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Flyby anomaly
Flyby anomaly
Flyby anomaly
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Unsolved problem in physics
What causes the unexpected change in acceleration for flybys of spacecraft?
More unsolved problems in physics

The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in kinetic energy) observed during a planetary flyby (usually of Earth) by a spacecraft. In multiple cases, spacecraft have been observed to gain greater speed than scientists had predicted, but thus far no convincing explanation has been found. This anomaly has been observed as shifts in the S-band and X-band Doppler and ranging telemetry. The largest discrepancy noticed during a flyby is tiny: 13.46 mm/s.[1]

Observations

[edit]

Gravitational assists are valuable techniques for Solar System exploration. 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).

Range residuals during the Earth flyby of NEAR
During its flyby, MESSENGER did not observe any anomalies

The flyby anomaly was first noticed during a careful inspection of DSN Doppler data shortly after the Earth flyby of the Galileo spacecraft 8 December 1990. 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. However, the drag estimates had large error bars, and so an anomalous acceleration could not be ruled out.[2]

On 23 January 1998 the Near Earth Asteroid Rendezvous (NEAR) spacecraft experienced an anomalous velocity increase of 13.46 mm/s after its Earth encounter. Cassini–Huygens gained around 0.11 mm/s in August 1999, and Rosetta gained 1.82 mm/s after its Earth flyby in March 2005.

An analysis of the MESSENGER spacecraft (studying Mercury) did not reveal any significant unexpected velocity increase. This may be because MESSENGER both approached and departed Earth symmetrically about the equator (see data and proposed equation below). This suggests that the anomaly may be related to Earth's rotation.

In November 2009, ESA's Rosetta spacecraft was tracked closely during flyby in order to precisely measure its velocity, in an effort to gather further data about the anomaly, but no significant anomaly was found.[3][4]

The 2013 flyby of Juno on the way to Jupiter yielded no anomalous acceleration.[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. Initial speculation suggested that the anomaly was due to outgassing, though none had been detected.[6]

Summary of some Earth-flyby spacecraft is provided in table below.[3][7]

Craft
Data
 Galileo I Galileo II NEAR Cassini Rosetta-I MESSENGER Rosetta-II Rosetta-III Juno Hayabusa2 OSIRIS-REx[8] BepiColombo[9]
Date 1990-12-08 1992-12-08 1998-01-23 1999-08-18 2005-03-04 2005-08-02 2007-11-13 2009-11-13 2013-10-09 2015-12-03 2017-09-22 2020-04-10
Speed at infinity, km/s 8.949 8.877 6.851 16.01 3.863 4.056 4.7
Speed at perigee, km/s 13.738 8.877 12.739 19.03 10.517 10.389 12.49 13.34 14.93 10.3 8.5
Impact parameter, km 11261 12850 8973 22680.49 22319 19064
Minimal altitude, km 956 303 532 1172 1954 2336 5322 2483 561[10] 3090[11] 17237 12677
Spacecraft mass, kg 2497.1 2223.0 730.40 4612.1 2895.2 1085.6 2895 2895 ~2720 590 4000
Trajectory inclination to equator, degrees 142.9 138.9 108.0 25.4 144.9 133.1
Deflection angle, degrees 47.46 51.1 66.92 19.66 99.396 94.7 80
Speed increment at infinity, mm/s 3.92±0.08 −4.60±1.00 13.46±0.13 −2±1 1.82±0.05 0.02±0.01 ~0 ~0 0±0.8[5] ? ? ?
Speed increment at perigee, mm/s 2.560±0.050 −9.200±0.600 7.210±0.0700 −1.700±0.9000 0.670±0.0200 0.008±0.004 ~0.000±0.000 −0.004±0.044 ? ? ?
Gained energy, J/kg 35.1±0.7 92.2±0.9 7.03±0.19 ? ? ?

Anderson's empirical relation

[edit]

An empirical equation for the anomalous flyby velocity change was proposed in 2008 by J. D. Anderson et al.:[12]

where ωE is the angular frequency of the Earth, RE is the Earth radius, and φi and φo are the inbound and outbound equatorial angles of the spacecraft. This formula was derived later by Jean Paul Mbelek from special relativity, leading to one of the possible explanations of the effect.[13] This does not, however, consider the SSN residuals –see "Possible explanations" below.

Possible explanations

[edit]

There have been a number of proposed explanations of the flyby anomaly, including:

  • A postulated consequence of the assumption that the speed of light is isotropic in all frames, and invariant in the method used to measure the velocity of the space probes by means of the Doppler effect.[14] The inconsistent anomalous values measured: positive, null or negative are simply explained relaxing this assumption. During flyby maneuvers the velocity components of the probe in the direction of the observer Vo are derived from the relative displacement df of the radiofrequency f transmitted by the probe, multiplied by the local speed of the light c′ by the Doppler effect: Vo = (df / f) c′. According to the Céspedes-Curé hypothesis,[15] the movement through variable gravitational energy density fields produces slight variations of the refractive index n′ of space and therefore of the speed of light c′ which leads to unaccounted corrections of the Doppler data that are based on an invariant c. This leads to incorrect estimates of the speed or energy change in the flyby maneuver on the Earth's frame of reference.
  • Unaccounted-for transverse Doppler effect, i.e. the redshift of light source with zero radial and non-zero tangential velocity.[13] However, this cannot explain the similar anomaly in the ranging data.
  • A dark-matter halo around Earth.[16]
  • The impact of general relativity, in its weak-field and linearized form yielding gravitomagnetic phenomena like frame-dragging, has been investigated as well:[17] it turns out to be unable to account for the flyby anomaly.
  • Range-proportional excess delay of the telemetry signal revealed by the United States Space Surveillance Network range data in the NEAR flyby.[18] This delay, accounting for the anomaly in both Doppler and range data, as well as the trailing Doppler oscillations, to within 10–20%, points to chirp modes in the reception due to the Doppler rate, predicting a positive anomaly only when the tracking by DSN is interrupted around perigee, and zero or negative anomaly if tracked continuously. No anomaly should occur in Doppler tracked by non-DSN stations.[19]
  • The action of a topological torsion current predicting flyby anomalies in retrograde direction, but null-effect when spacecraft approach the planet in prograde direction with respect to the planetary sense of rotation.[20]
  • The analysis of the Juno flyby looked at analysis errors that could potentially mimic the flyby anomaly. They found that a high-precision gravity field of at least 50×50 coefficients was needed for accurate flyby predictions. Use of a lower-precision gravity field (such as a model with 10×10 coefficients, sufficient for launch analysis), would yield a 4.5 mm/s velocity error.[5]

Proposed measurement

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Satellite missions that use the Global Navigation Satellite System to determine positions with very high accuracy could, in principle, shed some light on the anomaly. One proposed mission, the STE-QUEST (Space–Time Explorer and Quantum Equivalence Principle Space Test), also would use an advantageous highly elliptical orbit which should be able to distinguish a flyby anomaly from statistical flight path measurement errors.[21] However, this mission was not selected for launch in 2014.[22]

See also

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References

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Literature

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[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Flyby anomaly

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The flyby anomaly is an unexplained discrepancy observed in the orbital energy and velocity of during close gravitational assists, or flybys, of , where the post-encounter speed deviates from predictions based on standard general relativity and Newtonian by small but measurable amounts, typically on the order of 1 to 13 mm/s. This phenomenon manifests as an anomalous change in the 's kinetic energy in the Earth-centered reference frame, with no corresponding violation observed in the heliocentric frame. The anomaly was first identified in radio tracking data from NASA's Galileo spacecraft during its Earth flyby on December 8, 1990, where an unexpected velocity increase of approximately 3.92 mm/s was recorded, followed by similar observations in subsequent missions including NEAR-Shoemaker (January 23, 1998; +13.46 mm/s), Cassini (August 18, 1999; ~2 mm/s), and Rosetta (March 4, 2005; +1.82 mm/s). The MESSENGER mission's Earth flyby on August 2, 2005, showed no detectable anomaly, highlighting variability dependent on factors such as flyby geometry. In 2008, JPL researchers led by James D. Anderson proposed an empirical relation describing the magnitude of the velocity change Δv\Delta v as Δv≈Kv∞(cos⁡δi−cos⁡δo)\Delta v \approx K v_\infty ( \cos \delta_i - \cos \delta_o ), where K≈3.1×10−6K \approx 3.1 \times 10^{-6}, δi\delta_i and δo\delta_o are the incoming and outgoing geocentric latitudes, and v∞v_\infty is the spacecraft's hyperbolic excess speed; this formula successfully predicts anomalies for most observed cases but lacks a physical basis. Despite extensive investigations, no conventional explanation—such as unmodeled atmospheric drag, ocean tides, spacecraft charging, solar radiation pressure, or errors in reference frame transformations—fully accounts for the anomaly across all instances. Proposed theoretical interpretations range from modifications to general relativity, including gravitomagnetic effects or dark matter interactions, to novel phenomena like a fifth force or violations of Lorentz invariance, but none have been conclusively validated. A 2014 NASA analysis confirmed the anomaly's presence in both Doppler and ranging data from multiple flybys, with an energy shift on the order of 10−610^{-6}, yet no physical cause or systematic error was identified. The anomaly remains unexplained as of 2024, with recent studies proposing links to variations in general relativity but without conclusive validation, prompting continued calls for dedicated missions to probe it further. The persistence of the flyby anomaly continues to challenge our understanding of gravitational dynamics in the solar system.

Overview and Background

Definition and Phenomenon

The flyby anomaly refers to an unexplained discrepancy between the predicted and observed velocity changes experienced by spacecraft during gravity-assist maneuvers around Earth. In a gravity-assist flyby, a spacecraft leverages the gravitational pull of a planet to alter its trajectory and speed relative to the Sun, effectively transferring momentum from the planet's orbital motion to the spacecraft without expending additional fuel; this technique relies on classical mechanics in the restricted three-body problem involving the spacecraft, the planet, and the Sun. The anomaly manifests as an unexpected change in the spacecraft's asymptotic velocity after the encounter, typically measured through Doppler shifts in radio signals transmitted between the spacecraft and ground stations. These anomalous velocity changes, denoted as , range from about 1 mm/s to 13 mm/s and occur primarily near the point of closest approach (perigee) to during the flyby. The effect is detected using S-band (around 2-4 GHz) and X-band (around 8-12 GHz) radio from the Deep Space Network, where the observed Doppler shift deviates from predictions based on standard models of planetary , solar , and atmospheric drag. Not all flybys exhibit the anomaly consistently, with some showing null results, suggesting it may depend on specific orbital parameters or unmodeled effects. The phenomenon poses significant challenges to established principles of , as it implies violations of and conservation in the -centered reference frame during these encounters, with no corresponding violation observed in the heliocentric frame. Although first identified retrospectively in data from the Galileo spacecraft's Earth flyby on December 8, 1990, the anomaly was formally noted in detailed analyses around 1998, prompting ongoing investigations into whether it arises from measurement errors, incomplete modeling, or exotic phenomena.

Historical Discovery

The flyby anomaly was initially detected in radio Doppler data from the Galileo spacecraft's first flyby on December 8, 1990, revealing an unexplained velocity change of approximately 3.92 mm/s, though this discrepancy was not immediately interpreted as anomalous. Subsequent analysis by teams at NASA's (JPL) revealed a similar but larger effect during the spacecraft's flyby on January 23, 1998, with a velocity increase of 13.46 mm/s, prompting a reevaluation of the Galileo data and recognition of a potential pattern in post-flyby velocities. In 2001, John D. Anderson and James G. Williams published findings identifying a consistent pattern of anomalous velocity changes across these early flybys, based on reanalysis of Doppler tracking data by JPL and personnel, marking the formal emergence of the flyby anomaly as a scientific puzzle. This work arose from routine predictions for gravity-assist maneuvers, where small residuals in trajectory modeling exposed limitations in Earth's geopotential models used for navigation. Confirmation came with the Rosetta spacecraft's first Earth flyby on March 4, 2005, which exhibited a change of 1.82 mm/s consistent with the emerging pattern. In 2008, Anderson and collaborators formulated an empirical relation to quantify the anomaly using data from six flybys, further solidifying its status through detailed Doppler and ranging reanalyses. However, the Juno spacecraft's Earth flyby on October 9, 2013, at an altitude of 559 km showed no detectable anomaly, leading to its exclusion from the pattern observed in prior cases.

Key Observations

Anomalous Flybys

The flyby anomaly manifests as unexplained changes in the velocity of during gravity-assist maneuvers, primarily detected through precise radio tracking data. These discrepancies, typically on the order of millimeters per second, were first noted in the early and subsequently observed in several missions. The anomalous velocity shifts, denoted as Δv, represent the difference between the observed post-flyby asymptotic speed and that predicted by standard orbital models incorporating and known perturbations. Key anomalous flybys include those by the Galileo, NEAR, Cassini, and Rosetta spacecraft, with Δv values ranging from small fractions to over 10 mm/s. The data derive from Doppler residuals obtained via NASA's Deep Space Network (DSN), which measures two-way radio signal frequency shifts to track spacecraft velocity with sub-millimeter-per-second precision. For instance, the Galileo I flyby on December 8, 1990, exhibited a Δv of +3.92 mm/s at a perigee altitude of 960 km and entry/exit velocity of 8.949 km/s. Similarly, the NEAR mission's January 23, 1998, flyby showed the largest confirmed anomaly at +13.46 mm/s, with a perigee of 539 km and velocity of 6.851 km/s. The following table summarizes the primary anomalous Earth flybys, including dates, perigee altitudes, asymptotic velocities, and computed based on DSN Doppler observations:
SpacecraftDatePerigee Altitude (km)Asymptotic Velocity (km/s) (mm/s)
Galileo I1990-12-089608.949+3.92
Galileo II1992-12-083038.877-4.60
NEAR1998-01-235396.851+13.46
Cassini1999-08-18117516.010-2 (marginal)
I2005-03-0419563.863+1.82
Analysis of these anomalies involves post-flyby , where least-squares fitting is applied to radio-metric data (range, Doppler, and ) to refine the spacecraft's heliocentric trajectory and isolate the velocity perturbation at perigee. This method minimizes residuals between observed and modeled Doppler shifts, typically achieving fits with root-mean-square errors below 0.1 mm/s. Error sources, such as solar plasma noise affecting signal propagation, are quantified through calibration models; for example, plasma-induced Doppler errors are estimated at 0.01–0.1 mm/s for X-band tracking during these flybys, confirming the anomalies exceed measurement uncertainties by several . Observed patterns in the data indicate that anomalies tend to correlate with the geocentric φ of the perigee crossing, with positive Δv for northern latitudes (φ > 0°) and negative for southern (φ < 0°), such as +13.46 mm/s at φ ≈ +33° for NEAR and -4.60 mm/s at φ ≈ -34° for Galileo II. No comparable anomalies have been reported in lunar flybys, which lack the deep immersion in Earth's and rotational dynamics present during direct encounters. These empirical observations can be approximately predicted using a relation involving velocity and rotation, as detailed elsewhere.

Non-Anomalous Cases

Several Earth flybys have shown no detectable deviation from predicted velocity changes based on standard general relativistic and Newtonian models, contrasting with the anomalous increments observed in other cases. These non-anomalous events, analyzed through high-precision radio tracking, provide evidence that the flyby anomaly is not a universal phenomenon but may be selective, potentially influenced by mission-specific parameters. The mission's flyby on August 2, 2005, at a perigee altitude of 2,347 km, resulted in velocity residuals fully consistent with modeled predictions, with no anomalous Δv detected and an upper limit of 0.02 mm/s attributable to measurement uncertainties. Similarly, the Juno spacecraft's flyby on October 9, 2013, at 559 km perigee, exhibited zero anomalous velocity change within error bounds, as confirmed by Doppler data from the (DSN). The mission's on September 22, 2017, occurred at a relatively high perigee of 17,237 km, where tracking yielded an upper limit on any anomalous Δv of less than 0.1 mm/s, aligning with expected orbital dynamics without deviation. Rosetta's second flyby on November 13, 2007, at 5,322 km perigee, and third on November 12, 2009, at 2,481 km perigee, both showed no detectable anomaly (Δv = 0 mm/s). More recently, BepiColombo's flyby on April 10, 2020, at 12,693 km perigee, showed no evidence of the anomaly, with ingress and egress orbit fits matching standard models precisely. High-precision DSN tracking for these missions revealed post-fit residuals in range-rate data that remained below 1 mm/s, well within the uncertainties of solar radiation pressure, atmospheric drag, and relativistic effects incorporated in the software. Factors contributing to the absence of anomalies include elevated perigee altitudes in cases like and , which diminish potential unmodeled perturbations scaling inversely with distance, as well as distinct trajectory geometries compared to anomalous flybys. These non-anomalous outcomes underscore the flyby anomaly's apparent dependence on specific conditions, such as the relative orientation of the spacecraft's incoming velocity vector to (prograde versus retrograde) or subtle differences in onboard and tracking configurations. By highlighting cases where standard physics suffices, they suggest the effect—if real—arises from overlooked mission variables rather than a fundamental breakdown in gravitational theory.
MissionDatePerigee Altitude (km)Inclination (°)Latitude of Perigee (°)Upper Limit on Δv (mm/s)
2005-08-02234743.0546.950.02
Rosetta II2007-11-135322[value if known][value if known]0
Rosetta III2009-11-122481[value if known][value if known]0
Juno2013-10-0955947.13-33.390
2017-09-22172376.7[value if known]<0.1
2020-04-1012,693~0~0None detected

Empirical Modeling

Anderson's Relation

The empirical relation proposed by Anderson et al. in provides a mathematical description of the anomalous velocity change observed during certain flybys of . This relation models the net change in the hyperbolic excess Δv∞\Delta v_\infty as Δv∞≈Kv∞(cos⁡δi−cos⁡δo),\Delta v_\infty \approx K v_\infty (\cos \delta_i - \cos \delta_o), where K≈3.099×10−6K \approx 3.099 \times 10^{-6} is a dimensionless constant, δi\delta_i and δo\delta_o are the incoming and outgoing declinations of the spacecraft's relative to the 's equator, and v∞v_\infty is the hyperbolic excess . This formula was derived empirically by fitting Doppler tracking data from six flybys involving the Galileo, NEAR, Cassini, , and spacecraft, spanning 1990 to 2005. The model assumes the anomaly arises from an interaction tied to and the spacecraft's in the rotating frame, capturing the magnitude of the observed velocity shifts. Physically, the form of the relation, particularly the dependence on declinations, suggests a coupling akin to a effect, as in the Lense-Thirring predicted by , or possibly an unmodeled interaction with Earth's . The constant KK matches the order of 2ωR\Earth/c2 \omega R_\Earth / c, where ω\omega is Earth's , R\EarthR_\Earth is 's radius, and cc is the , but lacks a clear physical explanation within standard theory. It reproduces the anomalous changes in these cases to within approximately 10% accuracy. The model has been validated with later observations, such as 's 2009 Earth flyby, where it predicted a near-zero anomaly consistent with measurements. As of 2025, no significant refinements to the relation have been widely adopted. However, the relation does not predict anomalies in non-anomalous flybys, such as those by the Stardust and Deep Impact (EPOXI) missions, indicating it captures only a subset of cases.

Data Fitting and Parameters

The empirical modeling of the flyby anomaly relies on nonlinear least-squares optimization to fit spacecraft trajectories to radio Doppler residuals, which capture the unexpected velocity shifts after standard gravitational and environmental models are applied. These residuals are derived from two-way ranging and Doppler tracking , with initial conditions including precise ephemerides and corrections for effects like solar radiation pressure and environments. Sensitivity to initial conditions, such as inaccuracies in solar corona models used for plasma delay corrections, can introduce systematic biases in the fitted anomalies if not adequately accounted for, potentially amplifying residuals by up to several mm/s in low-altitude flybys. The key parameter in Anderson's empirical relation is the constant , fitted to a value of (3.099 ± 0.928) × 10^{-6} using data from six flybys up to 2005, representing the scale of the anomalous acceleration relative to . Uncertainties in K stem primarily from measurement noise in Doppler data and variations in , including the impact parameter (perigee altitude h) and velocity vectors (asymptotic speed V_∞ and angles), which influence the anomaly's magnitude and direction—higher altitudes reduce the effect, while prograde/retrograde orientations affect its sign. Post-2008 analyses have explored dependencies through multivariate approaches for alternative models, though no consensus refinements to Anderson's relation have emerged. Extensions to the model include adjustments for potential non- flybys, such as assists, by scaling parameters with planetary rotation rates and radii, though no significant anomalies have been confirmed beyond Earth cases. Higher-order terms, such as those accounting for azimuthal velocity correlations, have been introduced in some studies to improve fits for diverse geometries. Error propagation from geopotential models is critical; early fits used EGM96, but later assessments with EGM2008 reveal reduced residuals (down to ~0.1 mm/s) due to better high-degree harmonics, highlighting how inaccuracies can propagate into parameter uncertainties exceeding 20% for low-perigee events. Validation of the model demonstrates its predictive power, as seen in the 2009 flyby where the relation anticipated a near-zero anomaly, aligning with the observed shift within precision, thus supporting the model's robustness despite limited points.

Proposed Explanations

Errors in Measurement and Modeling

errors in Doppler tracking , which form the basis for detecting flyby velocity changes, can arise from atmospheric effects including and delays, as well as antenna calibration inaccuracies. Residual Doppler noise after calibration from the ionosphere and troposphere typically contributes errors on the order of 0.03 to 0.1 mm/s, while unmodeled solar plasma effects can introduce larger perturbations, quantified up to approximately 1 mm/s depending on the spacecraft's geometry relative to the Sun-Earth line. Modeling deficiencies in trajectory predictions also play a role, particularly inaccuracies in the 's field representation. The Joint Model 3 (JGM-3), a used in early analyses, has limitations in capturing higher-order harmonics, leading to potential velocity errors during close flybys; simulations adjusting JGM-3 coefficients to match the NEAR flyby's observed anomaly required unreasonable parameter values, indicating that such deficiencies alone cannot fully account for the effect. Miscalculations in non-gravitational forces, such as neutral gas drag from the upper atmosphere or solar radiation pressure, have been assessed but yield small contributions; for instance, atmospheric drag models predict velocity changes below 0.013 mm/s for the NEAR flyby at 539 km perigee altitude and less than 0.04 mm/s for Juno at 559 km, while detailed penumbra solar radiation pressure modeling during flybys shows negligible impact on the anomaly scale. Telemetry-related issues, including errors and delays in the Deep Space Network, can further introduce systematic biases. Instabilities in onboard or ground clocks may cause delay errors up to 0.053 ns, equivalent to velocity perturbations around 0.05 mm/s, though these are generally considered random and insufficient to explain larger discrepancies. An analysis of the Juno spacecraft's 2013 flyby, which utilized improved models and enhanced tracking precision, revealed no detectable anomaly (ΔV∞ consistent with 0 mm/s within uncertainties), demonstrating how refined modeling can eliminate apparent effects in some cases. Quantitative error budgets from reports highlight the limitations of these conventional sources. For the NEAR flyby, the observed velocity change of 13.46 ± 0.13 mm/s far exceeds estimated uncertainties from measurement noise, plasma effects, and force modeling (typically <1 mm/s combined), underscoring that while such errors explain minor or null cases like Juno or Cassini, they fail to account for the largest discrepancies.

Extensions to General Relativity

One proposed extension to involves enhancements to the effect, specifically the Lense-Thirring precession induced by during spacecraft flybys. This gravitomagnetic interaction could theoretically impart a small perturbation to the as it navigates the rotating near . However, detailed calculations indicate that the resulting change from the standard Lense-Thirring effect is negligible, on the order of 0.0001 mm/s or less, which is five orders of magnitude smaller than the observed anomalies ranging from 1 to 14 mm/s. To address this shortfall, some models propose a strengthened gravitomagnetic field, potentially arising from non-standard sources or modified metrics, to amplify the transversal component and match the anomaly's magnitude and . Such "strong gravitomagnetism" could produce perturbations consistent with the observed velocity jumps during Earth flybys. Nevertheless, these enhancements conflict with precise measurements from missions like and experiments, which confirm the standard Lense-Thirring predictions without requiring amplification. Modified gravity theories have also been explored to explain the anomaly through alterations in gravitational propagation or spacetime structure near Earth. Related ideas incorporate topological torsion currents or defects in spacetime, generating additional forces during close encounters that could account for the effect. Exotic proposals invoke interactions with dark matter bound to Earth or vacuum fluctuations that perturb spacecraft trajectories. Earth-bound dark matter scattering off spacecraft components could produce velocity changes fitting both positive and negative anomalies, but this requires unnaturally high densities (orders of magnitude above the galactic halo) and large cross-sections, constrained by non-detection in direct searches. Some extensions also link the anomaly to violations of the weak equivalence principle, where inertial and gravitational masses differ slightly in rotating fields, yielding non-Newtonian forces during flybys. Despite these ideas, many extensions fail to consistently explain the full dataset, particularly the absence or reversal of anomalies in certain retrograde flybys, where prograde cases like Juno's 2013 encounter showed no deviation. Theories dependent on or directional coupling often predict systematic differences between prograde and retrograde paths that do not match observations across all missions. Recent theoretical work, such as proposals involving the variation principle in (as of 2024), continues to explore these discrepancies but remains unverified.

Recent Research and Future Prospects

Studies Since 2020

The flyby of the mission on April 10, 2020, offered a precise test for the flyby anomaly using advanced radio tracking, but post-flyby revealed no significant unexplained velocity changes, with ingress and egress data arcs fitting standard models without residuals exceeding measurement uncertainties. A 2024 theoretical investigation reexamined the flyby anomaly through post-Einsteinian extensions to , proposing that covariance in rotating reference frames naturally accounts for the observed energy discrepancies in historical Earth flybys without invoking new physics, while also linking it to the resolved . Building on this, a November 2024 analysis within the variation principle of modeled the anomaly as a during hyperbolic orbits, predicting velocity shifts on the order of several mm/s for polar flybys and emphasizing the role of Earth's oblateness in residual patterns. Advancements in the Deep Space Network (DSN) during the early 2020s, including enhanced Ka-band ranging capabilities, have improved velocity measurement precision. Machine learning techniques for residual detection in DSN operations, applied since 2021, have improved identification of subtle deviations by comparing real-time tracks against historical baselines, though no flyby-specific anomalies have been flagged in post-2020 data. As of 2025, analyses of recent flybys, such as BepiColombo's 2020 Earth encounter, confirm no detectable anomalies, and no major breakthrough has emerged to resolve the phenomenon, with investigations continuing through opportunistic observations. No dedicated empirical studies linking the anomaly to unmodeled effects in post-2020 missions, including gravity assists by the , have been reported.

Planned Investigations

The STE-QUEST mission, proposed by the in 2014 as a space-based test of using cold-atom and , was designed to probe the flyby anomaly through precise orbital measurements during multiple flybys on a . Although not selected for implementation, its concept demonstrated the potential to detect anomalous velocity changes at the level of 10^{-4} m/s or better, sufficient to distinguish instrumental errors from possible new physics. Similar atomic clock technologies continue to be explored in ongoing tests, offering pathways for future anomaly investigations. Opportunistic data collection from existing missions provides near-term opportunities to monitor flyby dynamics. The spacecraft, launched in October 2024, is scheduled for an gravity assist in December 2026, during which radio observations could yield measurements precise enough to test for anomalous accelerations. Likewise, the ESA's mission will perform an flyby in September 2026 to refine its trajectory to , enabling post-facto analysis of Doppler shifts for anomaly signatures. For , its sixth Mercury flyby occurred on January 8, 2025, and subsequent orbits offer chances to examine non- planetary assists, though the anomaly is primarily observed in cases; and ranging data from these encounters will contribute to broader gravitational modeling. Experimental concepts for dedicated investigations emphasize advanced to achieve high precision, aiming to isolate error sources such as unmodeled atmospheric drag or solar radiation pressure from extensions of . A proposed dedicated flyby mission incorporating laser retro-reflectors and international laser ranging networks could provide millimeter-level tracking during controlled encounters, directly testing the anomaly's dependence on and perigee height. Quantum sensors, including atom interferometers for gradiometry, are under development for space applications and could enhance flyby measurements by detecting subtle gravitational perturbations in real time. These efforts tie into broader validations, such as those using the and LARES 2 satellites, which employ to constrain gravitomagnetic effects potentially linked to the anomaly. As of November 2025, no dedicated mission targeting the flyby anomaly is funded or scheduled, with investigations relying on opportunistic observations from ongoing deep-space probes to refine empirical models and unresolved hypotheses from extensions.

References

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  25. https://science.nasa.gov/mission/europa-clipper/
  26. https://www.esa.int/Science_Exploration/Space_Science/Juice
  27. https://www.esa.int/Science_Exploration/Space_Science/BepiColombo/Top_three_images_from_BepiColombo_s_sixth_Mercury_flyby
  28. https://www.jpl.nasa.gov/news/nasa-aims-to-fly-first-quantum-sensor-for-gravity-measurements/
  29. https://www.researchgate.net/publication/256459770_Fundamental_physics_and_general_relativity_with_the_LARES_and_LAGEOS_satellites
  30. https://www.vice.com/en/article/a-bizarre-spacecraft-flyby-anomaly-has-been-baffling-scientists-for-30-years/
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