Flyby anomaly

In multiple cases, spacecraft have been observed to gain greater speed than scientists had predicted, but thus far no convincing explanation has been found.

Because the success of such flyby maneuvers depends on the exact geometry of the trajectory, the position and velocity of a spacecraft during its encounter with a planet is continually tracked with great precision by earth telemetry, e.g. via the Deep Space Network (DSN).

While the Doppler residuals (observed minus computed data) were expected to remain flat, the analysis revealed an unexpected 66 mHz shift, which corresponds to a velocity increase of 3.92 mm/s at perigee.

Investigations of this effect at the Jet Propulsion Laboratory (JPL), the Goddard Space Flight Center (GSFC) and the University of Texas have not yielded a satisfactory explanation.

No such anomaly was detected after the second Earth flyby of Galileo in December 1992, where the measured velocity decrease matched that expected from atmospheric drag at the lower altitude of 303 km.

An analysis of the MESSENGER spacecraft (studying Mercury) did not reveal any significant unexpected velocity increase.

[5] In 2018, a careful analysis of the trajectory of the presumed interstellar asteroid ʻOumuamua revealed a small excess velocity as it receded from the Sun.

This formula was derived later by Jean Paul Mbelek from special relativity, leading to one of the possible explanations of the effect.