory provided timely 37 years ago, and the resulting continued launch activ- warning of encounters between Telstar 401 and partner ity, has created a population of active and inactive geo- satellites and precision orbits for these objects for use synchronous satellites which will interact, with genu- in avoidance maneuver planning [1]. In all, 32 en- ine possibility of collision, for the foreseeable future. counters between Telstar 401 and a partner satellite As a result of the failure of Telstar 401 three years ago, were supported in 24 months leading to nine avoidance MIT Lincoln Laboratory, in cooperation with commer- maneuvers incorporated into routine station keeping cial partners, began an investigation into this situation. and six dedicated avoidance maneuvers. This process Under the agreement, Lincoln worked to ensure a col- has led to a validated concept of operations for en- lision did not occur between Telstar 401 and partner counter support at Lincoln. satellites and to understand the scope and nature of the Active problem. The results of this cooperative activity and Satellites recent results to carefully characterize the actual prob- SOLIDARIDAD 02 ANIK E1 04-Oct-1999 ability of collision in the geostationary orbit are de- 114 SOLIDARIDAD 1 GOES 07 scribed. ANIK E2 112 MSAT M01 ) ANIK C1 110 GSTAR 04 deg USA 0114 1.