|This article is outdated. (March 2010)|
|What causes the unexpected change in acceleration for flybys of spacecraft?|
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 over 13 mm/s during flybys.
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 that MESSENGER both approached and departed Earth symmetrically about the equator (see data and proposed equation below). This may suggest that the anomaly is related to Earth's rotation.
Summary of Earth-flyby spacecraft is provided in table below. The Rosetta data are for its first flyby in 2005; the second flyby produced no significant anomalous increase, and the third a negligible decrease.
|Quantity||Galileo I||Galileo II||NEAR||Cassini||Rosetta-I||Messenger||Rosetta-II||Rosetta-III|
|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|
|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|
Proposed equation 
An empirical equation for the anomalous flyby velocity change was proposed by J.D. Anderson et al.:
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.
Possible explanations 
Possible explanations of the flyby anomaly include
- 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 the 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 anomaly may be due to the rotation of the Earth. This rotation induces an azimuthally symmetric gravitational field.
See also 
- "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 13 March 2010.
- Anderson, John D.; James K. Campbell, Michael Martin Nieto (July 2007), "The energy transfer process in planetary flybys", New Astronomy 12 (5): 383–397, arXiv:astro-ph/0608087, Bibcode:2007NewA...12..383A, doi:10.1016/j.newast.2006.11.004
- "Mystery remains: Rosetta fails to observe swingby anomaly". ESA.
- Anderson, et. al. (7 March 2008), "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth", Phys. Rev. Lett..
- J. P. Mbelek (2008). "Special relativity may account for the spacecraft flyby anomalies". arXiv:0809.1888 [gr-qc]. Bibcode 2008arXiv0809.1888M
- S.L.Adler (2008), "Can the flyby anomaly be attributed to Earth-bound dark matter?", Physical Review D 79 (2), arXiv:0805.2895, Bibcode:2009PhRvD..79b3505A, doi:10.1103/PhysRevD.79.023505
- M.E. McCulloch (2008), "Modelling the flyby anomalies using a modification of inertia", MNRAS Letters 389 (1): L57–L60, arXiv:0806.4159, Bibcode:2008MNRAS.389L..57M, doi:10.1111/j.1745-3933.2008.00523.x
- L. Iorio (2009), "The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly", Scholarly Research Exchange 2009: 1, arXiv:0811.3924, Bibcode:2009ScReE2009.7695I, doi:10.3814/2009/807695, 807695
- G. G. Nyambuya (2010). "Are Flyby Anomalies and the Pioneer Effect an ASTG Phenomenon?". arXiv:0803.1370 [physics.gen-ph]. Bibcode 2008arXiv0803.1370N
- P.G. Antreasian; J.R. Guinn (1998), "Investigations into the unexpected delta-v increase during the Earth Gravity Assist of GALILEO and NEAR", AIAA/AAS Astrodynamics Specialist Conf. and Exhibition, Boston, paper no. 98-4287
- J.D. Anderson; J.G. Williams (2001), "Long-range tests of the equivalence principle", Class. Quantum Grav. 18 (13): 2447–2456, Bibcode:2001CQGra..18.2447A, doi:10.1088/0264-9381/18/13/307
- C. Lämmerzahl; O. Preuss; H. Dittus (2006), "Is the physics within the Solar system really understood?", Proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity", Preprint at arXiv:gr-qc/0604052. Associated presentation slides
- J.D. Anderson; J.K. Campbell; M.M. Nieto (2006), "The Energy Transfer Process in Planetary Flybys", New Astronomy 12 (5): 383, arXiv:astro-ph/0608087, Bibcode:2007NewA...12..383A, doi:10.1016/j.newast.2006.11.004
- NASA Baffled by Unexplained Force Acting on Space Probes, at Space.com
- J.D. Anderson; J.K. Campbell; J.E. Ekelund; J. Ellis; J.F. Jordan (2008), "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth", Phys. Rev. Lett. 100 (91102): 091102, Bibcode:2008PhRvL.100i1102A, doi:10.1103/PhysRevLett.100.091102
- Wanted: Einstein Jr, at Economist.com
- K. Svozil (2008). "Microphysical analogues of flyby anomalies". arXiv:0804.2198 [quant-ph]. Bibcode 2008arXiv0804.2198S
- 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
- Andreas Aste, University of Basel:Spacecraft Anomalies: An Update(PDF file; 9.8 MB, talk/slides)