The 'flyby anomaly' is a tiny and hereto unexplained extra velocity boost that a spacecraft gets, over and above the expected gravity-assist boost when performing a correctly oriented flyby of a planet. The largest anomaly so far was recorded for NEAR, whose velocity changed 13 millimeters per second more than it should have.
Earlier this year, a group of JPL researchers that had been working on the problem for years basically threw up their hands, saying they hoped other physicists could come up with a solution. They had concluded the anomaly was too large to be explained by known effects related to Einstein's general theory of relativity. But a new paper by Jean Paul Mbelek of Service d'Astrophysique, France, proposes that Special Relativity may explain everything.
Abstract: "The empirical formula proposed by J. D. Anderson et al. [1] to reproduce the data on the Earth flyby anomalies is derived from special relativity (SR). The transverse Doppler shift together with the addition of velocities account for the Doppler data. Time dilation together with the addition of velocities account for the ranging data."
It's a short paper and an easy read. If accepted, it is amazing that so many people worked for so long, just to be fooled by an incomplete incorporation of well-known relativistic effects.
-J