Space systems Determining orbit lifetime

ISO 2004 All rights reserved Reference number of working document: ISO/TC 20/SC 14 27852 Date: 2007-04-25 Reference number of document: ISO/CD/27852 Committee identification: ISO/TC 20/SC 14/WG 3 Secretariat: ANSI Space systems Determining orbit lifetime Titre Titre Partie n: Titre de la partie Warning This document is not an ISO International Standard. It is distributed for review and comment. It is subject to change without notice and may not be referred to as an International Standard. Recipients of this document are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation. Document type: International standard Document subtype: Document stage: (00)NWIP Stage Document language: E

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Contents 1 Scope... 1 2 Normative References... 1 3 Definitions, symbols and abbreviated terms... 1 3.1 Definitions... 1 3.1.1 Orbit lifetime... 1 3.1.2 Long-duration orbit lifetime prediction... 1 3.1.3 LEO-crossing orbit... 1 3.1.4 ephemeris... 2 3.1.5 orbit... 2 3.1.6 solar cycle... 2 3.2 Symbols and abbreviated terms... 3 4 Orbit Lifetime Assessment... 3 4.1 General Requirements... 3 4.2 Definition of Orbit Lifetime Estimation Process... 3 4.3 Orbit Lifetime Assessment Methods and Applicability... 4 4.3.1 Method 1: Numerical Table Look-Up... 4 4.3.2 Method 2: Rapid semi-analytical orbit propagation... 5 4.3.3 Method 3: High-order numerical integration... 5 5 Atmospheric density modeling... 6 5.1 Atmospheric Drag Models... 6 5.2 Long-Duration Solar Flux and Geomagnetic Indices Prediction... 7 Bibliography... 11 (informative) Space population distribution... 12 A.1 Space object distribution... 12 Annex B (informative) Definition of current launch hold practices & criteria. Error! Bookmark not defined. B.1 General... Error! Bookmark not defined. Annex C (informative) TBD... 13 C.1 General... 13 iii

Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and nongovernmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this part of ISO may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. This International Standard was prepared by Technical Committee ISO/TC 20, Aircraft and Space Vehicles, Subcommittee SC 14, Space Systems and Operations. iv

Introduction A spacecraft is exposed to the risk of collision with orbital debris and operational satellites throughout its launch and early orbit phase. This risk is especially high during passage through the LEO region and when inserting into specific orbital belts (e.g., geosynchronous or Molniya orbit regimes). It is been widely advocated by the Inter- Agency Space Debris Coordination Committee (IADC) that spacecraft and constellation designers ensure their spacecraft do not continue to occupy the LEO-crossing orbit regime for more than a specified duration of time after their end-of-life to minimize such collision risk. Specific recommendations (IADC presentation to the 41st Session of the Scientific and Technical Subcommittee, United Nations Committee on the Peaceful Uses of Outer Space) are that (1) Systems terminating operational phases in orbits passing through the LEO region should be de-orbited or, where appropriate, manoeuvred to an orbit with suitably-reduced lifetime; (2) Systems should be left in an orbit where drag and other perturbations will limit lifetime after completion of operations; and (3) a reasonable and appropriate duration of time can be specified as the post-mission orbital lifetime for LEO-crossing orbits to reduce collision rate in LEO. The commonality between these three guidelines is the ability to assess orbital lifetime. Ensuring that a spacecraft designer s spacecraft meet or exceed these IADC lifetime guidelines will reduce overall space population growth over the long-term and will reduce space population within specific, crowded orbital regimes. Yet, the assessment of orbital lifetime is not a simple task; recent studies have shown that higher-order, long-term orbit perturbations can drastically affect orbital lifetime of selected orbits and initial conditions if not modelled or modelled inappropriately. This project offers standardized guidance and methods to assess orbital lifetime for all LEOcrossing orbit classes. This international standard serves to help reduce long-term collision risk in the LEO orbit regime by ensuring that the pre-launch assessment of orbital lifetime is done carefully and accurately, using standardized analysis methods. v

Space systems Determining Orbit Lifetime 1 Scope This standard describes a process for the estimation of orbit lifetime for spacecraft and associated debris in LEOcrossing orbits. The international standard also clarifies the following: modeling approaches and resources for solar and geomagnetic activity modeling; approaches for satellite cross-sectional area estimation. resources for atmosphere model selection and initialization. 2 Normative References. IADC Guidelines Existing orbit lifetime algorithm documentation 3 Definitions, symbols and abbreviated terms 3.1 Definitions For the purpose of this document, the following terms and definitions shall apply. 3.1.1 Orbit lifetime the elapsed time between the orbiting satellite s initial or reference position (e.g., post-mission orbit) and orbit demise/reentry. The orbit s decay is typically represented by the reduction in perigee and apogee altitudes (or radii) as shown in Figure 1. 3.1.2 Long-duration orbit lifetime prediction a prediction of orbit lifetime spanning two solar cycles or more (i.e., 20-year orbit lifetime) 3.1.3 LEO-crossing orbit The acronym LEO (Low-Earth Orbit) has a multitude of definitions, such as: 140-740 km (Merriam Webster online dictionary) 500 2000 km (www.atis.org) something less than 1600 km (another online source); But as can be seen in Figure 2, there is no distinct breakpoint that should delineate the difference between LEO and a higher regime. But, it can be seen that the highest spatial density of satellite objects occurs at altitudes less than 2000 km and approaches the background spatial density above 5000 km. i

400 350 Apogee & Perigee Altitudes (km) 300 250 200 150 100 50 0 0 5 10 15 20 25 30 35 40 Days From Epoch Figure 1: Sample orbit lifetime decay profile Figure 2: Sample assessment of space population 3.1.4 ephemeris a list of positions and velocities of a space vehicle or debris as a function of time. 3.1.5 orbit the path followed by a space vehicle or debris. 3.1.6 solar cycle the approximately 10.82-year cycle in solar activity, as measured by solar radio flux measurements at the 10.7cm wavelength. Historical records back to the earliest recorded data (1945) are shown in Figure 3. For reference, the current 25-year post-mission IADC orbit lifetime recommendation is overlaid onto the historical data; it can be seen that multiple solar cycles are encapsulated by this long time duration. 25-year IADC Lifetime Constraint Figure 3: 10.82-year Solar cycle ii

3.2 Symbols and abbreviated terms F10.7 Solar Flux index at 10.7 cm wavelength Ap Earth daily geomagnetic index LEO low Earth orbit NASA National Aeronautics and Space Administration NASDA National Space Development Agency Japan (predecessor of JAXA) NORAD North American Aerospace Defence Command (to be supplied.) 4 Orbit Lifetime Assessment 4.1 General Requirements This standard requires that the satellite designer, owner and operator take steps to ensure that their boosters, upper stages, satellites, and associated platforms and/or debris do not have a post-mission orbit lifetime which exceeds the IADC recommended criterion of 25 years (TBR). This criterion can be met by a combination of (1) initial orbit selection; (2) satellite vehicle design; (3) spacecraft launch and early orbit concepts of operation which minimize LEO-crossing objects; (4) satellite safing and other ballistics modifications at EOL; and (5) satellite deorbit maneuvers. 4.2 Definition of Orbit Lifetime Estimation Process The orbit lifetime estimation process is represented generically in Figure 3. Spacecraft Orbit Initial Conditions at Epoch Spacecraft Ballistic Characteristics, Attitude Rules Orbit Integration and Propagation Package Orbit Lifetime Estimate Anticipated Long- Duration Solar & Geomagnetic Activity Atmosphere Model Figure 4: Sample assessment of space population iii

4.3 Orbit Lifetime Assessment Methods and Applicability There are three basic analysis methods used to estimate orbit lifetime. Method 1 is simply a table lookup of values derived from the extensive and repetitive application of Methods 2 and/or 3. Method 2 utilizes a definition of mean orbital elements (Ref. 2 & 3), semi-analytic orbit theory and average satellite ballistic coefficient to permit the very rapid integration of the equations of motion, while still retaining reasonable accuracy. Method 3, clearly the highest fidelity model, utilizes a numerical integrator with a detailed gravity model, third-body effects, solar radiation pressure, and a detailed satellite ballistic coefficient model. 4.3.1 Method 1: Numerical Table Look-Up An approach has been implemented by the authors of this standard which implements the solar and geomagnetic modeling technique which will be presented in Section 5.2 of this document. The software implementation is a Method 2-type orbit lifetime estimator, using semi-analytic propagation of mean orbit elements (as defined by Ref. 3), coupled with gravity zonals J2 and J3 and the MSISE2000 atmosphere model. This software has been used to analyze over 100,000 cases, spanning perigee and apogee altitudes ranging from 50 to 5000 km, with ballistic coefficients ranging from 50 to 500 cm^2/kg. The results of this analysis are shown in Figures 5 and 6. Be detecting those cases which resulted in a 25-year orbit lifetime, the dependencies between ballistic coefficient and orbit initial condition can be found. Ballistic Coefficients Yielding 25yr Orbit Life (Orbit Inclination = 0 deg) 600 Ballistic Coefficient (cm^2/kg) 500 400 300 200 100 Ecc>0.20 0.15<Ecc<0.20 0.10<Ecc<0.15 0.05<Ecc<0.10 Ecc<0.05 0 0 100 200 300 400 500 600 700 Perigee Altitude Figure 5: Ballistic coefficient verus perigee altitude for equatorial orbits (i.e. inclination = 0 deg) iv

Ballistic Coefficients Yielding 25yr Orbit Life (Orbit Inclination = 90 deg) 600 Ballistic Coefficient (cm^2/kg) 500 400 300 200 100 Ecc>0.20 0.15<Ecc<0.20 0.10<Ecc<0.15 0.05<Ecc<0.10 Ecc<0.05 0 0 100 200 300 400 500 600 700 Perigee Altitude Figure 6: Ballistic coefficient verus perigee altitude for polar orbits (i.e. inclination = 90 deg) Careful comparison of Figures 5 and 6 shows that polar orbits experience reduced atmospheric drag, due to a polar orbit s reduced time spend under the solar subpoint (where solar heating causes the atmosphere to expand outward into space, thereby causing atmospheric density to rise). Therefore, a polar orbit requires a larger ballistic coefficient (perhaps 100cm^2/kg increase) to match the same 25-year orbit lifetime constraint observed in an equatorial orbit case. 4.3.2 Method 2: Rapid semi-analytical orbit propagation In this approach, mean orbit elements (again, as defined in Ref. 2 & 3) are rapidly propagated accounting for orbit perturbations J2 and J3 as demonstrated in Chapter 10 of Ref. 3, but additionally accounting for drag-induced orbit perturbations. The advantage of this method over direct 3-dimensional numerical integration of the equations of motion is that long-duration orbit lifetime cases can be quickly analyzed (e.g. 45 seconds CPU time for a 30-year orbit lifetime case). While incorporation of an attitude-dependent ballistic coefficient is doable for this method, an average ballistic coefficient is typically used. 4.3.3 Method 3: High-order numerical integration Method 3 is the direct numerical integration of all accelerations in Cartesian space, with the ability to incorporate a detailed gravity model (e.g. up to a 300 x 300 spherical harmonics model), third-body effects, solar radiation pressure, vehicle attitude rules or aerotorque-driven attitude torques, and a detailed satellite ballistic coefficient model based on the angle-of-attack with respect to the relative wind. Atmospheric rotation at the Earth s rotational rate is also easily incorporated in this approach. The only negative aspects to such simulations is (1) they run much slower than Method 2 (e.g. 1700 seconds for a 30-year analysis case); (2) many of the detailed data inputs required to make Method 3 realize its full accuracy potential are not available; and (3) any gains in orbit lifetime prediction accuracy are frequently overwhelmed by inherent inaccuracies of atmospheric modelling. However, to analyze a few select cases where such detailed model inputs are known, this is undoubtedly the most accurate method. v

5 Atmospheric density modeling The two biggest factors in orbit lifetime estimation are (1) the selection of an appropriate atmosphere model to incorporate into the orbit acceleration formulation; and (2) the selection of appropriate inputs to such a model. We will now spend some time discussing these two aspects. 5.1 Atmospheric Drag Models There are a wide variety of atmosphere models available to the orbit analyst. The background, technical basis, utility and functionality of these atmosphere models are described in detail in Ref. 4. This standard will not presume to dictate which atmosphere model the analyst shall use. However, it is worth noting that in general, the heritage, expertise and especially the observational data that went into creating each atmosphere model play a key role in that model s ability to predict atmospheric density, which is in turn a key factor in estimating orbit lifetime. Many of the early atmosphere models were low fidelity and were created on the basis of only one, or perhaps even just a part of one, solar cycle s worth of data. The advantage of some of these early models is that they typically run much faster than the latest high-fidelity models (Figure 7), without losing a great deal of accuracy (Figure 9) at any given instant of time. However, the use of atmosphere models that were designed to fit a select altitude range (e.g., the exponential atmosphere model depicted in Figure 8 & 9) or models that do not accommodate solar activity variations should be avoided as they miss too much of the atmospheric density variations to be of accurate use. There are some early models (e.g. the Jacchia 1971 model shown below) which do accommodate solar activity variations yet run very fast; these models, while perhaps not ideal, can work well for long-duration orbit lifetime studies where numerous cases are to be examined. Use of the more recent atmosphere models (e.g., MSISE2000 and Jacchia-Bowman) are encouraged because they have substantially more atmospheric drag data incorporated as the foundation of their underlying assumptions. 2000.00 1800.00 Atmosphere Model Runtime (1.8M evals) 1600.00 Exponential 1.422 1400.00 Atm1962 Atm1976 1.812 2.188 Temperature (deg K) 1200.00 1000.00 800.00 AtmExp T(K) Atm62 T(K) Atm76 T(K) MSIS00 T(K) Jacchia 1971 MSIS 2000 10.125 203.687 600.00 400.00 200.00 0.00 0 200 400 600 800 1000 1200 Altitude (km) Figure 7: Solar flux estimated upper, lower and representative trends Figure 8: Temperature Comparison by Atmosphere Model vi

0.00 0 200 400 600 800 1000 1200 1400 1600 1800 2000-10.00 Log(Density in kg/m^3) -20.00-30.00 AtmExp log(rho) Atm62 log(rho) Atm76 log(rho) Jac71 log(rho) MSIS00 log(rho) -40.00-50.00 Altitude (km) Figure 9: Comparison of a small sampling of atmosphere models 5.2 Long-Duration Solar Flux and Geomagnetic Indices Prediction The goal of this standard is to help minimize space object overpopulation for objects in the LEO-crossing orbit regimes. This is accomplished by standardizing on an anticipated post-mission lifetime of 25 years or less. Utilization of the higher-fidelity atmosphere models mentioned in the previous section requires the orbit analyst to specify the solar and geomagnetic indices required by such models. As can be seen by the careful comparison of Figures 3 and 10, attempts to generalize or abstract solar indices are fraught with error, since they do not capture the true upper and lower variations. Also, note that the estimate value from typical solar cycle predictions appears to be located at the mean value of the upper and lower curves. But as shown in Figure 11, the frequency of occurrence is highest near the lowest prediction boundary. There are other problems with the use of the F10.7 curve shown in Fig. 10, notably that the timing of the cycle minima and maxima are always imprecise. The resultant time bias that such a prediction error would introduce could easily yield large F10.7 prediction errors of 100% or more. Due to the long time duration currently being advocated by the IADC (25 years, although this is still under review), a different approach has been adopted for this standard. Rather than attempt to predict a mean curve, which would ignore the highly non-linear aspects of solar storms and quiet periods, the adopted approach is to utilze the historical F10.7 and Ap (geomagnetic) data directly. Note that we already have more than five solar cycles of data to choose from. By processing this data, a coupled triad of datum (F10.7, F10.7 Bar, and Ap) can be mapped into a single solar cycle range of 10.82272 years. Implementation of this historical data, mapped into a single solar cycle, then uses random draws upon the number of data triads available on any day within the single solar cycle. Since we have accumulated data collected daily since the 1940s, that means that for each of the 3953 days of one solar cycle we have at least five data triads to choose from. It is important that the random draw retain the integrity of each data triad, since F10.7, F10.7 Bar and Ap are interrelated. vii

ISO/WD NWIP Frequency of F10.7 Occurance W.R.T. min/max bounds 100000 90000 Occurrence from 1947 to 2006 80000 70000 60000 50000 40000 30000 20000 10000 0 1 2 3 4 5 6 7 8 9 10 F10.7: Percent of Min/Max Variation (1 denotes F10.7 between Min and 10% of Variation; 10=90% to Max); Figure 10: Solar flux estimated upper, lower and representative trends Figure 11: Sample orbit lifetime decay profile 500 450 400 F10.7 Solar Flux Index 350 300 250 200 150 100 50 0 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 Days From Start of Cycle Figure 12: F10.7 Normalized to Avg Cycle viii

ISO/WD NWIP 300.00 F10.7 Bar Solar Flux Index (Avg F10.7 over 3 Solar Rotations ~ 81 days) 250.00 200.00 150.00 100.00 50.00 0.00 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 Days From Start of Cycle Figure 13: F10.7 Bar Normalized to Avg Cycle 300 250 Ap Daily Geomag. Index 200 150 100 50 0 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 3500.00 4000.00 Days From Start of Cycle Figure 14: Ap Normalized to Avg Cycle ix

It can also be seen from Figure 14 that Ap is (1) unpredictable; (2) loosely correlated with the solar cycle; and (3) volatile. Figure 15 demonstrates that density varies greatly depending upon Ap; thus, a geomagnetic storm could induce large decreases in orbital energy (orbit decay) during such storms that the use of some average Ap value would miss. 0.00 0 500 1000 1500 2000 Log(Density in kg/m^3) -10.00-20.00-30.00 MSIS00 Ap=40 log(rho) MSIS00 Ap=4 log(rho) MSIS00 Ap=200 log(rho) -40.00-50.00 Altitude (km) Figure 15: Log(Density) Variation as a Function of Ap Value The C++ code which implements this atmospheric variation will be made publicly available so that users of this orbit lifetime standard can adopt a standardized F10.7, F10.7 Bar and Ap prediction if desired. x

Bibliography [1] IADC Guidelines [2] Kozai, Y., The Motion of a Close Earth Satellite, Astronomical Journal 64, 367 377, November 1959. [3] Orbital Motion 2 nd Edition, Roy, A.E., Publ. by Adam Hilger, Ltd, Bristol, ISBN 0-85274-462-5. [4] NASA Atmosphere model comparisons (to be supplied.) xi

(informative) Space population distribution A.1 Space object distribution The launch vehicle and its family of deployed objects pass through various orbit regimes during the ascent phase from launch up to the mission orbit. As can be seen in Figures A.1 and A.2, the collision risk is especially high in specific orbital regimes (the LEO and GEO belts and at the altitudes of deployed constellations). Figure A-1: Near-earth space spatial density Figure A-2: Distribution in low-earth orbit 40000 35000 30000 Altitude Range (km) 25000 20000 15000 10000 5000 0 0.000 0.001 0.002 0.004 0.007 0.013 0.026 0.100 0.725 Eccentricity (Each Tick Mark Represents 1000 objects) Figure A-3: Space population by altitude and eccentricity Figure A-4: Distribution in near-earth space xii

Annex B (informative) TBD B.1 General xiii