Can an asymetrical radiation explain the Pioneer anomaly?

Three recent publications support a thermal origin of the Pioneer Anomaly:

- Support for the thermal origin of the Pioneer anomaly, S. Turyshev (JPL) et al (1)

- Modelling the reflective thermal contribution to the acceleration of the Pioneer spacecraft, Bertolami et al (2)

- High precision thermal modeling of complex systems with application to the flyby and Pioneer anomaly B. Rievers , C. Lammerzahl (3)

According to (3), page 446: " two major contributors to the Thermal Radiation Pressure (TRP) can be identified. The louver blades, although completely closed for the later mission time, still emit a major part of the waste heat produced in the compartment which is mainly caused by the high insulating properties of the MLI." This is because the compartment is completely shielded by the Multi Layor Insulator (MLI) except at the location of the louver blades.

According to (2), page 13: one needs to assume that "the front wall, including the louvers, is responsible for at least
70% of the emission (scenarii 2, 3 , 4, 5) from the main compartment", otherwise one could not explain more than ~25% of the Pioneer anomaly (scenario 1)..

According to (1), page 4 : the thermal analysis shows that 45% of the Pioneer anomaly, thus the main contribution to it, can be explained by an asymetrical radiation (27 Watts more projected power emitted in the front direction than the back direction) of the heat produced inside the main compartment (~60Watts).

 Though it is not clearly specified exactly in (1) (at the contrary to (2) and (3)) whether the closed louver blades were responsible for a major part of the waste heat from the main compartment, this is probably the case since neither (2) nor (3) could explain a significant part of the anomaly without this contribution. This is confirmed in this April 2008 presentation by the JPL (4) where we read that "Louvers are modeled with effective emittance between 0.13 (closed) and 0.74 (open)". Indeed as we shall check later this 0.13 assumption alone explains their ability to account for a significant part of the anomaly.

The idea that the asymetric radiation of the spacecraft is mainly due to the louvers high effective emissivity relative to the other surfaces shielded by the MultiLayerInsulator was first supported by Scheffer, LK in Conventional Forces can explain the anomalous acceleration of Pioneer 10. and Support for a prosaic explanation for the anomalous acceleration of Pioneer 10 and 11. Citation, page 2: "Multi-layer insulation is specifically designed to reduce heat losses, whereas the louvers have at most one layer of obstruction even when closed....Therefore a majority of the heat will be radiated from the front of the spacecraft."
Considering the effective emissivities as advocated by Scheffer, one must compute the radiated power by each surface using the Stefan Boltzmann law : P= sigma S e T4 where e is the effective emissivity and T the internal temperature.
According to Scheffer the effective emissivity is ~0.01 for the MLI and would need to be around 0.27 (thus much higher) for the louvers to explain the Pioneer anomaly.
Such a high postulated effective emissivity of the louvers is contested by Anderson et al in Un-prosaic exposition of a prosaic explanation, arguing that (page 2): "the louvers when closed are designed not to radiate heat but to retain heat. There are second surface mirrors on the insides of the louvers."
Then Anderson considers the real emissivities (rather than the effective ones) which are the emissivities of the exterior surfaces and are well known (0.70 for the exterior surface of the MLI and 0.04 for the bare Aluminum of the louvers). Of course both approaches are valid to compute the radiated power : either use external surface emissivity and external surface temperature or effective emissivity and internal temperature in the Stefan -Boltzmann law.
In the Anderson approach it is the external temperature that is the main unknown however Anderson comments: "In fact saying all the 57 W goes out the louvers with an area of ∼1 m2 and the Stefan -Boltzmann law would mean the exterior louver temperature was 398 K . This explains why it is difficult to understand the hypothesized louver, directed-heat emission mechanism.".

Now if publications (1) and (3) really were able to convincingly show that Scherrer was right through detailed thermal modeling and simulations ((2) just assumes this to be the case), this can be checked by inspecting their published temperature maps. One can either check that the louvers exterior surface temperature is as high as needed, or equivalently that the temperature on the other surfaces is as low as needed for the major part of the power to be radiated through the closed louvers. One can additionally check that the louver exterior surface temperature is not greater than the mean internal temperature which would be a complete nonsense!

- The maps in (3) are shown in Fig 7 page 445: the louvers external surface temperature is not shown (!!!?) but the internal temperature is shown to be quite homogeneous : between 250K and 260K, which of course cannot be exceeded by the temperature on any external surface, for instance that of the louvers. Therefore the power emitted by the external surface of the louvers (0.36 m2 to be compared with total exterior surface 4.6 m2 according table 2.3 page 25. ) cannot exceed (is certainly much smaller than):
P = 5.67 10-8 x 0.04 x 0.36 x (260)4= 3.7 Watts. This is not even directional power and is completely unsignificant relative to the total waste heat in the main compartment at this time (~80 Watts): so where is the bug ?!

The maps in (1) are shown in Fig 1 page 2:
- The mean temperature on the visible external surfaces (front and side) varies between -155C=118K and -108C=165K. Let's take a reasonable mean (check the map) of  141K  and a total exterior surface excepting the louvers external surface of 4.24  m2. Thanks to the emissivity of  0.7 the computed Power is P = 66 Watts which is a significant part of the total 94 Watts available at that time (40 UA from the sun).
- It's not clear at all whether what's shown on the map for the louvers is the temperature of their exterior surfaces (if yes, it's at most -100C=173K and their radiated power is negligible given their very small surface emissivity, ... notice that a few louvers are even left  uncolored!!!???)  but again the temperature at the exterior surface of the louvers cannot reasonably exceed the internal temperature of about 270K and an upper bound for the power emitted by the louvers can be computed.
We get a similar result as that deduced from the temperatures in (3). P is certainly much smaller than 4.3 Watts which is again completely unsignificant relative to the total waste heat in the main compartment (94 Watts) at that time: so again where is the bug ?!

Therefore the contribution of the louvers to the radiated power has been found to be negligible in all cases, as expected from basic arguments already published a long time ago by Anderson.

We know that the spacecrafts were actually designed to be as isotropic as possible in their radiated power. Since the presence of the HGA breaks the geometrical fore-aft isotropy by modifying the heat flow in the rear direction, this had to be compensated and only the louver blade system could do that by equally retaining the heat (when closed) in the front direction. Given their very small external surface emissivities and the fact that their external surface temperature was necessarily much smaller than the ones inside the main compartment (necessarily because again: "the louvers when closed are designed not to radiate heat but to retain heat. There are second surface mirrors on the insides of the louvers") the radiated power through the louvers was actually negligible.  In other words the front side of the main compartment sees its effective surface reduced by 0.36 m2 , from 4.6 m2 to 4.24 m2 resulting in the reduction of its radiated power in the same proportion ~ 8% and this must compensate the following effects of the HGA:
- A large fraction of the back emitted power reflected by the HGA comes back to the back face of the main compartment and is reabsorbed then
- Directly or after several reflections or absorption-reemissions a fraction escapes at large angles
- Another fraction is absorbed by the HGA and should be preferentially reemitted by its front face toward the sun which emissivity is much larger (white paint instead of bare Al)...

Then what could explain that from a total of 60 Watts available inside the main compartment, the total radiated projected power on the front direction exceeds the total radiated projected power on the back direction by 27 Watts which is needed to account for 45% of the Pioneer anomaly as explained in (1)?
The totally incorrect assumption that the effective emissivities of the louver blades could be as high as  0.13 can do a significant part of the job as we now want to show.

Indeed starting fron an isotropically radiating spacecraft replacing louvers with a surface emissivity of 0.04 and negligible radiated power by louvers with effective emissivity 0.13, now makes these louvers radiate a power P = 5.67 10-8 x 0.13 x 0.36 x (276)4= 15.4 Watts where we have taken a typical internal temperature  of 276K (see temperature maps in (4) and (1)) instead of P = 5.67 10-8 x 0.04 x 0.36 x (176)4= 0.8 Watts. This 14.6 Watts excess artificially generated on the front face of course means that there must be an equal deficit on the side and rear faces approximately (at first order) proportionnal to their surfaces. The deficit on the rear face will be 14.6 x 1.55/(1.55+0.65+1.21) = 6.6 Watts resulting in a breakdown of isotropy by 21.2 Watts hence 2/3  times 21.2 Watts ~14 Watts contribution to the anomaly. This is a significant part of the 27 Watts needed to explain 45% of the Pioneer anomaly from the asymetric radiation of the electrical power available inside the main compartment according to (1) and we dont know which exact effective emissivity "between 0.13 and 0.74" they eventually did use in the modelisation of the louver blades!

Additional remarks:
- Assuming 0.13 or more for the effective emissivity of the louver blades amounts to consider that there were an aperture anomaly of this system and eventually makes the spacecraft very anisoropic. Even the power emitted from the RTG and absorbed by the main compartment is now expected to be eventually radiated in free space very anisotropically, so may be we should not be surprised by a 35% contribution to the anomaly from the RTG according to (1) even though very simple solid angle computations by Anderson had shown that the reflection of the RTG radiated power off the HGA could only account for a very small part of the anomaly.
- The actual temperature on the external surfaces of the louvers which is a crucial info is either not documented (in 3) or appears in a very confusing way (in 1). Why? More looks like cover up and propaganda than anything else!