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| <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN" | |
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| <title> Testing of the Java Astrodynamics Toolkit Propagator</title> | |
| <h1 align="center">Testing of the Java Astrodynamics Toolkit Propagator </h1> | |
| <h3 align="center">Dr. David E. Gaylor<a href="#tthFtNtAAB" name="tthFrefAAB"><sup>1</sup></a> | |
| , Richard C. Page III<a href="#tthFtNtAAC" name="tthFrefAAC"><sup>2</sup></a><br /> | |
| and Kathryn V. Bradley<a href="#tthFtNtAAD" name="tthFrefAAD"><sup>3</sup></a><br /> | |
| <font size="+0"><i> | |
| Emergent Space Technologies, Greenbelt, MD, 20770, USA</i></font><br /> | |
| </h3> | |
| <h3 align="center">7 August 2006 </h3> | |
| <h2> Abstract</h2> | |
| The Java Astrodynamics Toolkit (JAT) is an open source software | |
| library of reusable software components for mission design, | |
| trajectory optimization, and simulation of navigation, guidance and | |
| control systems. This paper provides results of comparing various | |
| Earth orbit ephemerides created with JAT with those created using | |
| Analytical Graphics Inc.'s Satellite Tool Kit/High Precision Orbit | |
| Propagator (STK/HPOP) and a.i. solutions, Inc.'s FreeFlyer. | |
| Ephemerides produced using STK and FreeFlyer are also compared to | |
| each other. With careful attention to parameters and models, results | |
| show agreement of millimeter to meter level over several days. | |
| Differences are discussed including potential sources of error. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc1"> | |
| 1</a> Introduction</h2> | |
| The Java Astrodynamics Toolkit (JAT) is an open source library of | |
| reusable software components written in the Java programming | |
| language to support rapid development of spacecraft simulations | |
| including 2-D and 3-D visualization capabilities. JAT is distributed | |
| under the GNU General Public License and is available at | |
| http://jat.sourceforge.net. Potential applications of JAT include: | |
| <ul> | |
| <li> Simulations of autonomous spacecraft navigation, guidance and | |
| control | |
| <div class="p"><!----></div> | |
| </li> | |
| <li> Space mission design and analysis including trajectory | |
| optimization | |
| <div class="p"><!----></div> | |
| </li> | |
| <li> Operational orbit determination and orbital events | |
| generation | |
| <div class="p"><!----></div> | |
| </li> | |
| </ul> | |
| <div class="p"><!----></div> | |
| This paper provides results of comparing ephemerides created by | |
| propagating various Earth orbits using JAT with those created using | |
| Satellite Tool Kit/High Precision Orbit Propagator (STK/HPOP) from | |
| Analytical Graphics, Inc. (AGI) and FreeFlyer (FF) from a.i. | |
| solutions, Inc. Ephemerides produced using STK and FreeFlyer are | |
| also compared to each other. FreeFlyer is a spacecraft simulation | |
| package currently in use at the NASA Goddard Space Flight Center. | |
| Version 5.5, build 5.5.0.25 of FreeFlyer and STK version 6.1 were | |
| used for comparison in the propagator validation. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc2"> | |
| 2</a> Initial State Vectors</h2> The following orbits were selected for testing: Sun-Synchronous, Geostationary (GEO), Molniya, International Space Station | |
| (ISS) and the Global Positioning Satellite System (GPS) orbit. The | |
| initial epoch was chosen to be June 1, 2004, 12:00:00. The initial | |
| conditions which were used for the test case orbits are presented in | |
| Table <a href="#Tab:Initial">1</a>. The corresponding osculating orbital elements | |
| at the initial epoch are presented in Table <a href="#Tab:OrbitalElements">2</a>. | |
| The orbit naming convention is based on the approximate altitude of | |
| the orbit and does not follow the exact path of any particular | |
| orbiting body. For example, ISS refers to an orbit which | |
| approximates that of the International Space Station, but does not | |
| refer to the actual location of the International Space Station. | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb1"> | |
| </a> <center> <center>Table 1: Initial Conditions</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Category </td><td align="center">Orbit </td><td align="center">X </td><td align="center">Y </td><td align="center">Z </td><td align="center">Vx </td><td align="center">Vy </td><td align="center">Vz </td></tr> | |
| <tr><td></td><td align="center">Type </td><td align="center">(km)</td><td align="center">(km)</td><td align="center">(km)</td><td align="center">(km/s)</td><td align="center">(km/s) </td><td align="center">(km/s) </td></tr> | |
| <tr><td>LEO </td><td align="center">ISS </td><td align="center">-4453.783586 </td><td align="center">-5038.203756 </td><td align="center">-426.384456 </td><td align="center">3.831888 </td><td align="center">-2.887221 </td><td align="center">-6.018232 </td></tr> | |
| <tr><td>LEO </td><td align="center">Sun-Sync </td><td align="center">-2290.301063 </td><td align="center">-6379.471940 </td><td align="center">0 </td><td align="center">-0.883923 </td><td align="center">0.317338 </td><td align="center">7.610832 </td></tr> | |
| <tr><td>MEO </td><td align="center">GPS </td><td align="center">5525.33668 </td><td align="center">-15871.18494 </td><td align="center">-20998.992446 </td><td align="center">2.750341 </td><td align="center">2.434198 </td><td align="center">-1.068884 </td></tr> | |
| <tr><td>HEO </td><td align="center">Molniya </td><td align="center">-1529.894287 </td><td align="center">-2672.877357 </td><td align="center">-6150.115340 </td><td align="center">8.717518 </td><td align="center">-4.989709 </td><td align="center">0 </td></tr> | |
| <tr><td>GEO </td><td align="center">GEO </td><td align="center">36607.358256 </td><td align="center">-20921.723703 </td><td align="center">0 </td><td align="center">1.525636 </td><td align="center">2.669451 </td><td align="center">0 </td></tr><tr><td></td></tr><a name="Tab:Initial"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb2"> | |
| </a> <center> <center>Table 2: Initial Osculating Orbital Elements</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Orbit </td><td align="center">a </td><td align="center">e </td><td align="center">i </td><td align="center">Arg of Perigee </td><td align="center">RAAN </td><td align="center">True Anomaly </td></tr> | |
| <tr><td>Type </td><td align="center">km </td><td align="center"></td><td align="center">Deg </td><td align="center">Deg </td><td align="center">Deg </td><td align="center">Deg </td></tr> | |
| <tr><td>ISS </td><td align="center">6747.414767 </td><td align="center">.001646462 </td><td align="center">51.667871 </td><td align="center">151.908712 </td><td align="center">45.649594 </td><td align="center">32.718375 </td></tr> | |
| <tr><td>Sun-Sync </td><td align="center">6778.137291 </td><td align="center">.000000046 </td><td align="center">97.034619 </td><td align="center">337.556006 </td><td align="center">250.251300 </td><td align="center">22.443994 </td></tr> | |
| <tr><td>GPS </td><td align="center">26558.859022 </td><td align="center">.015930402 </td><td align="center">56.286490 </td><td align="center">33.142451 </td><td align="center">52.707850 </td><td align="center">216.676430 </td></tr> | |
| <tr><td>Molniya </td><td align="center">26553.376213 </td><td align="center">.740969399 </td><td align="center">63.4 </td><td align="center">270.000001 </td><td align="center">330.214160 </td><td align="center">359.999998 </td></tr> | |
| <tr><td>GEO </td><td align="center">42164.165718 </td><td align="center">.000000135 </td><td align="center">0 </td><td align="center">103.882708 </td><td align="center">0 </td><td align="center">226.368596 </td></tr><tr><td></td></tr><a name="Tab:OrbitalElements"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| The integrator step size, propagation length and output frequency | |
| were varied for the different test cases as shown in | |
| Table <a href="#Tab:Frequency">3</a>. The propagation length and output frequency | |
| were chosen based on a previous study performed by The Aerospace | |
| Corporation to validate STK/HPOP[<a href="#Chao:2000" name="CITEChao:2000">1</a>]. | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb3"> | |
| </a> <center> <center>Table 3: Step Size, Propagation Length and Output | |
| Frequency</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Orbit Type </td><td align="center">Integrator </td><td align="center">Propagation </td><td align="center">Output </td></tr> | |
| <tr><td>Type </td><td align="center">Step Size </td><td align="center">Length </td><td align="center">Frequency </td></tr> | |
| <tr><td></td><td align="center">(s) </td><td align="center">(days) </td><td align="center">(mins) </td></tr> | |
| <tr><td>ISS </td><td align="center">5 </td><td align="center">1 </td><td align="center">1 </td></tr> | |
| <tr><td>Sun-Sync </td><td align="center">5 </td><td align="center">1 </td><td align="center">1 </td></tr> | |
| <tr><td>GPS </td><td align="center">60 </td><td align="center">2 </td><td align="center">2 </td></tr> | |
| <tr><td>Molniya </td><td align="center">5 </td><td align="center">3 </td><td align="center">5 </td></tr> | |
| <tr><td>GEO </td><td align="center">60 </td><td align="center">7 </td><td align="center">10 </td></tr><tr><td></td></tr><a name="Tab:Frequency"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| Twelve test cases were performed for each orbit type. Test cases | |
| were run to verify JAT's ability to perform accurate propagation of | |
| Earth orbits using various force models. The force models considered | |
| in this study were two-body Earth gravity, JGM2 and JGM3 spherical | |
| harmonic gravity models; Solar/Lunar third-body perturbation | |
| effects; atmospheric drag using the Harris-Priester density model, | |
| and the Naval Research Laboratory Mass Spectrometer and Incoherent | |
| Scatter Radar Exosphere (NRLMSISE 2000) atmospheric density model; | |
| and solar radiation pressure (SRP). Each of the force models was run | |
| independently to test their individual accuracy, using two-body | |
| Earth except for spherical harmonic cases. A final test case was run | |
| for each satellite orbit which included an atmospheric drag model, | |
| the SRP model, a spherical harmonic gravity model and third-body | |
| perturbations from both the Sun and the Moon. These last test cases | |
| were performed to validate the capability of JAT to accurately | |
| propagate satellite orbits with multiple models. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc3"> | |
| 3</a> Earth Orientation Parameters</h2> | |
| The use of spherical harmonic gravity | |
| models requires precise calculation of the Earth's orientation. | |
| Earth orientation involves parameters for the following | |
| transformations: Nutation, Precession, Pole Wander, and Sidereal | |
| Time, including the exact UT1 time obtained from the UT1-UTC | |
| correction in the International Earth Rotation Service (IERS) | |
| Bulletin A [<a href="#IERS:2004" name="CITEIERS:2004">4</a>]. It is important to understand how the | |
| numerical integrators handle the rotation. FreeFlyer does not appear | |
| to update the perturbations in the Earth's orientation during a | |
| propagation run. Our testing seemed to indicate that STK/HPOP is | |
| updating some information less frequently than every time step. | |
| Currently, JAT updates the Earth orientation every time the | |
| integrator calls for the derivatives. This was done to ensure that | |
| JAT was at its highest accuracy. | |
| <div class="p"><!----></div> | |
| JAT implements the conventions established by the International | |
| Astronomical Union (IAU), in the Explanatory Supplement to the | |
| Astronomical Almanac [<a href="#Seidelmann:1992" name="CITESeidelmann:1992">6</a>] [<a href="#Hohenkerk:1992" name="CITEHohenkerk:1992">7</a>], | |
| and by the IERS 1996 conventions [<a href="#McCarthy:1996" name="CITEMcCarthy:1996">8</a>] . Exhaustive | |
| comparisons were conducted between the Almanac, and IERS 96 | |
| conventions for Nutation, Precession, and Greenwhich Hour Angle. | |
| <div class="p"><!----></div> | |
| The Earth orientation computation in FreeFlyer, however, does not | |
| seem to implement pole wander, though it uses the UT1-UTC value from | |
| the IERS. Because of this discrepancy, pole wander was turned off | |
| for the purpose of validation between the three programs. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc4"> | |
| 4</a> Integrator</h2> The JAT fixed step-size, 8th order Runge-Kutta numerical integrator was used. The Runge-Kutta 8th order integrator within FreeFlyer was utilized in fixed step size mode for all of the | |
| propagation comparisons. The Runge-Kutta-Fehlberg 7th order | |
| integrator with 8th order error control within STK/HPOP was used as | |
| a fixed step integrator with error control turned off. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc5"> | |
| 5</a> Atmospheric Drag</h2> Currently, JAT contains two high | |
| fidelity atmospheric drag models: NRLMSISE2000 and Harris-Priester. | |
| The NRLMSISE2000 model was adapted from code developed by the Naval | |
| Research Laboratory [<a href="#NRLMSISE" name="CITENRLMSISE">13</a>]. The Harris Priester Model is | |
| based on the model in <em>Satellite Orbits</em> [<a href="#Montenbruck" name="CITEMontenbruck">14</a>]. | |
| STK/HPOP also has both the NRLMSISE2000 and Harris-Priester models | |
| available in version 6.1 and later. FreeFlyer does not have the | |
| NRLMSISE2000 model, but it does have the Harris-Priester model. The | |
| value used for the F10.7 cm solar flux was 150 W/m<sup>2</sup>/Hz and | |
| a<sub>p</sub> was 14.918648166. | |
| <div class="p"><!----></div> | |
| <h3><a name="tth_sEc5.1"> | |
| 5.1</a> Ap/Kp Indicies</h3> | |
| When using the NRLMSISE 2000 in STK, the geomagnetic index (k<sub>p</sub>), | |
| was set to 3 for this study. STK allows the user to input k<sub>p</sub> (the | |
| planetary index) and F10.7 values in the force model. However, STK | |
| does not allow the user to enter in an a<sub>p</sub> (planetary amplitude) | |
| value. The NRLMSISE 2000 model in JAT requires the a<sub>p</sub> value in | |
| order to calculate the density in the drag model. Therefore a | |
| correlation between the k<sub>p</sub> value and the a<sub>p</sub> value was needed. | |
| Wertz presents the equation for the correlation as: | |
| [<a href="#Wertz:1978" name="CITEWertz:1978">12</a>] | |
| <a name="Eqn:Vallado apkp"> | |
| </a> | |
| <br clear="all" /><table border="0" width="100%"><tr><td> | |
| <table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> | |
| a<sub>p</sub> = <span class="roman">e</span><sup>[(k<sub>p</sub>+1.6)/1.75]</sup> </td></tr></table> | |
| </td><td width="1%">(1)</td></tr></table> | |
| As previously mentioned, a k<sub>p</sub> value of 3 was used for the test | |
| cases, which according to Equation <a href="#Eqn:Vallado apkp">1</a> above | |
| results in an a<sub>p</sub> value of 13.85396. However, when this value is | |
| entered into JAT the error in position is approximately 500 meters | |
| for the LEO satellite orbits. Therefore, it was determined that the | |
| a<sub>p</sub> was incorrect. In order to validate the value of a<sub>p</sub> which | |
| should be used in the JAT, other sources were investigated. | |
| <div class="p"><!----></div> | |
| According to NOAA, for a k<sub>p</sub> value of 3, the corresponding value | |
| of a<sub>p</sub> is 15 [<a href="#NOAA:2005" name="CITENOAA:2005">5</a>]. Since the nature of atmospheric | |
| density is empirical, there are several different analytical | |
| approaches which disagree slightly on the exact value which should | |
| be used in the calculation of density for atmospheric drag. When a | |
| value of 15 is used for the a<sub>p</sub> in JAT, the position error is | |
| approximately 51 meters for the ISS case and 28 meters for Sun-Sync. | |
| <div class="p"><!----></div> | |
| NOAA presents the following equation for the correlation: | |
| [<a href="#NOAA:2005" name="CITENOAA:2005">5</a>] | |
| <a name="Eqn:STK apkp"> | |
| </a> | |
| <br clear="all" /><table border="0" width="100%"><tr><td> | |
| <table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> | |
| 28*k<sub>p</sub>+0.03*<span class="roman">e</span><sup>k<sub>p</sub></sup> = a<sub>p</sub> + 100*1<font face="symbol">-</font | |
| ><span class="roman">e</span><sup><font face="symbol">-</font | |
| >0.08*a<sub>p</sub></sup> </td></tr></table> | |
| </td><td width="1%">(2)</td></tr></table> | |
| <div class="p"><!----></div> | |
| When a k<sub>p</sub> value of 3 is used in Equation <a href="#Eqn:STK apkp">2</a> the | |
| a<sub>p</sub> value is 14.918648166. A position error of approximately 1 | |
| meter over a day is found when this value of a<sub>p</sub> is used with the | |
| ISS orbit. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc6"> | |
| 6</a> Third Body Perturbations</h2> Models for Solar and | |
| Lunar perturbations have been created in JAT. These models use the | |
| JPL DE405 ephemerides for the Sun and Moon. FreeFlyer and STK/HPOP | |
| were also set to utilize Sun and Moon positions obtained from the | |
| DE405 ephemeris. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc7"> | |
| 7</a> Gravity Models</h2> JAT and STK/HPOP contain both JGM2 and | |
| JGM3 spherical harmonic gravity models. FreeFlyer only contains the | |
| JGM2 model. For all cases using the JGM2 and JGM3 models, the degree | |
| and order were both set to 20 for all three programs. STK/HPOP has | |
| the ability to model solid and ocean tides. JAT currently does not | |
| have this ability and so this was option turned off in STK/HPOP. | |
| STK/HPOP was also set to not include relativistic accelerations. In | |
| STK/HPOP, JGM2 and JGM3 gravity files were applied with a zero | |
| degree and order for the two-body cases. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc8"> | |
| 8</a> Solar Radiation Pressure</h2> A solar radiation pressure (SRP) | |
| model is also included in JAT. The SRP model assumes a uniform | |
| spherical spacecraft with a given cross-sectional area. The SRP | |
| model has a discontinuity at the boundary between full illumination | |
| and entering the shadow of the Earth. To handle this, a cylindrical | |
| partial illumination model is implemented to provide some continuity | |
| in the derivatives as the radiation component becomes zero. The | |
| vector to the sun is computed using the JPL DE405 ephemeris. In | |
| FreeFlyer, a basic solar radiation pressure model is available, | |
| although documentation on this model is not very detailed. The | |
| settings for the altitude of the atmosphere for the Earth's shadow | |
| were set to zero in STK/HPOP and JAT. | |
| <h2><a name="tth_sEc9"> | |
| 9</a> Ephemeris Comparison Results and Discussion</h2> | |
| The ephemerides produced by JAT, STK/HPOP and FreeFlyer were | |
| compared with each other. Table <a href="#Tab:ISS">4</a> presents the maximum | |
| position and velocity differences for the ISS orbit. In all cases, | |
| JAT agrees well with STK/HPOP. The largest differences in this set | |
| of tests was between JAT and FreeFlyer when using the | |
| Harris-Priester model, however, it is interesting to note that | |
| STK/HPOP and FreeFlyer also do not agree well in these cases. | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb4"> | |
| </a> <center> <center>Table 4: Position and Velocity Differences for ISS | |
| Orbit</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Description </td><td align="center">JAT-STK </td><td align="center">JAT-STK </td><td align="center">JAT-FF </td><td align="center">JAT-FF </td><td align="center">FF-STK </td><td align="center">FF-STK</td></tr> | |
| <tr><td></td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity</td></tr> | |
| <tr><td></td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s)</td></tr> | |
| <tr><td>2-body </td><td align="center">0.000829 </td><td align="center">0.000808 </td><td align="center">0.000048 </td><td align="center">0.0000008 </td><td align="center">0.000838 </td><td align="center">0.000809 </td></tr> | |
| <tr><td>2-body+Moon </td><td align="center">0.000830 </td><td align="center">0.000815 </td><td align="center">0.000329 </td><td align="center">0.000001 </td><td align="center">0.000996 </td><td align="center">0.000815 </td></tr> | |
| <tr><td>2-body+Sun </td><td align="center">0.000827 </td><td align="center">0.000838 </td><td align="center">0.000037 </td><td align="center">0.0000008 </td><td align="center">0.000826 </td><td align="center">0.000838 </td></tr> | |
| <tr><td>2-body+NRL </td><td align="center">0.269426 </td><td align="center">0.000995 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>2-body+HP </td><td align="center">1.031710 </td><td align="center">0.001802 </td><td align="center">2.33001 </td><td align="center">0.002665 </td><td align="center">5.495820 </td><td align="center">0.006752 </td></tr> | |
| <tr><td>2-body+SRP </td><td align="center">0.103515 </td><td align="center">0.000875 </td><td align="center">0.069386 </td><td align="center">0.000071 </td><td align="center">0.136046 </td><td align="center">0.000885 </td></tr> | |
| <tr><td>JGM2 </td><td align="center">0.368138 </td><td align="center">0.001085 </td><td align="center">0.500248 </td><td align="center">0.000552 </td><td align="center">0.836881 </td><td align="center">0.001576 </td></tr> | |
| <tr><td>JGM3 </td><td align="center">0.368124 </td><td align="center">0.001076 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+NRL </td><td align="center">0.857388 </td><td align="center">0.001496 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+HP </td><td align="center">1.053890 </td><td align="center">0.001723 </td><td align="center">4.39748 </td><td align="center">0.005034 </td><td align="center">5.441040 </td><td align="center">0.006492 </td></tr> | |
| <tr><td>All+JGM3+NRL </td><td align="center">0.857146 </td><td align="center">0.001572 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM3+HP </td><td align="center">1.053360 </td><td align="center">0.001730 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr><tr><td></td></tr><a name="Tab:ISS"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| Table <a href="#Tab:Sun-Sync">5</a> presents the maximum position and velocity | |
| differences for the Sun Synchronous orbit. JAT and STK/HPOP agree | |
| well for all cases except for the cases that include atmospheric | |
| drag as would be expected based on the previous discussion on the | |
| difficulties in matching atmospheric density models. | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb5"> | |
| </a> <center> <center>Table 5: Position and Velocity Differences for Sun-Sync | |
| Orbit</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Description </td><td align="center">JAT-STK </td><td align="center">JAT-STK </td><td align="center">JAT-FF </td><td align="center">JAT-FF </td><td align="center">FF-STK </td><td align="center">FF-STK</td></tr> | |
| <tr><td></td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity</td></tr> | |
| <tr><td></td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s)</td></tr> | |
| <tr><td>2-body </td><td align="center">0.00081 </td><td align="center">0.00080 </td><td align="center">0.00003 </td><td align="center">0.0000008 </td><td align="center">0.00082 </td><td align="center">0.00080 </td></tr> | |
| <tr><td>2-body+Moon </td><td align="center">0.00083 </td><td align="center">0.00083 </td><td align="center">0.00028 </td><td align="center">0.0000009 </td><td align="center">0.00093 </td><td align="center">0.00083 </td></tr> | |
| <tr><td>2-body+Sun </td><td align="center">0.00082 </td><td align="center">0.00082 </td><td align="center">0.00003 </td><td align="center">0.0000008 </td><td align="center">0.00081 </td><td align="center">0.00082 </td></tr> | |
| <tr><td>2-body+NRL </td><td align="center">8.66478 </td><td align="center">0.01035 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>2-body+HP </td><td align="center">3.33383 </td><td align="center">0.00439 </td><td align="center">1.61195 </td><td align="center">0.00181 </td><td align="center">1.77066 </td><td align="center">0.00261 </td></tr> | |
| <tr><td>2-body+SRP </td><td align="center">0.09203 </td><td align="center">0.00083 </td><td align="center">0.03162 </td><td align="center">0.00003 </td><td align="center">0.09110 </td><td align="center">0.00083 </td></tr> | |
| <tr><td>JGM2 </td><td align="center">0.17022 </td><td align="center">0.00096 </td><td align="center">0.27362 </td><td align="center">0.000296 </td><td align="center">0.37380 </td><td align="center">0.00111 </td></tr> | |
| <tr><td>JGM3 </td><td align="center">0.16998 </td><td align="center">0.00089 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+NRL </td><td align="center">8.22196 </td><td align="center">0.00970 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+HP </td><td align="center">3.53857 </td><td align="center">0.00461 </td><td align="center">1.8332 </td><td align="center">0.00209 </td><td align="center">1.70622 </td><td align="center">0.00258 </td></tr> | |
| <tr><td>All+JGM3+NRL </td><td align="center">8.22146 </td><td align="center">0.00995 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM3+HP </td><td align="center">3.53792 </td><td align="center">0.00455 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr><tr><td></td></tr><a name="Tab:Sun-Sync"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| Table <a href="#Tab:GPS">6</a> presents the maximum position and velocity | |
| differences for the GPS orbit. All three programs have close | |
| agreement in this case due to the nature of the GPS orbit, which was | |
| chosen to minimize the effects of perturbations. | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb6"> | |
| </a> <center> <center>Table 6: Position and Velocity Differences for GPS | |
| Orbit</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Description </td><td align="center">JAT-STK </td><td align="center">JAT-STK </td><td align="center">JAT-FF </td><td align="center">JAT-FF </td><td align="center">FF-STK </td><td align="center">FF-STK</td></tr> | |
| <tr><td></td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity</td></tr> | |
| <tr><td></td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s)</td></tr> | |
| <tr><td>2-body </td><td align="center">0.00080 </td><td align="center">0.00083 </td><td align="center">0.000008 </td><td align="center">0.0000008 </td><td align="center">0.00080 </td><td align="center">0.00083 </td></tr> | |
| <tr><td>2-body+Moon </td><td align="center">0.00080 </td><td align="center">0.00085 </td><td align="center">0.03287 </td><td align="center">0.000005 </td><td align="center">0.03298 </td><td align="center">0.00085 </td></tr> | |
| <tr><td>2-body+Sun </td><td align="center">0.00084 </td><td align="center">0.00080 </td><td align="center">0.00064 </td><td align="center">0.0000008 </td><td align="center">0.00122 </td><td align="center">0.00080 </td></tr> | |
| <tr><td>2-body+NRL </td><td align="center">0.00782 </td><td align="center">0.00083 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>2-body+HP </td><td align="center">0.00080 </td><td align="center">0.00083 </td><td align="center">0.000008 </td><td align="center">0.0000008 </td><td align="center">0.00080 </td><td align="center">0.00083 </td></tr> | |
| <tr><td>2-body+SRP </td><td align="center">0.08960 </td><td align="center">0.00084 </td><td align="center">0.72128 </td><td align="center">0.00008 </td><td align="center">0.72511 </td><td align="center">0.00088 </td></tr> | |
| <tr><td>JGM2 </td><td align="center">0.01950 </td><td align="center">0.00081 </td><td align="center">0.01660 </td><td align="center">0.000002 </td><td align="center">0.02076 </td><td align="center">0.00081 </td></tr> | |
| <tr><td>JGM3 </td><td align="center">0.01940 </td><td align="center">0.00081 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+NRL </td><td align="center">0.11936 </td><td align="center">0.00083 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+HP </td><td align="center">0.12493 </td><td align="center">0.00083 </td><td align="center">0.61088 </td><td align="center">0.00006 </td><td align="center">0.52284 </td><td align="center">0.00086 </td></tr> | |
| <tr><td>All+JGM3+NRL </td><td align="center">0.11951 </td><td align="center">0.00085 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM3+HP </td><td align="center">0.12509 </td><td align="center">0.00085 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr><tr><td></td></tr><a name="Tab:GPS"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| Table <a href="#Tab:Molniya">7</a> presents the maximum position and velocity | |
| differences for the Molniya orbit. The Molniya orbit is the most | |
| challenging for a number of reasons. JAT and STK/HPOP agree well for | |
| the cases that did not include atmospheric drag or a spherical | |
| harmonic gravity model. It is interesting to note that JAT and | |
| FreeFlyer did agree well in the cases with atmospheric drag. | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb7"> | |
| </a> <center> <center>Table 7: Position and Velocity Differences for Molniya | |
| Orbit</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Description </td><td align="center">JAT-STK </td><td align="center">JAT-STK </td><td align="center">JAT-FF </td><td align="center">JAT-FF </td><td align="center">FF-STK </td><td align="center">FF-STK</td></tr> | |
| <tr><td></td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity</td></tr> | |
| <tr><td></td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s)</td></tr> | |
| <tr><td>2-body </td><td align="center">0.00090 </td><td align="center">0.00084 </td><td align="center">0.00047 </td><td align="center">0.0000008 </td><td align="center">0.00082 </td><td align="center">0.00084 </td></tr> | |
| <tr><td>2-body+Moon </td><td align="center">0.00082 </td><td align="center">0.00080 </td><td align="center">0.08194 </td><td align="center">0.000068 </td><td align="center">0.08180 </td><td align="center">0.00080 </td></tr> | |
| <tr><td>2-body+Sun </td><td align="center">0.00085 </td><td align="center">0.00082 </td><td align="center">0.03110 </td><td align="center">0.000025 </td><td align="center">0.03129 </td><td align="center">0.00082 </td></tr> | |
| <tr><td>2-body+NRL </td><td align="center">28.39440 </td><td align="center">0.02389 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>2-body+HP </td><td align="center">15.16700 </td><td align="center">0.01287 </td><td align="center">0.02214 </td><td align="center">0.000018 </td><td align="center">15.18920 </td><td align="center">0.01289 </td></tr> | |
| <tr><td>2-body+SRP </td><td align="center">0.63727 </td><td align="center">0.00092 </td><td align="center">2.77142 </td><td align="center">0.00229 </td><td align="center">2.13422 </td><td align="center">0.00190 </td></tr> | |
| <tr><td>JGM2 </td><td align="center">5.57807 </td><td align="center">0.00456 </td><td align="center">7.72931 </td><td align="center">.006160 </td><td align="center">2.30217 </td><td align="center">0.00184 </td></tr> | |
| <tr><td>JGM3 </td><td align="center">5.57807 </td><td align="center">0.00481 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+NRL </td><td align="center">27.86270 </td><td align="center">0.02052 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM2+HP </td><td align="center">7.57025 </td><td align="center">0.00460 </td><td align="center">5.43094 </td><td align="center">0.00417 </td><td align="center">12.97950 </td><td align="center">0.00862 </td></tr> | |
| <tr><td>All+JGM3+NRL </td><td align="center">27.86160 </td><td align="center">0.02082 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr> | |
| <tr><td>All+JGM3+HP </td><td align="center">7.57107 </td><td align="center">0.00493 </td><td align="center">- </td><td align="center">- </td><td align="center">- </td><td align="center">- </td></tr><tr><td></td></tr><a name="Tab:Molniya"> | |
| </a></table> | |
| </center> | |
| <div class="p"><!----></div> | |
| Table <a href="#Tab:GEO">8</a> presents the maximum position and velocity | |
| differences for the GEO orbit. In all cases, JAT agrees well with | |
| STK/HPOP. The largest differences in this set of tests was between | |
| JAT and FreeFlyer when including SRP, however, it is interesting to | |
| note that STK/HPOP and FreeFlyer also do not agree well in these | |
| cases. | |
| <div class="p"><!----></div> | |
| <div class="p"><!----></div> | |
| <a name="tth_tAb8"> | |
| </a> <center> <center>Table 8: Position and Velocity Differences for GEO | |
| Orbit</center> | |
| <table border="1"><tr><td></td></tr> | |
| <tr><td>Description </td><td align="center">JAT-STK </td><td align="center">JAT-STK </td><td align="center">JAT-FF </td><td align="center">JAT-FF </td><td align="center">FF-STK </td><td align="center">FF-STK</td></tr> | |
| <tr><td></td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity </td><td align="center">Position </td><td align="center">Velocity</td></tr> | |
| <tr><td></td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s) </td><td align="center">(m) </td><td align="center">(m/s)</td></tr> | |
| <tr><td>2-body </td><td align="center">0.00070 </td><td align="center">0.00070 </td><td align="center">0.00009 </td><td align="center">0.0000007 </td><td align="center">0.00070 </td><td align="center">0.00070 </td></tr> | |
| <tr><td>2-body+Moon </td><td align="center">0.00090 </td><td align="center">0.00081 </td><td align="center">0.07980 </td><td align="center">0.00005 </td><td align="center">0.07989 </td><td align="center">0.00081 </td></tr> | |
| <tr><td>2-body+Sun </td><td align="center">0.00087 </td><td align="center">0.00081 </td><td align="center">0.05206 </td><td align="center">0.000004 </td><td align="center">0.05230 </td><td align="center">0.00081 </td></tr> | |
| <tr><td>2-body+NRL </td><td align="center">0.00070 </td><td align="center">0.00070 </td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr> | |
| <tr><td>2-body+HP </td><td align="center">0.00070 </td><td align="center">0.00070 </td><td align="center">0.00009 </td><td align="center">0.0000007 </td><td align="center">0.00070 </td><td align="center">0.00070 </td></tr> | |
| <tr><td>2-body+SRP </td><td align="center">0.00080 </td><td align="center">0.00082 </td><td align="center">2.73497 </td><td align="center">0.00012 </td><td align="center">2.89851 </td><td align="center">0.00087 </td></tr> | |
| <tr><td>JGM2 </td><td align="center">0.07287 </td><td align="center">0.00081 </td><td align="center">1.58727 </td><td align="center">0.000116 </td><td align="center">1.65447 </td><td align="center">0.00083 </td></tr> | |
| <tr><td>JGM3 </td><td align="center">0.07276 </td><td align="center">0.00081 </td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr> | |
| <tr><td>All+JGM2+NRL </td><td align="center">0.72280 </td><td align="center">0.00084 </td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr> | |
| <tr><td>All+JGM2+HP </td><td align="center">0.72280 </td><td align="center">0.00084 </td><td align="center">2.99845 </td><td align="center">0.00014 </td><td align="center">3.41299 </td><td align="center">0.00090 </td></tr> | |
| <tr><td>All+JGM3+NRL </td><td align="center">0.72298 </td><td align="center">0.00082 </td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr> | |
| <tr><td>All+JGM3+HP </td><td align="center">0.72298 </td><td align="center">0.00082 </td><td align="center"></td><td align="center"></td><td align="center"></td><td align="center"></td></tr><tr><td></td></tr><a name="Tab:GEO"> | |
| </a></table> | |
| </center> | |
| <h2><a name="tth_sEc10"> | |
| 10</a> Conclusions</h2> | |
| JAT achieves agreement below meter levels for all cases except those | |
| with atmospheric drag. The sensitivity to differences in the density | |
| calculation make an exact match difficult. Atmospheric drag depends | |
| on proper modeling of geomagnetic and molecular behavior influencing | |
| atmospheric density. Care must be taken to model the geomagnetic | |
| index correctly. However, given that the range of modeling error can | |
| be on the order of kilometers or more for low Earth orbits, meters | |
| or tens of meters in the Molniya case is expected. | |
| <div class="p"><!----></div> | |
| The verification of the spherical harmonic gravity models revealed | |
| ambiguities in which IERS convention and update procedure is used in | |
| the rotation from the Earth Centered Inertial frame to the Earth | |
| Centered Earth Fixed frame. Ultimately, due to the complexity of the | |
| IAU and IERS conventions and their subsequent corrections, it is | |
| extremely difficult to match algorithms exactly without knowledge of | |
| all equations and values used or access to the source code. | |
| <div class="p"><!----></div> | |
| This study shows that JAT has the capability to closely match the | |
| ability of commercial packages. However, the uncertainty of the | |
| models for both spherical harmonic and atmospheric drag indicates | |
| that exact agreement does not necessarily correspond to accurate | |
| propagation. It is recommended that propagators seek to ensure the | |
| current, correct algorithms for Earth rotation from the IAU and IERS | |
| as well as the correct atmospheric data from NOAA in addition to | |
| validation against existing codes. Commercial packages such as | |
| STK/HPOP and FreeFlyer often implement different conventions and | |
| data sets in different versions, so care should be taken in | |
| determining the standards used. | |
| <div class="p"><!----></div> | |
| <h2><a name="tth_sEc11"> | |
| 11</a> Future Work</h2> | |
| The goal of JAT is to provide high-fidelity models for simulation of | |
| guidance, navigation, and control of spacecraft. As an open source | |
| project, the Java Astrodynamics Toolkit will continue to be updated | |
| with new conventions and updated data from the IERS, IAU, and NOAA. | |
| It will grow in both accuracy and functionality as the project | |
| progresses. | |
| <div class="p"><!----></div> | |
| <h2>References</h2> | |
| <dl compact="compact"> | |
| <dt><a href="#CITEChao:2000" name="Chao:2000">[1]</a></dt><dd> | |
| C. C. Chao and J. W. Cook et al. | |
| <i>Independent Verification and Validation for Analytical Graphics, | |
| Inc. of Three Astrodynamic Functions of the Satellite Tool Kit: | |
| Version 4.1.0.</i> | |
| Aerospace Corporation. El Segundo, CA. ATR-2000(7605)-1. 15 February 2000. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITECarpenter:2003" name="Carpenter:2003">[2]</a></dt><dd> | |
| J. R. Carpenter, editor. | |
| <i>Global Positioning Service Enhanced Onboard Navigation System, | |
| Mathematical Specifications.</i> | |
| Version 2, Release 2.1 December 2003. | |
| Goddard Space Flight Center, Mission Engineering and Systems | |
| Analysis Division/Code 595. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEGaylor:2005" name="Gaylor:2005">[3]</a></dt><dd> | |
| D. Gaylor, R. Page, T. Berthold. | |
| Java Astrodynamics Toolkit. | |
| URL: <a href="http://jat.sourceforge.net"><tt>http://jat.sourceforge.net</tt></a>, Accessed July 2006. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEIERS:2004" name="IERS:2004">[4]</a></dt><dd> | |
| International Earth Rotation and Reference Systems Service. | |
| <i>IERS Bulletin A Reports</i>, 2004. | |
| URL: <a href="ftp://cddisa.gsfc.nasa.gov/pub/reports/iers/bulletin_a/volume_xvii/iers_bulletina.xvii_021"><tt>ftp://cddisa.gsfc.nasa.gov/pub/reports/iers/bulletin_a/volume_xvii/iers_bulletina.xvii_021</tt></a>, Accessed July 2005. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITENOAA:2005" name="NOAA:2005">[5]</a></dt><dd> | |
| NOAA. | |
| Geomagnetic k<sub>p</sub> and a<sub>p</sub> Indices. | |
| URL: <a href="http://www.ngdc.noaa.gov/stp/GEOMAG/kp_ap.html"><tt>http://www.ngdc.noaa.gov/stp/GEOMAG/kp_ap.html</tt></a> | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITESeidelmann:1992" name="Seidelmann:1992">[6]</a></dt><dd> | |
| P.K. Seidelmann, B. Guinot and L.E. Doggett. | |
| "Time". <i>Explanatory Supplement to the Astronomical | |
| Almanac.</i> | |
| University Science Books. Mill Valley, CA, 1992:[48-53] | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEHohenkerk:1992" name="Hohenkerk:1992">[7]</a></dt><dd> | |
| C.Y. Hohenkerk, B.D. Yallop, C.A. Smith, and A.T. Sinclair. | |
| "Celestial Reference Systems". <i>Explanatory Supplement to the | |
| Astronomical Almanac.</i> | |
| University Science Books. Mill Valley, CA, 1992:[95-120] | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEMcCarthy:1996" name="McCarthy:1996">[8]</a></dt><dd> | |
| D.D. McCarthy. | |
| IERS Standards. IERS Technical Note 21. | |
| U.S. Naval Observatory. 1996. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEIERSB" name="IERSB">[9]</a></dt><dd> | |
| International Earth Rotation and Reference Systems Service. | |
| <i>IERS Bulletin B Reports</i>, 2004. | |
| URL: <a href="http://www.iers.org/iers/publications/bulletins/"><tt>http://www.iers.org/iers/publications/bulletins/</tt></a>, Accessed July 2005. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEVallado:2001" name="Vallado:2001">[10]</a></dt><dd> | |
| D. A. Vallado. | |
| <i>Fundamentals of Astrodynamics and Applications, 2nd Edition.</i> | |
| Microcosm Press. El Segundo, CA. 2001:[528] | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEVallado:2005" name="Vallado:2005">[11]</a></dt><dd> | |
| D. A. Vallado. 2005. | |
| An Analysis of State Vector Propagation using Differing Flight Dynamics | |
| Programs. | |
| Paper AAS 05-199 presented at the AAS/AIAA | |
| Space Flight Mechanics Conference. Copper Mountain, CO. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEWertz:1978" name="Wertz:1978">[12]</a></dt><dd> | |
| J. R. Wertz. | |
| <i>Spacecraft Attitude Determination and Control.</i> | |
| D. Reidel Publishing Company. Dordrecht, Holland. 1978:[3,8,9] | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITENRLMSISE" name="NRLMSISE">[13]</a></dt><dd> | |
| M. Picone, A.E. Hedin, and D. Drob. | |
| <i>NRLMSISE-00 Model 2001.</i> | |
| URL: | |
| <a href="http://modelweb.gsfc.nasa.gov/atmos/nrlmsise00.html"><tt>http://modelweb.gsfc.nasa.gov/atmos/nrlmsise00.html</tt></a>, Accessed | |
| July 2006. | |
| <div class="p"><!----></div> | |
| </dd> | |
| <dt><a href="#CITEMontenbruck" name="Montenbruck">[14]</a></dt><dd> | |
| O. Montenbruck, E. Gill. | |
| <i>Satellite Orbits.</i> | |
| Springer-Verlag Berlin Heidelberg. The Netherlands. | |
| 2000:[88]</dd> | |
| </dl> | |
| <div class="p"><!----></div> | |
| <hr /><h3>Footnotes:</h3> | |
| <div class="p"><!----></div> | |
| <a name="tthFtNtAAB"></a><a href="#tthFrefAAB"><sup>1</sup></a>VP Aerospace Systems, dave.gaylor@emergentspace.com | |
| <div class="p"><!----></div> | |
| <a name="tthFtNtAAC"></a><a href="#tthFrefAAC"><sup>2</sup></a>Aerospace Engineer, richard.page@emergentspace.com | |
| <div class="p"><!----></div> | |
| <a name="tthFtNtAAD"></a><a href="#tthFrefAAD"><sup>3</sup></a>Aerospace Engineer, kate.bradley@emergentspace.com | |
| <br /><br /><hr /><small>File translated from | |
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| by <a href="http://hutchinson.belmont.ma.us/tth/"> | |
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| version 3.74.<br />On 30 Aug 2006, 11:44.</small> | |
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