As early as Pioneer 10 and Pioneer 11, NASA and other spaceflight agencies have noticed a small discrepancy in the expected and actual trajectories of space probes. The twin probes from the mid-70's flew by Jupiter and then Saturn. The spacecraft was then flung on its way out of the solar system using Saturn's gravity assist. The spacecraft, for the most part, has followed its expected path out of the solar system. There has been, however, a tiny discrepancy in the orbital trajectory of the spacecraft. This discrepancy has become known as the "Pioneer Anomaly". The Pioneer probes are not the only spacecraft to exhibit this strange effect, which has been observed numerous times more recently.
This effect has been observed by tracking the spacecraft's radio doppler shift. Using this data, scientists can obtain very accurate readings of its position and velocity. Standard gravitational models are used to predict its exact location and trajectory. These models, however, have been shown to be off by the most minute amount, and show a tiny acceleration towards the sun, not accounted for by gravity. What could this mean? There are many explanations, ranging from the mundane to the exotic. Some such explanations are given below, as partially quoted from this article on wikipedia:
Several modern spacecraft are also reporting Pioneer anomalies. Six recent flybys of the Earth were considered: two by Galileo, the NEAR mission to Eros, Rosetta, Cassini, and the recent Messenger. In five of these six flybys, the anomaly was detected. The anomaly measured in these craft are very much real. The NEAR mission's anomaly was measured to be off by 13 mm/s with an accuracy of 0.1 mm/s. The spacecraft's velocity error was less than 0.0000001 %, which may seem tiny, but it is very much real, and previously unaccounted for. If this seems tiny, think about it on astronomical scales. Data shows that Pioneer 10 and Pioneer 11 are both about 240,000 miles (400,000 kilometers) closer to the sun than they should be. Now that's cause for concern. The question is, how will we account for this anomaly? What could really be causing it?
Recent theories propose that Pioneer's anomalous acceleration towards the sun [(8.74 ± 1.33) x 10−10 m/s2] is actually quite close to the product of the Hubble constant, which pertains to galaxies' redshifts [70.4+1.5−1.6 (km/s)/Mpc] and the speed of light [c = 2.99 x 108]. This is an interesting proposal. We will have to wait, however, to see what its implications are, and whether it is correct. Scientists will be closely watching the trajectory of Rosetta's second flyby and New Horizon's trajectory as it speeds towards Pluto. We'll see if these two craft exhibit similar anomalies. If they do, it could mean a rethinking of our current physical models.