Mysteriously, five spacecraft that flew past the Earth have each displayed unexpected anomalies in their motions. These newfound enigmas join the so-called "Pioneer anomaly" as hints that unexplained forces may appear to act on spacecraft. A decade ago, after rigorous analyses, anomalies were seen with the identical Pioneer 10 and 11 spacecraft as they hurtled out of the solar system. Both seemed to experience a tiny but unexplained constant acceleration toward the sun. A host of explanations have been bandied about for the Pioneer anomaly. At times these are rooted in conventional science — perhaps leaks from the spacecraft have...