Anomalies were detected over gaps in the two-way coherent Doppler tracking of multiple spacecraft during flybys of Earth for gravitational assist [1, 2], with the following principal characteristics:
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A velocity discrepancy ΔV between pre- and post-encounter trajectory segments inferred from the tracking data. With standard deviation (σ) of 0.01 mm/s in the asymptotic velocity change ΔV∞ [2], the gain of 13.46 mm/s for NEAR [3] is in fact in excess of 100σ [4].
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Large diurnal oscillation in Doppler (range rate) residuals post-encounter, extending for all 4 days examined for both NEAR [1, 3] and Rosetta [2]. Similar oscillation was also seen with Rosetta for 4 days pre-encounter [2].
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For both NEAR and Galileo, independent range data from US DOD's Space Surveillance Network (SSN) radars exhibited linear residuals disagreeing with the NASA-computed trajectory by 5σ [1]. These were first shown to be light-time proportional [5], and subsequently proved in [6] entirely within the individual radar accuracies, i.e., represent essentially noise-free data, using range and range rate data from JPL Horizons [7].
That the same ΔV and residuals were obtained regardless of whether the trajectory was computed from range or Doppler data [3] had more particularly prompted a hypothesis of actual energy gain [3], and speculations as to its cause, including dark matter (in effect surrounding satellite orbits) and gravito-magnetic frame dragging [8], and most recently the Casimir effect [4].
However, the anomalies occurred below the orbits of hundreds of GNSS and geosynchronous satellites. NEAR's closest approach of 538 km is about the altitude of the Hubble Space Telescope, and the gap in its tracking began below 32,000 km. Any unanticipated dynamical effect manifesting in the single pass of a flyby should have been recurred cumulatively in every orbit of every satellite at and above the perigees of these flybys, and should have identically affected radars, as pointed out in [9].
Instead, the light-time lags implied by the radar residuals have turned out to explain NEAR's ΔV to 1% and Rosetta's perigee advance to 2.6% [6]. They were anticipated as peculiar to coherent reception under acceleration, thus also accounting for the absences of the anomalies in subsequent NASA flybys in which Doppler tracking has been non-coherent. The flyby-analysis graphs also account for the absence in Rosetta's later flybys of 2007 and 2009.