The Earth flyby anomaly

Galileo passed Earth at 960 km on 8 December 1990 and gained 3.92 ± 0.08 mm/s more than predicted. Its second flyby, on 8 December 1992, went to 303 km, through the thermosphere: the total residual was about −8 mm/s, of which about −3.4 mm/s was attributed to atmospheric drag, leaving −4.6 mm/s unexplained⁠[1]⁠[2]. NEAR passed at 539 km on 23 January 1998 with +13.46 mm/s⁠[1]. Antreasian and Guinn re-analysed all three with the best gravity field of 1998 and presented the results that year⁠[3].

Cassini passed at 1,175 km on 18 August 1999; thruster firings masked the anomaly at first, and later analysis gave 2 ± 1 mm/s in magnitude (listed as −2 mm/s in later tables)⁠[1]⁠[2]. Rosetta passed at 1,956 km on 4 March 2005 with +1.80 ± 0.03 mm/s, measured by ESA's navigators; MESSENGER passed at 2,347 km on 2 August 2005 with no significant change⁠[1]. Anderson's formula predicted an increase of under 1 mm/s for Rosetta's second flyby on 13 November 2007⁠[4]; none was seen then or at the third, on 13 November 2009⁠[2]⁠[5]. Juno passed at 559 km on 9 October 2013; the Anderson formula predicted about +6 mm/s and an alternative formula about −7 mm/s⁠[8], while standard physics predicted none⁠[9]. The result was at the threshold of detection or absent⁠[10].

The accounts are those of the navigation teams. JPL's analysis of Galileo and NEAR is the first⁠[3]; the 2008 paper by Anderson and colleagues at JPL is the standard summary⁠[4]. ESA's flight dynamics team at ESOC measured the Rosetta anomaly in 2005 and found none in the later flybys; its expert Trevor Morley called it "a real cosmic mystery" in 2013⁠[5]. Turyshev and Toth, who led the re-analysis of the Pioneer anomaly, reviewed the evidence in 2009 and argued that the modelling must be audited before new physics is considered⁠[1]. Other reviews place it among the claimed gravitational and navigation anomalies in the Solar System⁠[11]⁠[12].

Each anomaly is a number derived from a fit: tracking data (two-way Doppler and ranging from the Deep Space Network or ESA stations) before and after perigee are fitted with a trajectory model, and the anomaly is the velocity change at perigee needed to reconcile them⁠[1]. The published values, with the flybys' altitudes, inclinations, perigee latitudes and asymptotic speeds, are tabulated for nine flybys in a 2017 analysis⁠[2]. The tracking itself is the record that matters, and most of it is not public. NAIF distributes reconstructed trajectories for many missions, but its Galileo files begin in 1995, after both Earth flybys⁠[6]. ESA's archive of Rosetta radio-science data holds two data sets from the second Earth swing-by phase; the one opened in this research is a checkout a month before the flyby⁠[7]. Turyshev and Toth noted that older DSN data deposited by radio science teams can be retrieved from NASA's NSSDC, and urged that tracking and engineering telemetry be preserved⁠[1].

Conventional physics has been tested piece by piece. The Moon, the Sun and relativistic effects were dismissed by the first analysts⁠[3]; atmosphere, tides, spacecraft charge and magnetic moment, Earth-albedo radiation pressure, solar wind and spin-rotation coupling were judged too small⁠[13]. General relativity's gravito-magnetic and gravito-electric effects change NEAR's speed by 10⁻⁵ to 10⁻² mm/s, a thousand to a million times too little⁠[14]. Thermal recoil forces and Lorentz forces on a charged spacecraft have each been modelled in detail⁠[15]⁠[16]. None has explained the pattern.

Modelling and software are the explanation the navigation reviewers put first. Turyshev and Toth pointed to the handling of reference frames and spheres of influence in navigation codes, and to inconsistent definitions of Earth-orientation and tidal quantities between frames⁠[1]. Busack noted that his formula, which predicted the Rosetta null results, supports the idea of an error in older measuring software⁠[8]. This reading predicts that re-processing the early tracking data with a modern, consistent model would shrink the anomalies.

New physics proposals include a modification of inertia, which reproduces three of the six early values within error⁠[17]; dark matter bound to Earth, which needs implausible densities and properties⁠[18]; an unknown latitude-dependent force of about 300 km range⁠[2]; and a 2026 treatment within a variational formulation of general relativity⁠[19]. A 2026 preprint proposes that the distribution of land and sea under the trajectory modulates the effect⁠[20]. Each must explain the null results as well as the early anomalies, and the empirical formulas proposed so far have failed to predict new flybys⁠[2].

A uniform re-analysis of every Earth flyby from the original tracking data, by one team with one modern model of Earth's gravity, atmosphere, orientation and tides and with the spacecraft's thermal and attitude histories, would show whether the anomalies survive. That needs the raw Doppler and ranging files for each flyby, released with the engineering telemetry. A dedicated test, a spacecraft or satellite on a highly elliptical Earth orbit with precise tracking and an accelerometer, was proposed for this purpose⁠[21]. Each future Earth flyby, tracked continuously through perigee and published with its residuals, adds a test of any formula.