# Flyby anomaly

 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.[1]

## Observations

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

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.

Summary of Earth-flyby spacecraft is provided in table below.[2] The Rosetta data are for its first flyby in 2005; the second flyby produced no significant anomalous increase, and the third a negligible decrease.[3]

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
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

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]

## Future research

Upcoming missions with Earth flybys include BepiColombo.

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.[4]

### Proposed equation

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.[5]

## 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.[6] However, this cannot explain the similar anomaly in the ranging data;
• A dark matter halo around Earth;[7]
• A modification of inertia resulting from a Hubble-scale Casimir effect (MIHsC);[8]
• 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:[9] 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.[10]
• The classical time-retarded gravity explanation proposed by Joseph C. Hafele.[11]

## References

1. ^ "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 13 March 2010.
2. ^ 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
3. ^ a b
4. ^
5. ^ Anderson, et al. (7 March 2008), "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth", Phys. Rev. Lett..
6. ^ J. P. Mbelek (2008). "Special relativity may account for the spacecraft flyby anomalies". arXiv:0809.1888 [gr-qc]. Bibcode 2008arXiv0809.1888M
7. ^ 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
8. ^ 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
9. ^ 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
10. ^ G. G. Nyambuya (2010). "Are Flyby Anomalies and the Pioneer Effect an ASTG Phenomenon?". arXiv:0803.1370 [physics.gen-ph]. Bibcode 2008arXiv0803.1370N
11. ^ http://www.ptep-online.com/index_files/2013/PP-33-01.PDF - Causal Version of Newtonian Theory by Time–Retardation of the Gravitational Field Explains the Flyby Anomalies