A Mean Elements Orbit Propagator Program for Highly Elliptical Orbits
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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. -
A Highly Elliptical Orbit Space System for Hydrometeorological Monitoring of the Arctic Region by V
A highly elliptical orbit space system for hydrometeorological monitoring of the Arctic region by V. V. Asmus1, V. N. Dyadyuchenko2, Y. I. Nosenko3, G. M. Polishchuk4 and V. A. Selin3 The lack of reliable, frequently high latitudes. It has therefore been • Monitoring of climate change updated information on the Earth’s suggested that demonstration of polar ice caps is a signifi cant problem a hydrometeorological system of • Data collection and relay for weather forecasting, affecting satellites on highly elliptical orbit from land-, sea- and air-based forecast skill for the entire planet. The (HEO), called the “Arctica” system, observing platforms poor numerical weather prediction should be created to provide the (NWP) skill for the Arctic region necessary complex information for the • Exchange and dissemination of and the Earth’s northern territories diffi cult tasks involved in developing processed hydrometeorological is caused primarily by errors in the whole Arctic region. and heliogeophysical data. determining initial conditions, which depend on the quality of initial Signifi cantly, the hydrometeorological Further progress in global and data. Until now, initial data have observations carried out in the regional numerical weather prediction been received from meteorological Arctic within the framework of the depends to a large extent on: geostationary satellites, which are International Polar Year 2007-2008 not very effective in scanning high are not provided with remote-sensing • Quasi-continuous reception latitudes and polar-orbiting -
GPS Applications in Space
Space Situational Awareness 2015: GPS Applications in Space James J. Miller, Deputy Director Policy & Strategic Communications Division May 13, 2015 GPS Extends the Reach of NASA Networks to Enable New Space Ops, Science, and Exploration Apps GPS Relative Navigation is used for Rendezvous to ISS GPS PNT Services Enable: • Attitude Determination: Use of GPS enables some missions to meet their attitude determination requirements, such as ISS • Real-time On-Board Navigation: Enables new methods of spaceflight ops such as rendezvous & docking, station- keeping, precision formation flying, and GEO satellite servicing • Earth Sciences: GPS used as a remote sensing tool supports atmospheric and ionospheric sciences, geodesy, and geodynamics -- from monitoring sea levels and ice melt to measuring the gravity field ESA ATV 1st mission JAXA’s HTV 1st mission Commercial Cargo Resupply to ISS in 2008 to ISS in 2009 (Space-X & Cygnus), 2012+ 2 Growing GPS Uses in Space: Space Operations & Science • NASA strategic navigation requirements for science and 20-Year Worldwide Space Mission space ops continue to grow, especially as higher Projections by Orbit Type* precisions are needed for more complex operations in all space domains 1% 5% Low Earth Orbit • Nearly 60%* of projected worldwide space missions 27% Medium Earth Orbit over the next 20 years will operate in LEO 59% GeoSynchronous Orbit – That is, inside the Terrestrial Service Volume (TSV) 8% Highly Elliptical Orbit Cislunar / Interplanetary • An additional 35%* of these space missions that will operate at higher altitudes will remain at or below GEO – That is, inside the GPS/GNSS Space Service Volume (SSV) Highly Elliptical Orbits**: • In summary, approximately 95% of projected Example: NASA MMS 4- worldwide space missions over the next 20 years will satellite constellation. -
Librational Response of Europa, Ganymede, and Callisto with an Ocean for a Non-Keplerian Orbit
A&A 527, A118 (2011) Astronomy DOI: 10.1051/0004-6361/201015304 & c ESO 2011 Astrophysics Librational response of Europa, Ganymede, and Callisto with an ocean for a non-Keplerian orbit N. Rambaux1,2, T. Van Hoolst3, and Ö. Karatekin3 1 Université Pierre et Marie Curie, Paris VI, IMCCE, Observatoire de Paris, 77 avenue Denfert-Rochereau, 75014 Paris, France 2 IMCCE, Observatoire de Paris, CNRS UMR 8028, 77 avenue Denfert-Rochereau, 75014 Paris, France e-mail: [email protected] 3 Royal Observatory of Belgium, 3 avenue Circulaire, 1180 Brussels, Belgium e-mail: [tim.vanhoolst;ozgur.karatekin]@oma.be Received 30 June 2010 / Accepted 8 September 2010 ABSTRACT Context. The Galilean satellites Europa, Ganymede, and Callisto are thought to harbor a subsurface ocean beneath an ice shell but its properties, such as the depth beneath the surface, have not been well constrained. Future geodetic observations with, for example, space missions like the Europa Jupiter System Mission (EJSM) of NASA and ESA may refine our knowledge about the shell and ocean. Aims. Measurement of librational motion is a useful tool for detecting an ocean and characterizing the interior parameters of the moons. The objective of this paper is to investigate the librational response of Galilean satellites, Europa, Ganymede, and Callisto assumed to have a subsurface ocean by taking the perturbations of the Keplerian orbit into account. Perturbations from a purely Keplerian orbit are caused by gravitational attraction of the other Galilean satellites, the Sun, and the oblateness of Jupiter. Methods. We use the librational equations developed for a satellite with a subsurface ocean in synchronous spin-orbit resonance. -
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. -
Nonlinear Filtering for Autonomous Navigation of Spacecraft in Highly Elliptical Orbit
Nonlinear Filtering for Autonomous Navigation of Spacecraft in Highly Elliptical Orbit by Adam C. Vigneron, B.Sc.(Eng.) A thesis submitted to the Faculty of Graduate and Postdoctoral Affairs in partial fulfillment of the requirements for the degree of Master of Applied Science Ottawa-Carleton Institute for Mechanical and Aerospace Engineering Department of Mechanical and Aerospace Engineering Carleton University Ottawa, Ontario May, 2014 c Copyright Adam C. Vigneron, 2014 The undersigned hereby recommends to the Faculty of Graduate and Postdoctoral Affairs acceptance of the thesis Nonlinear Filtering for Autonomous Navigation of Spacecraft in Highly Elliptical Orbit submitted by Adam C. Vigneron, B.Sc.(Eng.) in partial fulfillment of the requirements for the degree of Master of Applied Science Professor Anton H. J. de Ruiter, Thesis Supervisor Professor Bruce Burlton, Thesis Co-supervisor Professor Alex Ellery, Thesis Co-supervisor Professor Metin Yaras, Chair, Department of Mechanical and Aerospace Engineering Ottawa-Carleton Institute for Mechanical and Aerospace Engineering Department of Mechanical and Aerospace Engineering Carleton University May, 2014 ii Abstract To fill a gap in satellite services for the Canadian Arctic, the Canadian Space Agency has proposed a Polar Communication and Weather (PCW) mission to be flown in a highly elliptical Molniya orbit. In an era of increasingly capable space hardware, au- tonomous satellite navigation has become a standard means by which satellites in low Earth orbit can increase their independence and functionality. This study examined the accuracy to which autonomous navigation might be realized in a Molniya orbit. Using appropriate physical force models and simulated pseudorange signals from the Global Positioning System (GPS), a navigation algorithm based on the Extended Kalman Filter was demonstrated to achieve a three-dimensional root-mean-square accuracy of 58:9 m over a 500 km ¢ 40 000 km Molniya orbit. -
Synopsis of Euler's Paper E105
1 Synopsis of Euler’s paper E105 -- Memoire sur la plus grande equation des planetes (Memoir on the Maximum value of an Equation of the Planets) Compiled by Thomas J Osler and Jasen Andrew Scaramazza Mathematics Department Rowan University Glassboro, NJ 08028 [email protected] Preface The following summary of E 105 was constructed by abbreviating the collection of Notes. Thus, there is considerable repetition in these two items. We hope that the reader can profit by reading this synopsis before tackling Euler’s paper itself. I. Planetary Motion as viewed from the earth vs the sun ` Euler discusses the fact that planets observed from the earth exhibit a very irregular motion. In general, they move from west to east along the ecliptic. At times however, the motion slows to a stop and the planet even appears to reverse direction and move from east to west. We call this retrograde motion. After some time the planet stops again and resumes its west to east journey. However, if we observe the planet from the stand point of an observer on the sun, this retrograde motion will not occur, and only a west to east path of the planet is seen. II. The aphelion and the perihelion From the sun, (point O in figure 1) the planet (point P ) is seen to move on an elliptical orbit with the sun at one focus. When the planet is farthest from the sun, we say it is at the “aphelion” (point A ), and at the perihelion when it is closest. The time for the planet to move from aphelion to perihelion and back is called the period. -
Absolute and Relative Motion Satellite Theories for Zonal and Tesseral Gravitational Harmonics
ABSOLUTE AND RELATIVE MOTION SATELLITE THEORIES FOR ZONAL AND TESSERAL GRAVITATIONAL HARMONICS A Dissertation by BHARAT MAHAJAN Submitted to the Office of Graduate and Professional Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Chair of Committee, Srinivas R. Vadali Co-Chair of Committee, Kyle T. Alfriend Committee Members, John E. Hurtado Igor Zelenko Head of Department, Rodney Browersox May 2018 Major Subject: Aerospace Engineering Copyright 2018 Bharat Mahajan ABSTRACT In 1959, Dirk Brouwer pioneered the use of the Hamiltonian perturbation methods for con- structing artificial satellite theories with effects due to nonspherical gravitational perturbations in- cluded. His solution specifically accounted for the effects of the first few zonal spherical harmon- ics. However, the development of a closed-form (in the eccentricity) satellite theory that accounts for any arbitrary spherical harmonic perturbation remains a challenge to this day. In the present work, the author has obtained novel solutions for the absolute and relative motion of artificial satel- lites (absolute motion in this work refers to the motion relative to the central gravitational body) for an arbitrary zonal or tesseral spherical harmonic by using Hamiltonian perturbation methods, without resorting to expansions in either the eccentricity or the small ratio of the satellite’s mean motion and the angular velocity of the central body. First, generalized closed-form expressions for the secular, long-period, and short-period variations of the equinoctial orbital elements due to an arbitrary zonal harmonic are derived, along with the explicit expressions for the first six zonal harmonics. -
NOAA Technical Memorandum ERL ARL-94
NOAA Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERIS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOAA 'Technical Memorandum ERL ARL-94 THE NOAA SOLAR EPHEMERlS PROGRAM Albion D. Taylor Air Resources Laboratories Silver Spring, Maryland January 1981 NOTICE The Environmental Research Laboratories do not approve, recommend, or endorse any proprietary product or proprietary material mentioned in this publication. No reference shall be made to the Environmental Research Laboratories or to this publication furnished by the Environmental Research Laboratories in any advertising or sales promotion which would indicate or imply that the Environmental Research Laboratories approve, recommend, or endorse any proprietary product or proprietary material mentioned herein, or which has as its purpose an intent to cause directly or indirectly the advertised product to be used or purchased because of this Environmental Research Laboratories publication. Abstract A system of FORTRAN language computer programs is presented which have the ability to locate the sun at arbitrary times. On demand, the programs will return the distance and direction to the sun, either as seen by an observer at an arbitrary location on the Earth, or in a stan- dard astronomic coordinate system. For one century before or after the year 1960, the program is expected to have an accuracy of 30 seconds 5 of arc (2 seconds of time) in angular position, and 7 10 A.U. in distance. A non-standard algorithm is used which minimizes the number of trigonometric evaluations involved in the computations. 1 The NOAA Solar Ephemeris Program Albion D. Taylor National Oceanic and Atmospheric Administration Air Resources Laboratories Silver Spring, MD January 1981 Contents 1 Introduction 3 2 Use of the Solar Ephemeris Subroutines 3 3 Astronomical Terminology and Coordinate Systems 5 4 Computation Methods for the NOAA Solar Ephemeris 11 5 References 16 A Program Listings 17 A.1 SOLEFM . -
Euler's Forgotten Equation of the Center
Advances in Historical Studies, 2021, 10, 44-52 https://www.scirp.org/journal/ahs ISSN Online: 2327-0446 ISSN Print: 2327-0438 Euler’s Forgotten Equation of the Center Sylvio R. Bistafa University of São Paulo, São Paulo, Brazil How to cite this paper: Bistafa, S. R. Abstract (2021). Euler’s Forgotten Equation of the Center. Advances in Historical Studies, 10, In a 1778 publication in Latin, titled Nova Methodvs Motvm Planetarvm De- 44-52. terminandi (New method to determine the motion of planets), Euler derives https://doi.org/10.4236/ahs.2021.101005 an equation of the center, which, apparently, has been forgotten. In the present work, the developments that led to Euler’s equation of the center are Received: January 9, 2021 Accepted: March 12, 2021 revisited, and applied to three planets of the Solar System. These are then Published: March 15, 2021 compared with results obtained from an equation of center that has been proposed, showing good agreement for planets with not so high eccentrici- Copyright © 2021 by author(s) and ties. Nonetheless, Euler’s derivation was not influential, and since then, the Scientific Research Publishing Inc. resulting equation of the center has been neglected by scholars and by specia- This work is licensed under the Creative Commons Attribution International lized publications alike. License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Keywords Open Access Euler’s Works on Astronomy, Equation of the Center, History of Orbital Calculations, Investigations on Planets’ Orbits, Astronomical Calculations, Keplerian Orbital Mechanics 1. Introduction Since antiquity, the problem of predicting the motions of the heavenly bodies has been simplified by reducing it to one of a single body in orbit about another. -
End-Of-Life Disposal Concepts for Libration Point and Highly Elliptical Orbit Missions
(Preprint) IAA -AAS -DyCoSS2 -03 -01 END-OF-LIFE DISPOSAL CONCEPTS FOR LIBRATION POINT AND HIGHLY ELLIPTICAL ORBIT MISSIONS Camilla Colombo 1, Francesca Letizia 2, Stefania Soldini 3, Hugh Lewis 4, Elisa Maria Alessi 5, Alessandro Rossi 6, Massimiliano Vasile 7, Massimo Vetrisano 8, Willem Van der Weg 9, Markus Landgraf 10 Libration Point Orbits (LPOs) and Highly Elliptical Orbits (HEOs) are often se- lected for astrophysics and solar terrestrial missions. No guidelines currently ex- ist for their end-of life, however it is a critical aspect to other spacecraft and on- ground safety. This paper presents an analysis of possible disposal strategies for LPO and HEO missions as a result of an ESA study. The dynamical models and the design approach are presented. Five missions are selected: Herschel, Gaia, SOHO as LPOs, and INTEGRAL and XMM-Newton as HEOs. A trade-off is made considering technical feasibility, as well as the sustainability context and the collision probability. INTRODUCTION Libration Point Orbits (LPOs) and Highly Elliptical Orbits (HEOs) are often selected for as- trophysics and solar terrestrial missions as they offer vantage points for the observation of the Earth, the Sun and the Universe. Orbits around L 1 and L 2 are relatively inexpensive to be reached from the Earth and ensure a nearly constant geometry for observation and telecoms, in addition to advantages for thermal system design. On the other hand, HEOs about the Earth guarantee long dwelling times at an altitude outside the Earth’s radiation belt; therefore, long periods of uninter- rupted scientific observation are possible with nearly no background noise from radiations. -
19740004369.Pdf
IA-4 TheOrbitalMechanics of Fli_htMechanics A--A Am-m ---_._ _--_-_ :5::_¸¸¸:_:::_!_:_:_i:::_!:i:_:._::::_:i_;::::,::::,:::_:.:::i::i¸:5: ::':?::!:i:!:!:!:!::':i:i:::::::;_:;::_,.'__;_:::::::........... .... ===================================================: )) T .... -...: ==================================================================================================================================== ...... :::7:_))_):)):::_:i!._...............iii_i)))))))i)i):_::_)i0j))::::!:):::))))):)).." •.........)i'::::_).............!:!:i_)i::i)iii)))))i!_. L-73-3009 Apollo 9 Landing Module as viewed from the Comm_md Module in orbit over the earth. ii ! ,\ \ i ii-il NASASP-325 TheOrbitalMechanics of Fli_htMechanics RobertScottDunnin_ LangleyResearchCenter PreparedbyNASALangleyResearchCenter Scientific and Technical ln/ormation Office 1973 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION _ Washington, D.C. If If 1 lf_;;_:'_,-li'-,,_,. A-AA A-I v_? V For sale by the National Technical Information Service Springfield, Virginia 22151 Price - Domestic, $4.75; Foreign, $7.25 Library of Congress Catalog Card Number 73-600091 ,WTT i di-ll PREFACE Despite the existence of numerous authoritative books in the field of orbital mechanics, the author has felt the need for a book which places emphasis on the con- ditions encountered with actively controlled satellites and spaceships rather than on observation and analysis of the passive heavenly bodies treated in classical astron- omy. Present-day space research, includiflg the use of computers, has made much of the material in previous books outmoded; less emphasis is now placed on closed-form solutions and more on iterative techniques. It is also apparent that a greater empha- sis on the basic formulas has become necessary. The problem of relative motion between two vehicles, which was rarely encountered in classical astronomy, has become a routine operational matter today and deserves consideration appropriate to its present importance.