|Unsolved problem in physics:
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. Numerically larger discrepancies (400–1000 m) have been observed at least in one flyby (NEAR) against Space Surveillance Network (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. 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 anomaly was detected after the second Earth-flyby of the Galileo spacecraft 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.
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, 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.
- "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 13 March 2010.
- C, Edwards, J. Anderson, P, Beyer, S. Bhaskaran, J. Borders, S. DiNardo, W. Folkner, R. Haw, S. Nandi, F. Nicholson, C. 0ttenhoff, S. Stephens (1993). "TRACKING GALILEO AT EARTH-2 PERIGEE USING THE TRACKING AND DATA RELAY SATELLITE SYSTEM". line feed character in
|title=at position 46 (help). The two [measurement] methods yielded similar fits to the data, Within an uncertainty of eight percent, both methods yielded a decrease in velocity along track of -5.9±0.2 mm/s. A priori predictions for the drag-induced velocity change, based on the Jacchia-Roberts model, were -6.2±4.O mm/s , clearly consistent with the observed velocity change. In contrast, DSN data from the December 1990 Earth flyby, at altitude 956 km, indicated an unexplained increase in along-track velocity of 4 mm/s, after accounting for the much smaller drag effects. Given the uncertainty in drag models, we cannot conclusively rule out the possibility that a similar increase occurred at Earth 2. For example, an unmodeled increase of 4 mm/s and a drag decrease of -10 mm/s would be compatible with our results and our a priori atmospheric model. Significantly larger anomalous velocity increases, however, would appear inconsistent with the drag model.
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- Claus Lämmerzahl, University of Bremen:The Pioneer Anomaly or Do We Really Understand the Physics With the Solar System? PDF file; 6.25 MB, 139 pages (2008)
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