The debate has been raging ever since an astronomer named John Anderson first noticed the anomaly in 1980. Anderson created an impossibly complicated algorithm so that he and other JPL scientists could use the radio transmission data to study gravitational effects in the outer solar system.
But it didn't seem to work. Or rather, he noticed a small discrepancy between the Doppler shifts predicted by his algorithm, and the actual shifts being measured in the radio signals coming from the Pioneer spacecraft.
Dark Matter Drag?
The discrepancy is 10 billion times smaller than the acceleration due to gravity, but it was unmistakably there in Anderson's calculations. (The canonical number, for those who care, is 8.74 x 10-10 m/s2.)
What could be causing this discrepancy? Theories have abounded over the years. One popular hypothesis is that there are huge quantities of dark matter -- as yet undetected -- hanging around in the universe and exerting a little extra drag on the spacecraft, thereby slowing them down.
Another possible explanation is that gravity doesn't follow an inverse square law as formulated by Isaac Newton; this falls under the rubric of MOND (MOdified Newtonian Dynamics), the focus of a flurry of technical papers over the last 10-15 years. It's among the alternatives to dark energy to explain the fact that the expansion of our universe is accelerating.
Evidence for this hypothesis appeared to be bolstered in 1994, when Los Alamos cosmologist Michael Martin Nieto noticed that the value for the deviations of the Pioneer spacecraft was almost exactly equivalent to cosmic acceleration (the speed of light multiplied by Hubble's constant).
For Nieto, and others who noticed this strange coincidence, "The Pioneer anomaly could be the first evidence that gravity deviates from an inverse square dependence," he told Popular Science last year. "It could be huge." ...
On the more mundane side of things, there was always the possibility that the culprit might just be heat. Specifically, heat from the plutonium inside the spacecrafts' generators, some of which got converted into electricity while the rest of it radiated into space. If it did so unevenly, radiating more heat in one direction than in another -- only a 5 percent difference is required -- that might be sufficient to give rise to the Pioneer anomaly. ...
Previous calculations have only estimated the effect of reflections. So Francisco and co used a computer modeling technique called Phong shading to work out exactly how the the emitted heat is reflected and in which direction it ends up traveling.
Phong shading was dreamt up in the 1970s and is now widely used in many rendering packages to model reflections in three dimensions. It was originally developed to handle the reflections of visible light from 3D objects but it works just as well for infrared light, say Francisco and co.
In particular, Phong shading has allowed the Portuguese team to include for the first time the effect of heat emitted from a part of the spacecraft called the main equipment compartment. It turns out that heat from the back wall of this compartment is reflected from the back of the spacecraft's antenna. Since the antenna points Sunward, towards Earth, reflections off its back would tend to decelerate the spacecraft. "The radiation from this wall will, in a ﬁrst iteration, reﬂect off the antenna and add a contribution to the force in the direction of the sun."
via Mysterious Pioneer Anomaly May Finally Be Solved : Discovery News.
I was really hoping for some momentous variation in the force of gravity, but it seems that possibility with regard to the Pioneer data, has been vanquished.