L1/L5 SBAS MOPS Ephemeris Message to Support Multiple Orbit Classes
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Analysis of Perturbations and Station-Keeping Requirements in Highly-Inclined Geosynchronous Orbits
ANALYSIS OF PERTURBATIONS AND STATION-KEEPING REQUIREMENTS IN HIGHLY-INCLINED GEOSYNCHRONOUS ORBITS Elena Fantino(1), Roberto Flores(2), Alessio Di Salvo(3), and Marilena Di Carlo(4) (1)Space Studies Institute of Catalonia (IEEC), Polytechnic University of Catalonia (UPC), E.T.S.E.I.A.T., Colom 11, 08222 Terrassa (Spain), [email protected] (2)International Center for Numerical Methods in Engineering (CIMNE), Polytechnic University of Catalonia (UPC), Building C1, Campus Norte, UPC, Gran Capitan,´ s/n, 08034 Barcelona (Spain) (3)NEXT Ingegneria dei Sistemi S.p.A., Space Innovation System Unit, Via A. Noale 345/b, 00155 Roma (Italy), [email protected] (4)Department of Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ (United Kingdom), [email protected] Abstract: There is a demand for communications services at high latitudes that is not well served by conventional geostationary satellites. Alternatives using low-altitude orbits require too large constellations. Other options are the Molniya and Tundra families (critically-inclined, eccentric orbits with the apogee at high latitudes). In this work we have considered derivatives of the Tundra type with different inclinations and eccentricities. By means of a high-precision model of the terrestrial gravity field and the most relevant environmental perturbations, we have studied the evolution of these orbits during a period of two years. The effects of the different perturbations on the constellation ground track (which is more important for coverage than the orbital elements themselves) have been identified. We show that, in order to maintain the ground track unchanged, the most important parameters are the orbital period and the argument of the perigee. -
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 -
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. -
Download Paper
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. -
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. -
Spacecraft Trajectories in a Sun, Earth, and Moon Ephemeris Model
SPACECRAFT TRAJECTORIES IN A SUN, EARTH, AND MOON EPHEMERIS MODEL A Project Presented to The Faculty of the Department of Aerospace Engineering San José State University In Partial Fulfillment of the Requirements for the Degree Master of Science in Aerospace Engineering by Romalyn Mirador i ABSTRACT SPACECRAFT TRAJECTORIES IN A SUN, EARTH, AND MOON EPHEMERIS MODEL by Romalyn Mirador This project details the process of building, testing, and comparing a tool to simulate spacecraft trajectories using an ephemeris N-Body model. Different trajectory models and methods of solving are reviewed. Using the Ephemeris positions of the Earth, Moon and Sun, a code for higher-fidelity numerical modeling is built and tested using MATLAB. Resulting trajectories are compared to NASA’s GMAT for accuracy. Results reveal that the N-Body model can be used to find complex trajectories but would need to include other perturbations like gravity harmonics to model more accurate trajectories. i ACKNOWLEDGEMENTS I would like to thank my family and friends for their continuous encouragement and support throughout all these years. A special thank you to my advisor, Dr. Capdevila, and my friend, Dhathri, for mentoring me as I work on this project. The knowledge and guidance from the both of you has helped me tremendously and I appreciate everything you both have done to help me get here. ii Table of Contents List of Symbols ............................................................................................................................... v 1.0 INTRODUCTION -
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. -
Small Satellites in Inclined Orbits to Increase Observation Capability Feasibility Analysis
International Journal of Pure and Applied Mathematics Volume 118 No. 17 2018, 273-287 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu Small Satellites in Inclined Orbits to Increase Observation Capability Feasibility Analysis DVA Raghava Murthy1, V Kesava Raju2, T.Ramanjappa3, Ritu Karidhal4, Vijayasree Mallikarjuna Kande5, G Ravi chandra Babu6 and A Arunachalam7 1 7 Earth Observations System, ISRO Headquarters, Bengaluru, Karnataka India [email protected] 2 4 5 6ISRO Satellite Centre, Bengaluru, Karnataka, India 3SK University, Ananthapur, Andhra Pradesh, India January 6, 2018 Abstract Over the period of past four decades, Remote Sensing data products and services have been effectively utilized to showcase varieties of applications in many areas of re- sources inventory and monitoring. There are several satel- lite systems in operation today and they operate from Po- lar Orbit and Geosynchronous Orbit, collect the imagery and non-imagery data and provide them to user community for various applications in the areas of natural resources management, urban planning and infrastructure develop- ment, weather forecasting and disaster management sup- port. Quality of information derived from Remote Sensing imagery are strongly influenced by spatial, spectral, radio- metric & temporal resolutions as well as by angular & po- larimetric signatures. As per the conventional approach of 1 273 International Journal of Pure and Applied Mathematics Special Issue having Remote Sensing satellites in near Polar Sun syn- chronous orbit, the temporal resolution, i.e. the frequency with which an area can be frequently observed, is basically defined by the swath of the sensor and distance between the paths. -
GRAVITATION UNIT H.W. ANS KEY Question 1
GRAVITATION UNIT H.W. ANS KEY Question 1. Question 2. Question 3. Question 4. Two stars, each of mass M, form a binary system. The stars orbit about a point a distance R from the center of each star, as shown in the diagram above. The stars themselves each have radius r. Question 55.. What is the force each star exerts on the other? Answer D—In Newton's law of gravitation, the distance used is the distance between the centers of the planets; here that distance is 2R. But the denominator is squared, so (2R)2 = 4R2 in the denominator here. Two stars, each of mass M, form a binary system. The stars orbit about a point a distance R from the center of each star, as shown in the diagram above. The stars themselves each have radius r. Question 65.. In terms of each star's tangential speed v, what is the centripetal acceleration of each star? Answer E—In the centripetal acceleration equation the distance used is the radius of the circular motion. Here, because the planets orbit around a point right in between them, this distance is simply R. Question 76.. A Space Shuttle orbits Earth 300 km above the surface. Why can't the Shuttle orbit 10 km above Earth? (A) The Space Shuttle cannot go fast enough to maintain such an orbit. (B) Kepler's Laws forbid an orbit so close to the surface of the Earth. (C) Because r appears in the denominator of Newton's law of gravitation, the force of gravity is much larger closer to the Earth; this force is too strong to allow such an orbit. -
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. -
Single Axis Tracking with the RC1500B the Apparent Motion Of
Single Axis Tracking with the RC1500B The apparent motion of an inclined orbit satellite appears as a narrow figure 8 pattern aligned perpendicular to the geo-stationary satellite arc. As the inclination of the satellite increases both the height and the width of the figure 8 pattern increase. The single axis tracker can follow the long dimension of the figure 8 but cannot compensate for the width of the figure 8 pattern. A paper (available on our web site - http://www.researchconcepts.com/Files/track_wp.pdf) describes the height and width of the figure 8 pattern as a function of the inclination of the satellite’s orbit. Note that the inclination of the satellite increases with time. The maximum rate of increase is approximately 0.9 degrees per year. As the inclination increases, the width of the figure 8 pattern will also increase. This has two implications for system performance. One, the maximum signal loss due to antenna misalignment will increase with time, and two, the antenna must have range a of motion sufficient to accommodate the greatest satellite inclination that will be encountered. Many people feel that single axis tracking is viable for antenna’s up to 3.8 meters at C band and 2.4 meters at Ku band. Implicit in this is the fact that the inclination of most commercial satellites is not allowed to exceed 5 degrees. This assumption should be verified before a system is fielded. A single axis tracking system must be in precise mechanical alignment to minimize loss due to the mount’s inability to compensate for the width of the figure eight pattern. -
Measurement Techniques and New Technologies for Satellite Monitoring
Report ITU-R SM.2424-0 (06/2018) Measurement techniques and new technologies for satellite monitoring SM Series Spectrum management ii Rep. ITU-R SM.2424-0 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio- frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statements and licensing declarations by patent holders are available from http://www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Reports (Also available online at http://www.itu.int/publ/R-REP/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodetermination, amateur and related satellite services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management Note: This ITU-R Report was approved in English by the Study Group under the procedure detailed in Resolution ITU-R 1.