One of the main scientific goals of this thesis is the analysis of TRP acting on the Pioneer 10 during the 30 years of mission time where flight telemetry is available. In order to achieve this goal, subsequent thermal FE analysis and numerical TRP calcu-lations have been performed using the Pioneer 10 FE macro described in section 5.1 and the ray tracing algorithm introduced in section 3.4. The computations have been performed with a time resolution of 1 year between the simulated times, input param-eters and boundaries have been updated to the values valid for the simulated times.
For the computation of the resulting TRP accelerations acting on the craft a constant reference mass of 250 kg has been considered. The residual accelerations found by the JPL for Pioneer 10/11 are displayed in figure 6.7. Here the JPL residuals have been obtained for evaluating different ranges of available Doppler datA for both Pioneer 10 and 11. It can be seen that particularly for earlier mission times, errors bars in the resulting residuals are quite high. The general characteristics of the plot are an increase
6.4 Computation of TRP on the Pioneer 10 orbit 95
Figure 6.7: JPL Pioneer 10 acceleration residuals [18].
Figure 6.8: Computed TRP acting on Pioneer 10 [55].
of acceleration from close to zero at about 5 AU to a peak value at 20 AU. After this the acceleration stays in approximately the same range, although the error bars also allow to interpret a small linear decrease of TRP acceleration. The range from 15 AU - 45 AU has been used to obtain the published constant result for the Pioneer anomaly of aPio= 8.7410−10m/s2. Note that while the presented residuals have been acquired
for Pioneer 11 in the early mission range and for Pioneer 10 in the later mission times, Pioneer 10 should show corresponding results for the early mission as the spacecraft configuration is nearly identical and the trajectory does not differ drastically1.
Figure 6.8 shows the computed TRP acceleration aligned with global z-direction vs. heliocentric distance for the range of 1 AU - 50 AU to allow for a direct comparison with the evaluated JPL residuals. Here the discrete points in time for which TRP has been computed with the raytracing and thermal FE modelling method are marked with black quads. The heliocentric distances have been acquired from the available Pioneer 10 trajectory according to the simulated mission dates as described in section 5.1. For comparison the constant value of the PA as defined by the JPL is marked with a dashed line.
In general, the computed TRP matches the JPL residuals very closely and shows the same characteristic time evolution. TRP acceleration (aligned with globalz-direction) starts in the negative range for 1 AU and increases with growing heliocentric distance until it changes its sign in the region of 5 AU. It reaches a peak value at about 20 AU and decreases with a linear rate for larger heliocentric distances. With this the com-puted TRP results stay within the uncertainties of the JPL residuals. Note that due to the fact that the first data points given in the residuals acceleration have been eval-uated for Pioneer 11, in this range a larger deviation of the computed results seems reasonable since the trajectories of Pioneer 10 and 11 are slightly different.
The significant match of computed TRP and JPL residuals leads to the conclusion that the observed anomaly is caused by an unmodeled thermal recoil pressure. All characteristics of the residuals can be explained by different TRP effects. In the early mission, where the spacecraft is still close to the sun (between 1 AU - 5 AU) the HGA gets heated by direct solar illumination as displayed in figure 6.9 right. Here higher temperatures are displayed in red/orange and lower temperatures are displayed in blue.
Due to the considerable difference of HGA front and rear optical emissivities the ma-jor part of the heat energy introduced by solar illumination is emitted by the HGA front which leads to an effective TRP (not to be mixed with SRP, which is a different physical effect). The resulting contribution to the global TRP acts into flight direction and thus causes an acceleration of the craft. For small heliocentric distances this is the dominating thermal effect which explains that by global coordinate convention the resulting total TRP is in the negative range. Due to the dependency of the solar flux on the square root of the distance to the sun the resulting temperature of the HGA decreases in the course of the mission. This implies that the contribution of the HGA to the TRP also decreases with growing heliocentric distance and other thermal effects become dominant. Thus the TRP reaches the positive range (which implies a deceler-ation of the craft) at a heliocentric distance of about 5 AU.
The resulting TRP for distances larger than 5 AU is governed by two different ef-fects. The first larger fraction of the total TRP is caused by the emission of waste heat
1While Pioneer 10 only had a Jupiter flyby in 1973 after 1.5 years of mission, Pioneer 11 had an additional Saturn flyby after 6 years of operation. With this the flight velocity and the heliocentric distance varies slightly wit respect to Pioneer 10.
6.4 Computation of TRP on the Pioneer 10 orbit 97
Figure 6.9: Explanation for characteristic development of effective TRP direction. Red: high temperatures, orange: medium temperatures, blue: low temperatures.
from the RTG fins. Due to the geometric arrangement of RTGs, HGA and compart-ment a small fraction of the heat energy emitted by the RTGs is blocked by the highly reflective HGA rear surface and reflected into flight direction. The exact magnitude of the resulting TRP depends on the RTG surface temperatures as well as the radia-tion view factors which are computed accurately by 8-node Gauss integraradia-tion over all RTG/HGA surface pairs. The resulting recoil acts against flight direction and thus causes a deceleration of the craft in the range of 80 % of the PA at 25 AU. The effect is scaled by the mission time and subject to a small linear decrease which can be credited to the decreasing RTG fin root temperatures and the decreasing heat energy in the course of the mission.
The second dominant effect is the emission of waste heat produced within the com-partment. Due to the good isolation properties of the MLI as well as internal heat ra-diation waste heat is distributed almost homogeneously inside the compartment. This heat energy is now dissipated over the MLI, the louver system and the shunt radiator.
Due to the symmetry of the compartment and the attitude of the global coordinate sys-tem, the heat which is emitted by the side panel surfaces as well as the shunt radiator waste heat do not contribute to a TRP aligned with flight direction. The temperatures on the MLI front and rear faces are comparatively low which reduces the radiated heat flux. Furthermore radiation of the MLI front is mainly blocked by the HGA which results in multiple reflections between MLI and HGA surfaces. Effectively the thrust resulting from front MLI emission is mostly balanced by the emission of the MLI on the rear side of the compartment. This leaves the louver system as well as the MLI parts inside the launch adapter as only contributors for TRP. Here the louver system delivers the dominating fraction of compartment emission contributing to TRP which is caused by the much higher surface temperatures of the louver system and the dependence of the resulting heat flux to the fourth power of the temperature. Nevertheless the MLI inside the launch adapter contributes a small amount of emission to the resulting TRP. In combination both effects lead to an effective TRP of about 20 % PA at 25 AU directed against direction of flight which results from the geometric arrangement
of the components. As it is the case for the RTG contribution the magnitude of the effect scales with mission time which reflects the dependence on the available electrical energy as well as the compartment temperature sensor data.
In total the emission of waste heat from RTG, Louver system and partially the MLI leads to an effective TRP acting against flight direction in the magnitude of the PA at 25 AU which slowly decreases due to generally decreasing temperatures and available powers. Such a decrease in the evaluated residuals is expected by the JPL as result of the ongoing evaluation of the full Doppler data set [57]. Both the matching magnitude of the computed effect as well as the resembling characteristics of the JPL residuals and the computed results indicate that accurate modelling of TRP is the solution to the Pioneer anomaly.