Flyby anomaly

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Question dropshade.png Open problem in physics:
What causes the unexpected change in acceleration for flybys of spacecraft?
(more open problems 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.[1] 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).

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 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.[2][3]

Summary of Earth-flyby spacecraft is provided in table below.[2][4]

Quantity Galileo I Galileo II NEAR Cassini Rosetta-I Messenger Rosetta-II Rosetta-III Juno
Date 1990-12-08 1992-12-12 1998-01-23 1999-08-18 2005-03-04 2005-08-02 2007-11-13 2009-11-13 2013-10-09
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

Future research[edit]

Upcoming missions with Earth flybys include Hayabusa 2, launched in 2014 with an Earth flyby in December 2015,[5] and BepiColombo with its launch due in July 2016 and its Earth flyby due July 2018.

Some missions designed to study gravity, such as STE-QUEST or STEP, will make extremely accurate gravity measurement and may shed some light on the anomaly.[6]

Proposed equation[edit]

An empirical equation for the anomalous flyby velocity change was proposed by J.D. Anderson et al.:

 \frac{dV}{V} = \frac{2 \omega_e R_e (\cos \varphi_i - \cos \varphi_o)}{c}

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.[7] (This does not consider the SSN residuals - see Possible Explanations below.)

Possible explanations[edit]

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.[8] However, this cannot explain the similar anomaly in the ranging data;
  • A dark matter halo around Earth;[9]
  • A modification of inertia resulting from a Hubble-scale Casimir effect (MiHsC);[10]
  • 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:[11] it turns out to be unable to account for the flyby anomaly;
  • The classical time-retarded gravity explanation proposed by Joseph C. Hafele;[12]
  • Range proportional excess delay of the telemetry signal revealed by the United States Space Surveillance Network range data in the NEAR flyby.[13] 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.[14]
SSN range residuals with range, delay

See also[edit]


  1. ^ "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 13 March 2010. 
  2. ^ a b "Mystery remains: Rosetta fails to observe swingby anomaly". ESA. Archived from the original on 2009-12-23. 
  3. ^ J. Biele (2012). "Navigation of the interplanetary Rosetta and Philae spacecraft and the determination of the gravitational field of comets and asteroids - (DLR) @ TU München, 2012" (PDF). Retrieved 2014-11-18. 
  4. ^ 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 
  5. ^ Yuichi Tsuda, Takanao Saiki, Naoko Ogawa and Mutsuko Morimoto. "TRAJECTORY DESIGN FOR JAPANESE NEW ASTEROID SAMPLE RETURN MISSION HAYABUSA-2" (PDF). 
  6. ^ "Probing the Flyby Anomaly with the future STE-QUEST mission". 
  7. ^ Anderson; et al. (7 March 2008), "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" (PDF), Phys. Rev. Lett., Bibcode:2008PhRvL.100i1102A, doi:10.1103/physrevlett.100.091102. 
  8. ^ Mbelek, J. P. (2009). "Special relativity may account for the spacecraft flyby anomalies". arXiv:0809.1888v3 [qr-qc]. 
  9. ^ 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 
  10. ^ 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 
  11. ^ 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 
  12. ^ - Causal Version of Newtonian Theory by Time–Retardation of the Gravitational Field Explains the Flyby Anomalies
  13. ^ P.G. Antreasian; J.R. Guinn (1998), "Investigations into the unexpected delta-v increase during the Earth Gravity Assist of GALILEO and NEAR" (PDF), AIAA/AAS Astrodynamics Specialist Conf. and Exhibition, Boston, paper no. 98-4287 
  14. ^ V Guruprasad (2015), "Observational evidence for travelling wave modes bearing distance proportional shifts", EPL 110 (5): 54001, arXiv:1507.08222, Bibcode:2015EL....11054001G, doi:10.1209/0295-5075/110/54001 

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