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High Precision Modelling of Thermal Perturbations with Application to Pioneer 10 and Rosetta

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High Precision Modelling of Thermal Perturbations with Application to Pioneer 10 and Rosetta High precision modelling of thermal perturbations with application to Pioneer 10 and Rosetta Vom Fachbereich Produktionstechnik der UNIVERSITAT¨ BREMEN zur Erlangung des Grades Doktor-Ingenieur genehmigte Dissertation von Dipl.-Ing. Benny Rievers Gutachter: Prof. Dr.-Ing. Hans J. Rath Prof. Dr. rer. nat. Hansj¨org Dittus Fachbereich Produktionstechnik Fachbereich Produktionstechnik Universit¨at Bremen Universit¨at Bremen Tag der m¨undlichen Pr¨ufung: 13. Januar 2012 i Kurzzusammenfassung in Deutscher Sprache Das Hauptthema dieser Doktorarbeit ist die pr¨azise numerische Bestimmung von Thermaldruck (TRP) und Solardruck (SRP) f¨ur Satelliten mit komplexer Geome- trie. F¨ur beide Effekte werden analytische Modelle entwickelt und als generischen numerischen Methoden zur Anwendung auf komplexe Modellgeometrien umgesetzt. Die Analysemethode f¨ur TRP wird zur Untersuchung des Thermaldrucks f¨ur den Pio- neer 10 Satelliten f¨ur den kompletten Zeitraum seiner 30-j¨ahrigen Mission verwendet. Hierf¨ur wird ein komplexes dreidimensionales Finite-Elemente Modell des Satelliten einschließlich detaillierter Materialmodelle sowie dem detailliertem ¨außerem und in- nerem Aufbau entwickelt. Durch die Spezifizierung von gemessenen Temperaturen, der beobachteten Trajektorie sowie detaillierten Modellen f¨ur die W¨armeabgabe der verschiedenen Komponenten, wird eine genaue Verteilung der Temperaturen auf der Oberfl¨ache von Pioneer 10 f¨ur jeden Zeitpunkt der Mission bestimmt. Basierend auf den Ergebnissen der Temperaturberechnung wird der resultierende Thermaldruck mit Hilfe einer Raytracing-Methode unter Ber¨ucksichtigung des Strahlungsaustauschs zwischen den verschiedenen Oberf¨achen sowie der Mehrfachreflexion, berechnet. Der Verlauf des berechneten TRPs wird mit den von der NASA ver¨offentlichten Pioneer 10 Residuen verglichen, und es wird aufgezeigt, dass TRP die so genannte Pioneer Anomalie inner- halb einer Modellierungsgenauigkeit von 11.5 % vollst¨andig erkl¨aren kann. Durch eine Modifizierung des Algorithmus f¨ur die Bestimmung von TRP, wird ein numerisches Vefahren f¨ur die Analyse von SRP entwickelt. Beide Methoden werden f¨ur die Analyse von SRP und TRP f¨ur die Rosetta Sonde am Beispiel ausgew¨ahlter heliozen- trische Freiflugphasen sowie f¨ur den ersten Erd-Flyby verwendet. F¨ur die untersuchten Freiflugphasen ergibt sich die H¨ohe des TRPs im Bereich von 10 % der berechneten SRP Gr¨oßenordnung, was Abweichungen der erwarteten Rosetta-Trajektorie erkl¨art, die von ESA/ESOC festgestellt wurden. Hierbei wurden f¨ur die Modellierung des SRPs Abweichungen im Bereich 5 % - 10 % festgestellt, welche nahezu perfekt mit der modellierten Gr¨oßenordung des TRP ¨ubereinstimmen. F¨ur den Flyby werden sowohl TRP als auch SRP als m¨ogliche Ursachen f¨ur die beobachtete Flyby Anomalie aus- geschlossen, da beide Effekte zu einer Abbremsung von Rosetta f¨uhren, wohingegen eine anomale Beschleunigung w¨ahrend des Flybys beobachtet wurde. ii Abstract The main topic of this thesis is the precise numerical determination of thermal re- coil pressure (TRP) and solar radiation pressure (SRP) acting on complex spacecraft bodies. Analytical models for both effects are developed and expanded into a generic numerical approach for the treatment of complex model geometries. The TRP analysis method is used for an evaluation of thermal recoils acting on the Pioneer 10 spacecraft during its 30 years mission. For this a complex three-dimensional Finite Element model of the craft with detailed material models and accurate exterior and interior geomet- rical configuration is developed. By specifying the available housekeeping data, the measured trajectory as well as detailed models for the heat generation of the different components, an accurate distribution of the Pioneer 10 surface temperatures can be computed for each part of the mission. Based on these surface temperature distribu- tions, the resulting recoil is computed by means of a ray tracing method, which allows for the radiation exchange between surfaces as well as the inclusion of multiple reflec- tions. The evolution of the computed TRP is compared to the Pioneer 10 residuals published by NASA and it is found that TRP can explain the so called Pioneer anomaly completely within a modelling accuracy of 11.5 %. By modifying the TRP algorithm, a numerical approach for the analysis of SRP is developed. Both methods are used to analyse SRP and TRP for the Rosetta spacecraft during chosen heliocentric cruise phases as well as for the first Rosetta Earth flyby. For the cruise phases it is found that the TRP is in the order of 10 % of the SRP magnitude which explains discrepancies from the expected Rosetta trajectory found by ESA/ESOC. Here acceleration errors in the order of 5 % to 10 % of the SRP magnitude have been observed during the heliocentric cruise phases which perfectly complies to the obtained TRP magnitude. For the flyby TRP and SRP are ruled out as possible causes for the flyby anomaly due to the fact that both effects lead to a deceleration of Rosetta on its flyby trajectory and not to an anomalous increase of the velocity, as is the case for the observed anomaly. iii Acknowledgements First of all, I would like to acknowledge the support of Prof. Dr. Hans J. Rath and Prof. Dr. Hansj¨org Dittus for being the referees of this thesis. In particular, I would like to thank Prof. Dr. Claus L¨ammerzahl for his support throughout the years, the many fruitful discussions, the cooperative work as well as initially providing me with the interesting research topic of the Pioneer anomaly. I would also like to acknowledge the cooperation with Prof. Dr. Jozef van der Ha and Dr. Takahiro Kato, who strongly supported my work regarding the Rosetta mission, especially during the last year. Furthermore, I would like to thank the ISSI institute for providing support for the meetings of the Pioneer collaboration as well as Dr. Slava G. Turyshev and the JPL for fruitful discussions. Likewise, I would like to thank all my colleagues of the fundamental physics group at ZARM for their support and the good time that I had. Additionally, I would like to express my gratitude to my office colleagues, Dr. Meike List and Stefanie Bremer, for all these years of kind support. Furthermore, many thanks go to Dr. Eva Hackmann, Dennis Lorek, Benjamin Tilch and Torben Prieß, who did a remarkable job at proof- reading this thesis in a very limited time. The financial support by the German Research Foundation DFG as well as the cluster of excellence QUEST is gratefully acknowledged. I would like to express my deep gratitude to my family, in particular my mother Petra, for supporting me by all means throughout all these years. Finally, I would like to thank my wife Silvia for all her love and patience. Without her support, this work would not have been possible. Bremen, August 2011 Benny Rievers iv Symbols a Gauss integration border 1 [-] ai Transformed triangle vertex point a [-] 2 ap SRP component perpendicular to sun direction [m/s ] 2 as SRP component aligned with sun direction [m/s ] A Surface area [m2] A Quaternion rotation matrix [-] A(i) Surface area of element i [m2] Ay Quaternion rotation matrix with axis y’ [-] Az Quaternion rotation matrix with axis z [-] 2 A1 Surface of active element [m ] 2 A2 Surface of receiving element [m ] α Coefficient of absorption [-] αgap Absorptivity of gabs between solar cells [-] αmean Mean absorptivity [-] αcell Solar cell absorptivity [-] αSP Solar panel absorptivity [-] b Gauss integration border 2 [-] bi Transformed triangle vertex point b [-] c1, c2, c3 Hit detection parameters 1-3 [-] Ci Polynomial term for DOF constraint equation [-] C0 Constant term for DOF constraint equation [-] χi, χj, χk, χl Uniform Gauss coordinates [-] dhs Diameter of hemisphere [m] dMLI Thickness of MLI [m] Di DOF parameter for DOF constraint equation [-] dΩ Solid angle element surface [-] ∆v Velocity jump during flyby [m/s] ∆T Temperature gradient [K] e Eccentricity [-] e1, e2, e3 Components 1-3 of Quaternion rotation axis [-] ~ec(i) Active element centre [-] ~ec(j) Receiving element centre [-] ~ec,Ω(i, φ, θ) Solid angle element centre [-] ~eN(i) Element normal vector on element i [-] E Energy [J] E~ Quaternion rotation axis [-] EHeat Heat energy [J] Einc Incoming energy [J] EPh Photon energy [J] EVolt Electrical energy [J] ε Coefficient of emission [-] εl,eff Effective louver emissivity [-] εγ Specific coefficient of emission [-] εmean Mean coefficient of emission [-] εss Emissivity of second surface mirrors [-] v εb Emissivity of louver blades [-] ε∗ Effective MLI emissivity [-] ηcell Efficiency of solar cells [-] ηc Efficiency of louver heat conduction [-] ηMLI MLI performance [-] f~a Force resulting from absorption [N] fp Cell packing factor [-] f~s Force resulting from specular reflection [N] f~s,abs Absorption component of specular reflection force [N] f~s,refl Reflection component of specular reflection force [N] f~d Force resulting from diffuse reflection [N] f~d,abs Absorption component of diffuse reflection force [N] f~d,refl Reflection component of diffuse reflection force [N] Fa Force component resulting from absorption [N] Fr Force component resulting from reflection [N] F~TRP Thermal recoil force [N] F~TRP,Ω,eff Effective thermal recoil force component [N] g(x) Parametric function [-] g˜(χ) Transformed parametric function [-] γ Coefficient of reflection [-] γd Coefficient of diffuse reflection [-] γmean Mean reflectivity [-] γs Coefficient of specular reflection [-] i Active Element number [-] I Intensity of radiation [W/m2] 2 In Intensity of radiation emitted
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