DOCSLIB.ORG

Trajectory Predictions for High Eccentricity Orbits of Space Debris Objects

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Trajectory Predictions for High Eccentricity Orbits of Space Debris Objects TRAJECTORY PREDICTIONS FOR HIGH ECCENTRICITY ORBITS OF SPACE DEBRIS OBJECTS D. Kruzynska, R. Pospieszynski, M. Kruzynski, J. Golebiewska, and E. Wnuk Astronomical Observatory Institute, Faculty of Physics, A. Mickiewicz University, Sloneczna 36, 60-286 Poznan, Poland, email: [email protected] ABSTRACT solar effects, solar radiation pressure and influence of Earth’s atmosphere. For satellites with altitude of perigee higher than 1000 km perturbations from the atmosphere Since 1957 the number of space debris has been increas- are negligible. However, for objects reaching very low ing and it cause threat of collision. To calculate precisely perigee altitude atmosphere is the most important per- space debris orbit we used several perturbations in our turbation. We used NRMLMSISE-00 empirical atmo- force model: geopotential, luni-solar effects, solar radi- spheric model in our calculations. Besides date and exact ation pressure and influence of Earth’s atmosphere. For place we have to include all necessary solar activity data satellites with altitude of perigee higher than 1000 km like local apparent solar time, 81 day average of F10.7 so- perturbations from the atmosphere is negligible. How- lar flux, daily F10.7 solar flux for previous day and daily ever for objects which reaches its lower parts is one of magnetic index. One of¡ the most influential parameter is S the most important perturbation. For the last perturbation area-to-mass ratio m . Small changes in the parame- we used NRMLMSISE-00 empirical model to calculate ter cause significant changes in satellite orbit prediction. precise parameters for the atmosphere. For large amount In this paper we have examined the influence on satellites of objects using numerical integration there appears to be orbits by using different value of this parameter. Also, for a problem with time of calculations. For this reason, we some objects’ population, with real data from TLE Cat- decided to use analytical model, which is much faster and alogue we have calculated some short and medium-term more convenient. Due to highly elliptical orbit we had to orbits using both analytical and numerical integration. exchange the eccentricity function by the Hansen coeffi- cients. 2. HEO OBJECTS IN TLE SATELLITE CATA- Key words: HEO, Highly Elliptical Orbit, Space debris, LOGUE Orbit Propagation. On 19 April 2013, there are 14941 objects in the 1. INTRODUCTION Two/Three Line Element Set (TLE) Satellite Catalogue and 16859 objects in the Satellite Situation Raport (SSR) which are still on Earth orbit. This includes 2526 objects Highly Elliptical Orbit (HEO) is an orbit with a low alti- with e > 0:4. Furthermore, 653 objects have altitude tude of perigee and high altitude of apogee. The HEO of perigee higher than 1000 km and 1873 lower. Fig. orbit usually crosses the Low Earth Orbit (LEO) and 1 shows the distribution of the orbital elements for 520 reaches regions even higher than Geostationary Earth Or- HEO objects with the eccentricity e > 0:4, perigee alti- bit (GEO). This kind of orbit has high eccentricity which tude q > 800 km and apogee altitude Q < 52000 km. can reach 0:7 0:8 value. The number of objects on HEO Semi-major axis definitely concentrates on value around orbits is high and increases. HEO objects could cause 26500 km. The majority of objects have the eccentricity hazard while in perigee due to their extremely high ve- around 0.55 and 0.72. The number of objects have the locity. In such case the most threatened objects are LEO inclination from 0 to 30, but most of them concentrate satellites. To predict and avoid a collision we have to de- around the critical inclination. terminate the orbit of a satellite precisely. In such case, long-term orbit propagation is useless. In our work we performed only short and medium-term predictions. For short-term propagation trajectories are calculated only for 3. FORCE MODEL FOR HEO ORBITS a few revolutions with high accuracy and medium-term predictions up to several weeks with less precision. To calculate precisely space debris orbits we used the force Space debris objects moving in the HEO region are model including perturbations from: geopotential, luni- strongly perturbed by geopotential and atmospheric drag _____________________________________ Proc. ‘6th European Conference on Space Debris’ Darmstadt, Germany, 22–25 April 2013 (ESA SP-723, August 2013) when they are close to their perigee, and by luni-solar ef- fects and solar radiation pressure in apogee. Precise mod- TLE Satellite orbits distribution eling of the HEO orbits is therefore very complicated task for e>0.4 altitude of perigee >800 km in the semi-major axis both in the case of analytical and numerical prediction 140 method applied. To keep an appropriate accuracy level of 120 trajectory prediction, all perturbing forces have to be in- cluded and modeled with very high precision. Prediction 100 algorithms for HEO have to be used in a specific way. 80 In the case of analytical methods, one of the most diffi- 60 cult cases is the calculation of the eccentricity function Glpq(e) values, for e = 0:7 0:8 and for high indices. Number of objects 40 20 0 10000 15000 20000 25000 30000 35000 Semi-major axis [km] 4. THE APPLIED ORBITAL MODEL TLE Satellite orbits distribution for e>0.4 altitude of perigee >800 km in the eccentricity 25 Predicted HEO orbits were calculated with the use of or- bital software tool developed in the Astronomical Obser- 20 vatory of the Adam Mickiewicz University in Poznan, Poland [3]. The tool works both in analytical and nu- 15 merical modes and includes influence of the following perturbing forces: 10 Number of objects 5 ~ ~ ~ ~ ~ ~ 0 ~r = (F0 + FG + FM + FS + FSR + FA)=m; (1) 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Eccentricity TLE Satellite orbits distribution for e>0.4 altitude of perigee >800 km where : in the inclination 70 60 50 ~ F0 is the keplerian term; 40 ~ FG 30 is the perturbation force due to ; 20 the geopotential Number of objects ~ 10 FM is the perturbation force due to 0 the Moon gravity; 0 10 20 30 40 50 60 70 80 90 100 o ~ Inclination [ ] FS is the perturbation force due to ; TLE Satellite orbits distribution the Sun gravity for e>0.4 altitude of perigee >800 km ~ in the perigee FSR is the perturbation force due to 80 the solar radiation pressure; 70 ~ 60 FA is the perturbation force due to 50 the atmospheric drag: 40 30 Number of objects 20 10 To get high precision of calculations we used the 0 NRLMSISE-00 atmosphere model. Unfortunately in so- 0 2000 4000 6000 8000 10000 12000 lar radiation pressure we didn’t use the shadow function. Perigee [km] Presented results have been obtained for the orbit of ob- Figure 1. Distribution of the semi-major axis, inclination, ject No. 23840 - ATLAS 2A CENTAUR R/B. The epoch eccentricity and altitude of perigee for 520 HEO objects of initial orbital elements was 2013/4/8.4214020700. We e > 0:4 with the eccentricity and with the perigee altitude used exact values of orbital elements from TLE Satellite q > 800 Q < 52000 km and apogee altitude km. Catalogue, which are shown in Tab. 1. As we can see the eccentricity of this object is really high, therefore, we have applied the value of index q = 50. Atmospheric perturbations Table 1. Set of initial input orbital elements. 0.12 S/m=0.02 a (km) 24656.4396648861 S/m=0.05 e 0.7008709 0.1 S/m=0.10 i (deg) 21.0075 ! (deg) 89.2578 0.08 (deg) 175.2247 0.06 M (deg) 5.5452 n (rev/day) 2.24209852 0.04 0.02 Changes in position vector r [km] 4.1. The eccentricity function 0 0 0.5 1 1.5 2 time [days] To calculate precisely orbital elements of the HEO ob- Solar radiation pressure perturbations 1.4 jects we have to use the Hansen coefficients instead of S/m=0.02 G (e) S/m=0.05 Kaula’s eccentricity function lpq which is related to 1.2 S/m=0.10 the Hansen function by the following relation: 1 0.8 (l 1);(l 2p) Glpq(e) = X (e) (2) l 2p+q 0.6 0.4 We calculated the Hansen function using the following formula [1] [2]: Changes in position vector r [km] 0.2 0 0 0.5 1 1.5 2 1 X1 time [days] X(k) = En;mJ (ke); n;m (1 + 2)n+1 k l l (3) l= 1 Figure 2. Changes in position vector due to the at- mospheric drag and solar radiation pressure perturba- tions which are dependent on S/m parameter. Each color where: presents different S/m parameter value. e Sun gravity perturbations = p ; (4) 35 1 + 1 e2 30 and 25 20 X1 15 n;m k l m k l m+s s 2s Ek l = ( ) Cn m+1 Cn+m+1 ; (5) 10 s=0 Changes in position vector r [km] 5 0 0.5 1 1.5 2 and Jl(ke) are the Bessel functions of the first kind. The time [days] Bessel function J0(ke) is calculated directly from the Moon gravity perturbations definition for small values of ke (ke < 20), and from Ja- 35 cobi asymptotic formula for the higher values. All other 30 Bessel functions Jl(ke); l > 0 are calculated by succes- 25 sive multiplication of J0(ke) by ps factors, that are deter- mined from the following recursive relation: 20 15 1 10 ps = : (6) 2s=ke ps+1 Changes in position vector r [km] 5 0 Then, 0 0.5 1 1.5 2 time [days] Figure 3.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Three-Apogee 16-H Highly Elliptical Orbit As Optimal Choice for Continuous Meteorological Imaging of Polar Regions
    NOVEMBER 2011 T R I S H C H E N K O E T A L . 1407 Three-Apogee 16-h Highly Elliptical Orbit as Optimal Choice for Continuous Meteorological Imaging of Polar Regions ALEXANDER P. TRISHCHENKO* Network Strategy and Design, Meteorological Service of Canada, Environment Canada, Ottawa, Ontario, Canada LOUIS GARAND Data Assimilation and Satellite Meteorology Research, Science and Technology Branch, Environment Canada, Dorval, Quebec, Canada LARISA D. TRICHTCHENKO Canadian Space Weather Forecast Center, Earth Sciences Sector, Natural Resources Canada, Ottawa, Ontario, Canada (Manuscript received 18 March 2011, in final form 24 June 2011) ABSTRACT A highly elliptical orbit (HEO) with a 16-h period is proposed for continuous meteorological imaging of polar regions from a two-satellite constellation. This orbit is characterized by three apogees (TAP) separated by 1208. The two satellites are 8 h apart, with repeatable ground track in the course of 2 days. Advantages are highlighted in comparison to the Molniya 12-h orbit described in detail in a previous study (Trishchenko and Garand). Orbital parameters (period, eccentricity, and inclination) are obtained as a result of an optimization process. The principles of orbit optimization are based on the following four key requirements: spatial res- olution (apogee height), the altitude of crossing the trapped proton region at the equator (minimization of radiation doze caused by trapped protons), imaging time over the polar regions, and the stability of the orbit, which is mostly defined by the rotation of perigee. The interplay between these requirements points to a 16-h period with an eccentricity of 0.55 as the optimum solution.
    [Show full text]
  • Artifical Earth-Orbiting Satellites
    Artifical Earth-orbiting satellites László Csurgai-Horváth Department of Broadband Infocommunications and Electromagnetic Theory The first satellites in orbit Sputnik-1(1957) Vostok-1 (1961) Jurij Gagarin Telstar-1 (1962) Kepler orbits Kepler’s laws (Johannes Kepler, 1571-1630) applied for satellites: 1.) The orbit of a satellite around the Earth is an ellipse, one focus of which coincides with the center of the Earth. 2.) The radius vector from the Earth’s center to the satellite sweeps over equal areas in equal time intervals. 3.) The squares of the orbital periods of two satellites are proportional to the cubes of their semi-major axis: a3/T2 is equal for all satellites (MEO) Kepler orbits: equatorial coordinates The Keplerian elements: uniquely describe the location and velocity of the satellite at any given point in time using equatorial coordinates r = (x, y, z) (to solve the equation of Newton’s law for gravity for a two-body problem) Z Y Elements: X Vernal equinox: a Semi-major axis : direction to the Sun at the beginning of spring e Eccentricity (length of day==length of night) i Inclination Ω Longitude of the ascending node (South to North crossing) ω Argument of perigee M Mean anomaly (angle difference of a fictitious circular vs. true elliptical orbit) Earth-centered orbits Sidereal time: Earth rotation vs. fixed stars One sidereal (astronomical) day: one complete Earth rotation around its axis (~4min shorter than a normal day) Coordinated universal time (UTC): - derived from atomic clocks Ground track of a satellite in low Earth orbit: Perturbations 1. The Earth’s radius at the poles are 20km smaller (flattening) The effects of the Earth's atmosphere Gravitational perturbations caused by the Sun and Moon Other: .
    [Show full text]
  • Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-Entry
    ORIGINAL RESEARCH published: 02 July 2019 doi: 10.3389/fspas.2019.00034 Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry Camilla Colombo* Department of Aerospace Science and Technology, Politecnico di Milano, Milan, Italy This paper investigates the long-term evolution of spacecraft in Highly Elliptical Orbits (HEOs). The single averaged disturbing potential due to luni-solar perturbations, zonal harmonics of the Earth gravity field is written in mean Keplerian elements. The double averaged potential is also derived in the Earth-centered equatorial system. Maps of long-term orbit evolution are constructed by measuring the maximum variation of the orbit eccentricity to identify conditions for quasi-frozen, long-lived libration orbits, or initial orbit Edited by: conditions that naturally evolve toward re-entry in the Earth’s atmosphere. The behavior Josep Masdemont, Universitat Politecnica de of these long-term orbit maps is studied for increasing values of the initial orbit inclination Catalunya, Spain and argument of the perigee with respect to the Moon’s orbital plane. In addition, to allow Reviewed by: meeting specific mission constraints, quasi-frozen orbits can be selected as graveyard Eduard D. Kuznetsov, orbits for the end-of-life of HEO missions, in the case re-entry option cannot be achieved Ural Federal University, Russia Catalin Bogdan Gales, due to propellant constraints. On the opposite side, unstable conditions can be exploited Alexandru Ioan Cuza to target Earth re-entry
    [Show full text]
  • Glossary of Terms
    Glossary of Terms Near-Earth Object (NEO): An asteroid or comet with a perihelion distance less than or equal to 1.3 AU. 99% of NEOs are asteroids. Ecliptic plane: Plane of the Earth’s orBit. Orbital parameters: 6 parameters that completely define an object’s orbit: Semi-major axis (a): One half of the major axis of the elliptical orBit; also the mean distance from the Sun. Eccentricity (e): A measure of the ellipticity of the orbit; e = 0 for a circular orBit, e is nearly 1 for a highly elliptical orbit. Inclination (i): Angle between the orbit plane and the ecliptic plane, Longitude of the ascending node (Ω): Angle in the ecliptic plane between the inertial-frame x- axis and the line through the ascending node. Argument of perihelion (ω): Angle in the orbit plane between the ascending node and the perihelion point. True anomaly (ν): Angle in the orbit plane between the perihelion point and the position of the orbiting object. Line of nodes: The line of intersection Between the orBit plane and the plane of the ecliptic (the Earth’s orBit plane). (Not defined if orbit lies exactly in the plane of the ecliptic.) Nodal points: The two points at which an orBit crosses through the ecliptic. The potential impact occurs at one of these points. Ascending node: Point on the orBit where the oBject “ascends” through the ecliptic plane, passing from below it to aBove it. Descending node: Point on the orBit where the oBject “descends” through the ecliptic plane, passing from above it to below it.
    [Show full text]
  • A Mean Elements Orbit Propagator Program for Highly Elliptical Orbits
    CEAS Space Journal manuscript No. (will be inserted by the editor) HEOSAT: A mean elements orbit propagator program for Highly Elliptical Orbits Martin Lara · Juan F. San-Juan · Denis Hautesserres CEAS Space Journal (ISSN: 1868-2502, ESSN: 1868-2510) (2018) doi:10.1007/s12567-017-0152-x (Pre-print version) Abstract The algorithms used in the construction of a semi- intermediary solutions to the J2 problem [34,11], the contin- analytical propagator for the long-term propagation of High- uous increase in the accuracy of observations demanded the ly Elliptical Orbits (HEO) are described. The software prop- use of more complex dynamical models to achieve a sim- agates mean elements and include the main gravitational and ilar precision in the orbit predictions. In particular higher non-gravitational effects that may affect common HEO or- degrees in the Legendre polynomials expansion of the third- bits, as, for instance, geostationary transfer orbits or Mol- body disturbing function are commonly required (see [17, niya orbits. Comparisons with numerical integration show 24], for instance). Useful analytical theories needed to deal that it provides good results even in extreme orbital config- with a growing number of effects, a fact that made that the urations, as the case of SymbolX. trigonometric series evaluated by the theory comprised tens of thousands of terms [5]. Keywords HEO · Geopotential · third-body perturbation · In an epoch of computational plenty, the vast possibili- tesseral resonances · SRP · atmospheric drag · mean ties offered by special perturbation methods clearly surpass elements · semi-analytic propagation those of general perturbation methods in their traditional application to orbit propagation.
    [Show full text]
  • Development of Techniques to Study the Dynamic of Highly Elliptical Orbits
    SF2A 2011 G. Alecian, K. Belkacem, R. Samadi and D. Valls-Gabaud (eds) DEVELOPMENT OF TECHNIQUES TO STUDY THE DYNAMIC OF HIGHLY ELLIPTICAL ORBITS G. Lion1 and G. M´etris1 Abstract. Many spacecrafts are or will be placed in highly eccentric orbits around telluric planets of the Solar system. Such eccentricities allow to cover a wide range of altitudes, mainly for planetology purposes. There are also orbits with very high eccentricity around the Earth, especially the GTO (Geostationary Transfer Orbit) and orbits of some space debris. In this case, the motion is strongly perturbed by the luni- solar attraction. For various reasons which will be recalled, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly eccentric orbits. Therefore, it is necessary to develop specific techniques for this configuration. This concerns numerical as well as analytical tools. We will show how to construct the expression of the disturbing function due to the presence of an external body, well- suited for highly eccentric orbits. Expansion of the elliptic motion in closed-form by using Fourier series in multiple of the eccentric anomaly will be presented. On the other hand, classical methods of numerical integration have often a poor efficiency. We will show the interest of geometric integrators and in particular the variational integrators. Keywords: Third-body, disturbing function, Hansen-like coefficients, elliptic motion, high eccentricity, closed-form, variational integrators 1 Introduction When dealing with highly elliptical orbits, we have to face several difficulties. Due to the fact that such orbits cover a wide range of altitudes, the hierarchy of the perturbations acting on the satellite changes with the position on the orbit.
    [Show full text]