During the last decade or so, the Pioneer Anomaly has become one of the great unsolved puzzles in astrophysics.

The problem is this. The Pioneer 10 and 11 spacecraft were launched towards Jupiter and Saturn in the early 1970s. After their respective flybys, they continued on escape trajectories out of the Solar System, both decelerating under the force of the Sun’s gravity. But careful measuremenrs show that the spacecraft are slowing faster than they ought to, as if being pulled by an extra unseen force towards the Sun.

This deceleration is tiny: just (8.74±1.33)×10^−10 ms^−2. The big question is where does it come from.

Spacecraft engineers’ first thought was that heat emitted by the spacecraft could cause exactly this kind of deceleration. But when they examined the way heat was produced on the craft, by on board plutonium, and how this must have been emitted, they were unable to make the numbers add up. At most, thermal effects could account for only 67 per cent of the deceleration, they said.

That led to a host of other ideas some of which I’ve covered in this blog. For example, last year we looked at work ruling out the possibility that gravity could be stronger at these distances, since we ought to be able to see a similar effect on the orbit of other distant objects such as Pluto.

Now Frederico Francisco at the Instituto de Plasmas e Fusao Nuclear in Lisbon Portugal, and a few pals, say they’ve worked out where the thermal calculations went wrong.

These guys have redone the calculations using a computer model of not only how the heat is emitted but how it is reflected off the various parts of the spacecraft too. The reflections turn out to be crucial.

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 travelling.

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 (see diagram above).

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,” say Francisco and co.

Lo and behold, this extra component of force makes all the difference. As Francisco and co put it: “With the results presented here it becomes increasingly apparent that, unless new data arises, the puzzle of the anomalous acceleration of the Pioneer probes can ﬁnally be put to rest.” In other words, the anomaly disappears.

Of course, other groups will want to confirm these results and a team at the Jet Propulsion Laboratory in Pasadena, which has gathered the data on the probes, is currently studying its own computer model of the thermal budgets.

It’ll be interesting to see whether they agree. If they do; problem solved. Probably!

Ref: arxiv.org/abs/1103.5222: Modelling The Reﬂective Thermal Contribution To The Acceleration Of The Pioneer Spacecraft

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