Thermal analysis of the Pioneer anomaly: A method to estimate radiative momentum transfer

We present a methodology based on pointlike Lambertian sources that enables one to perform a reliable and comprehensive estimate of the overall thermally induced acceleration of the Pioneer 10 and 11 spacecraft. We show, by developing a sensitivity analysis of the several parameters of the model, that one may achieve a valuable insight into the possible thermal origin of the so-called Pioneer anomaly.

Figure 1

Polar plot of the intensity variation with elevation of the radiation emitted by a surface on the $0xy$ plane (solid angle $\Omega$), when considering 1, 4, and 16 Lambertian sources (full, dashed, and gray curves, respectively), maintaining the total emitted power constant at 1 W (the curves for 64 or 144 sources overlap the one for 16 sources). The intensity at higher elevations (close to vertical) diminishes with the number of sources, compensating the slight increase at the lower angles.

Figure 2

Same as Fig. 1 but for intensity variation with the azimuthal angle $\theta$. All lines are superimposed, confirming that the total power is kept constant.

Figure 3

Geometry of test case 8 (cf. Table ): thermal emission from a surface is simulated by a different number of Lambertian sources evenly distributed on the surface, maintaining the total power emitted constant, and the effect on a second surface is observed. This is the test case where the highest variation in the number of sources considered was obtained.

Figure 4

Same as Fig. 3, for test case 1.

Figure 5

Pioneer spacecraft model geometry considered in calculations, back view: high gain antenna and hexagonal main bus compartment.

Figure 6

Schematics of our simplified model of the Pioneer spacecraft, with relevant dimensions (in cm); second RTG and truss are not represented to scale, for convenience. The lateral view indicates the relative position of the RTGs, the box compartment, and the gap between the latter and the high gain antennas.

Figure 7

Variation of the resulting acceleration with the temperature ratio between the louvers and the equipment platform, considering similar emissivities for both multilayer insulations.

Figure 8

Variation of the resulting acceleration with the temperature ratio between the base of the RTG cylinder and the fin temperature.