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
High precision thermal modeling of complex systems with application to
the flyby and Pioneer anomaly B. Rievers , C. Lammerzahl
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
of the emission (scenarii 2, 3 , 4, 5) from the main compartment",
otherwise one could not explain more than ~25% of the Pioneer anomaly
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).
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."
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
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 -155°C=118K and -108°C=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 -100°C=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.
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)?
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 =
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!
- 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!