The most obvious theory was that something on the spacecraft themselves created a braking force--leaking gas or heat radiation, perhaps. Over the years, however, researchers increasingly viewed this hypothesis as less likely, and some physicists began to explore possible flaws in Newton's laws and relativity. Others posited that dark matter was the culprit: it might exert a gravitational or drag force. A third theory embraces the idea that a minute acceleration exists in the velocity of light, which might result in the appearance that the probes are slowing down: if light travels faster, telemetry signals arrive faster, and the craft seem to be closer.
Anderson and theorist Michael M. Nieto of Los Alamos National Laboratory have proposed a way to filter the ideas, noting the interesting fact that the direction of the anomalous force would be different for each theory. If the force points toward the sun, then it should be a gravitational effect. If it points toward Earth, it should be an anomaly relating to the velocity of light. If it points in the direction of motion, it should be a drag force or a modification of inertia. And finally, if it points along the spin axis of the probes, it should indicate a force generated by the craft.
But determining the force's direction means studying telemetry when the Pioneer craft were closer than 20 astronomical units (1 AU equals the distance between Earth and the sun). Within this distance, to about Uranus's orbit, the angles between the sun, Earth and the craft's motions are sufficiently large. Until now, though, investigators have mostly analyzed telemetry covering the distance beyond 20 AU (to 70 AU so far--Pioneer 10's last useful transmission occurred at 80 AU in 2002). Experts had not bothered to study closer-in data in detail because they believed that radiation pressure of the sun and the many flight maneuvers would make it difficult to measure the anomaly.
Nieto and Anderson insist that it should be possible to correct for these factors and determine the direction of the anomalous force, especially in Pioneer 11's trajectory between Jupiter and Saturn. At that point, it traveled at practically a right angle to the direction of the sun and Earth, so any force toward the sun or Earth will be noticed by a sideways displacement of the probe. And rough measurements seem to show that the anomaly existed back to 10 AU, Nieto says. The telemetry for the early part of the Pioneer missions is available, so the analysis "is a relatively cheap thing to do, and at the very least it will give us more information and perhaps an indication," he remarks.
Especially if the mysterious force points toward the sun, then the explanation might be a deviation from Newtonian dynamics--termed modified Newtonian dynamics, or MOND--an idea originally proposed to explain why rotating galaxies do not fly apart. Dark matter may modify gravity, though as an alternative, Mordehai Milgrom of the Weizmann Institute of Science in Rehovot, Israel, proposes an additional component of gravity that should appear over large distances. In any case, MOND has become one of the more popular approaches to solving the anomaly problem. Jacob D. Bekenstein of the Hebrew University in Jerusalem applied a relativistic theory of MOND to the solar system and found that the Pioneer anomaly "is of crudely the right magnitude" to fall within MOND.