The flyby anomaly is an unexpected energy increase during Earth-flybys of spacecraft. This anomaly has been observed as shifts in the S-Band and X-Band Doppler and ranging telemetry. Taken together it causes a significant unaccounted velocity increase of up to 13 mm/s during flybys. Additionally much larger discrepancies (400–1000 m/s) have been observed at least in one flyby (NEAR) against SSN radars.
Gravitational assists are valuable techniques for Solar System exploration. Because the success of these flyby maneuvers depends on the geometry of the trajectory, the position and velocity of a spacecraft is continually tracked during its encounter with a planet by the Deep Space Network (DSN).
The flyby anomaly was first noticed during a careful inspection of DSN Doppler data shortly after the Earth-flyby of the Galileo spacecraft on 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. An investigation of this effect at the Jet Propulsion Laboratory (JPL), the Goddard Space Flight Center (GSFC) and the University of Texas has not yielded a satisfactory explanation. No anomaly was detected after the second Earth-flyby of the Galileo spacecraft in December 1992, because any possible velocity increase was masked by atmospheric drag of the lower altitude of 303 km.
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 ~0.11 mm/s in August 1999 and Rosetta 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.
|Quantity||Galileo I||Galileo II||NEAR||Cassini||Rosetta-I||Messenger||Rosetta-II||Rosetta-III||Juno|
|Speed at infinity, km/s||8.949||8.877||6.851||16.01||3.863||4.056|
|Speed at perigee, km/s||13.738||---||12.739||19.03||10.517||10.389||12.49||13.34|
|Impact parameter, km||11261||12850||8973||22680.49||22319|
|Minimal altitude, km||956||303||532||1172||1954||2336||5322||2483|
|Spacecraft mass, kg||2497.1||730.40||4612.1||2895.2||1085.6||2895||2895|
|Trajectory inclination to equator, degrees||142.9||138.9||108.8||25.4||144.9||133.1|
|Deflection angle, degrees||47.46||51.1||66.92||19.66||99.396||94.7|
|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|
|Speed increment at perigee, mm/s||2.56±0.05||7.21±0.07||−1.7±0.9||0.67±0.02||0.008±0.004||~0||−0.004±0.044|
|Gained energy, J/kg||35.1±0.7||92.2±0.9||7.03±0.19|
An empirical equation for the anomalous flyby velocity change was proposed by J.D. Anderson et al.:
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 does not consider the SSN residuals - see Possible Explanations below.)
There have been a number of proposed explanations of the flyby anomaly, including:
- Unaccounted transverse Doppler effect—i.e. the redshift of light source with zero radial and non-zero tangential velocity. However, this cannot explain the similar anomaly in the ranging data;
- A dark matter halo around Earth;
- A modification of inertia resulting from a Hubble-scale Casimir effect (MiHsC);
- The impact of general relativity, in its weak-field and linearized form yielding gravitoelectric and gravitomagnetic phenomena like frame-dragging, has been investigated as well: it turns out to be unable to account for the flyby anomaly;
- The classical time-retarded gravity explanation proposed by Joseph C. Hafele;
- Range proportional excess delay of the telemetry signal revealed by the United States Space Surveillance Network range data in the NEAR flyby. 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.
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