Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth

We report and characterize anomalous orbital-energy changes observed during six Earth flybys by the Galileo, NEAR, Cassini, Rosetta, and MESSENGER spacecraft. These anomalous energy changes are consistent with an empirical prediction formula which is proportional to the total orbital energy per unit mass and which involves the incoming and outgoing geocentric latitudes of the asymptotic spacecraft velocity vectors. We use this formula to predict a potentially detectable flyby velocity increase of less than $1\mathrm{mm}/\mathrm{s}$ for a second Rosetta flyby on November 13, 2007.

Figure 1

Equatorial view of the NEAR flyby, the most asymmetrical flyby with respect to the Equator and the flyby with the largest energy change. The extent of the bending in the Earth’s gravitational field, the geometry of the flyby and its time scale are illustrated. The tick marks are at 10-min intervals as measured from closest approach. Views of the five other flybys are similar and are not shown.

Figure 2

$X$-band Doppler residuals in the sense observed Doppler frequency shift minus calculated Doppler frequency shift in units of Hz [10] from separately fitting (a) the pre- and (b) the postencounter data for the NEAR flyby. The residuals cluster on opposite sides of the respective fits and demonstrate the impossibility of fitting both pre- and postencounter data with a single fit. The difference in Doppler frequency shift is approximately 0.760 Hz, consistent with an increase of $13.5\mathrm{mm}/\mathrm{s}$ in the $V_{\infty }$ needed to fit both sides of the encounter.

Figure 3

Panel (a) shows the osculating hyperbolic excess velocity $V_{\infty }$ for the NEAR flyby. Panel (b) shows the difference in osculating $V_{\infty }$ between the best-fit trajectory for Doppler data taken after closest approach minus the best-fit trajectory for Doppler data taken before closest approach. The osculating parameters are evaluated over the entire data interval from minus 88.4 h to plus 95.6 h.