After about twenty years studying of Pioneer-effect the theory that the origin of this anomaly is a recoil force associated with an anisotropic emission of thermal radiation off the spacecrafts received significant support. Although dependence of additional radial acceleration on radial velocity towards to Sun a=-Q(v_r)^2 with Q= 4.13*10^(-20) cm conforms to the basic properties of the Pioneer-effect. Estimation of its action on radial perturbations of Neptunian satellites Proteus and Triton in a first approximation gives close to observed values.
An alternative view, given in article at http://vixra.org/abs/1106.0035 , may be of interest.
Nainan
While both the heliocentric radial acceleration of the Pioneer 10 spacecraft and its "anomalous" acceleration decrease over time, I do not believe that a strong correlation exists between the two, even if we purposefully ignore the thermal recoil force. See attached image.
Can you explain what you mean by that question? If you are referring to the Pioneer 10-11 orbits, they are of course hyperbolic.
Coefficient Q was taken as constant in a first approximation. More precisely with this approach it probably decreases with distance.
In assumption of square dependence of Proteus and Triton radial perturbations on velocity towards to Sun the thermal recoil force can give about 60% in additional acceleration of Pioneer’s on the distance of 30 AU.
Graham,
This result was obtained using non-standard approach, which is known as cine-film. A particle, observed as moving in 4D space-time, is in 5D space-time a series of appearances of particles in 4D volume. The light owing to which we receive information about particle motion is assumed to moving in 4D volume. In 5D space-time the particles move along close to elliptical orbits, while their traces can form hyperbola in 4D.
Forgive me Graham but I have a hard time parsing your English. In any case, the Pioneer anomaly was never about positions: it was about computed vs. measured Doppler frequency observables. And the anomaly has been resolved once the thermal recoil force due to heat generated on board was properly modeled using appropriate engineering tools, and incorporated into the orbital model.
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