10.4 SRP and TRP analysis for Rosetta flyby 135
to the Sun vector, it is clear that the net contribution of TRP during the flyby is a deceleration of the craft because the accelerating TRP component after the flyby is negligible to the decelerating effect on the incoming branch. For the analysed time interval this leads to a total deceleration of the craft in the range of 2.510−3m/s2 which rules out TRP as source of the flyby anomaly as the observed anomalous velocity jump was positive. This result is confirmed by analytical models given in [89] and [90], which lead to a comparable evolution and effect of the Rosetta TRP during flyby.
Figure 10.8: Rosetta trajectory for first Earth flyby on fourth of March, 2005 (left) and com-puted course of the TRP during flyby, aligned with flight direction (right).
For SRP during the first Rosetta flyby the same directional behaviour as shown for the TRP evolution is visible as also for SRP the resulting direction of the acceleration is aligned to the Sun vector. Therefore figure 10.8 also shows the qualitative course of the SRP. In general the magnitude of the SRP aligned to flight direction is about 10 times higher than the corresponding TRP. Thus also the SRP cannot explain the observed anomalous velocity jump. Therefore the origin of the FA remains unknown and has to be analysed further. However, the analysis of TRP and SRP suggests that the magnitude of the resulting velocity jump during flyby is actually higher than the published value, if SRP and TRP are determined precisely.
Part IV
Conclusion
Chapter 11
Summary and outlook
This section summarises the work performed in this thesis and highlights the main scien-tific results. An outlook on suitable expansions of this work and possible applications is given.
11.1 Summary
This thesis treats the development and utilisation of high precision numerical models for the evaluation of TRP and SRP acting on spacecraft with complex geometrical shape. The work was motivated by the general need for an improved perturbation analysis and the existence of yet unresolved anomalous behaviour of spacecraft which have become known as the Pioneer anomaly and the flyby anomaly. As application for our developed perturbation analysis methods, the deep space probes Pioneer 10 and Rosetta have been chosen as evaluation cases. The work which has been performed in this respect aims at a precise computation of TRP (for Pioneer and Rosetta) and SRP (only for Rosetta) as well as an evaluation of the obtained results with respect to the observed anomalies.
An introduction to the basics of TRP modelling has been given and an analytical model for TRP has been expanded to a numerical approach for the calculation of TRP on complex bodies. The elaborated method consists of two subsequent modelling steps.
First a complete thermal FE analysis has to be performed in order to calculate the tem-perature distribution along the spacecraft surface. For this detailed material models and the complex geometrical shape of the spacecraft have to be specified as a detailed FE model of the craft. Housekeeping and trajectory data can be added as boundary conditions to enable the determination of the steady state surface temperatures. In a second computation step the obtained temperature distribution as well as a geomet-rical surface model are processed with a newly developed ray tracing method which computes the resulting TRP based on radiation exchange, reflection and shadowing.
After a short description of the Pioneer 10 spacecraft and its main mission charac-teristics, the numerical TRP analysis method has been used for the determination of the magnitude of the TRP acting on the spacecraft during its 30 years mission. For this a detailed FE model of the craft has been developed which allows for the simula-tion of exterior as well as interior temperatures for the complete Pioneer 10 mission.
Conductive and radiative heat transfer between all model components have been im-plemented. Here measured temperature sensor data as well as the measured Pioneer 10 trajectory have been taken into account as boundary conditions. Based on the calcu-lated temperatures for each mission time, the resulting TRP has been determined with the ray tracing approach. Here a high precision computation of radiation exchange (by means of numerical integration of radiation view factors) has been implemented. The computed TRP results have been compared to the Pioneer 10 residual accelerations published in [9]. It was found that the course of the TRP matches in characteristics as well as in magnitude nearly perfectly with the residual acceleration. Thus it can be stated that the Pioneer anomaly can fully be explained by an unmodeled TRP.
The performance of this solution has been evaluated by means of parameter sensitivity analyses. It has been shown that within realistic parameter sets (which include errors in sensor data, degradation of surface properties etc.) the resulting TRP may vary by a maximum of±11.5 %. This result proofs that a very robust solution to the Pioneer anomaly has been found.
The thermal recoil acting on the spacecraft is caused by two major sources. The major contribution results from RTG radiation reflected at the back of the HGA, a smaller fraction of the TRP can be credited to heat radiation emitted by the louver system and parts of the MLI on the compartment rear surface. Both effects together lead to a recoil acting against flight direction with the magnitude of the PA. An in-teresting aspect is that for the first time the complete characteristics of the evolution of the residuals could be explained in this thesis. Within the first part of the mission the heliocentric distance is quite small which leads to a high thermal load (resulting from solar illumination) on the HGA. Owing to the fact that the HGA always points towards the Earth, the main direction of emission is directed against flight direction and the resulting TRP leads to an acceleration of the craft. While the distance to the Sun increases, the thermal load on the HGA and its TRP contribution decrease until at a distance of about 5 AU the HGA contribution and the RTG/compartment contri-butions become competitive and cancel each other. With larger heliocentric distance, the RTG and compartment contribution become dominating and the resulting TRP acts against flight direction, leading to a decelerating the craft. At about 15 AU the contribution of the HGA becomes negligible with respect to the RTG and compartment contribution leading to a maximum of deceleration. From there on the TRP decreases with a slow rate corresponding to the decreasing available electrical and thermal en-ergy in the course of the mission. As the JPL assumes now that the constancy is only credited to the short evaluated time and that the recently finished evaluation of the longer Doppler interval shows a decrease of the residual acceleration over mission time, the computed evolution of the TRP also fits with the update of the observed anomaly [74].
Based on the principles of TRP determination a corresponding modelling method for SRP has been developed. A short review of the Rosetta mission profile and the main geometrical aspects has been given. TRP and SRP have been evaluated for the heliocentric cruise phases by means of a detailed Rosetta FE model. It has been found that the TRP reaches about 10 % of the SRP magnitude within the analysed mission periods. The coincidence of this result with the discrepancies of the modelled and
11.2 Main scientific results 141