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| {{Update|date=March 2010}}
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| {{unsolved|physics|What causes the unexpected change in [[acceleration]] for [[gravitational slingshot|flybys]] of spacecraft?}}
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| The '''flyby anomaly''' is an unexpected energy increase during Earth-[[gravity assist|flybys]] of spacecraft. This anomaly has been observed as shifts in the [[s band|S-Band]] and [[x band|X-Band]] [[Doppler effect|Doppler]] and ranging [[telemetry]]. Taken together it causes a significant unaccounted velocity increase of over 13 mm/s during flybys.<ref name="Rosetta">{{Cite web|url=http://www.spaceref.com/news/viewpr.html?pid=29609|title=ESA's Rosetta spacecraft may help unravel cosmic mystery|date=November 12, 2009|publisher=European Space Agency |accessdate=13 March 2010}}</ref>
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| ==Observations==
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| [[gravitational slingshot|Gravitational assists]] are valuable techniques for [[Timeline of Solar System exploration|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).
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| <!-- Deleted image removed: [[Image:AntreasianGuinn199803a.jpg|left|300px|thumb|Two-way X-Band Doppler residuals during the Earth-flyby of NEAR {{deletable image-caption}}]] -->[[Image:AntreasianGuinn199803b.jpg|right|300px|thumb|Range residuals during the Earth-flyby of NEAR]]
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| 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 [[millihertz|mHz]] shift, which corresponds to a velocity increase of 3.92 mm/s at [[Apsis|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.
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| 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 space probe|Rosetta]] 1.82 mm/s after its Earth-flyby in March 2005.
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| An analysis of the [[MESSENGER]] spacecraft (studying [[Mercury (planet)|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.
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| Summary of Earth-flyby spacecraft is provided in table below.<ref name="Anderson">{{citation|doi=10.1016/j.newast.2006.11.004|last=Anderson|first=John D.|coauthors=James K. Campbell, Michael Martin Nieto|date=July 2007|title=The energy transfer process in planetary flybys|journal=New Astronomy|volume=12|issue=5|pages=383–397|arxiv=astro-ph/0608087|postscript=<!--none-->|bibcode = 2007NewA...12..383A }}</ref> The Rosetta data are for its first flyby in 2005; the second flyby produced no significant anomalous increase, and the third a negligible decrease.<ref name="ESA">{{cite web|url=http://webservices.esa.int/blog/post/5/916 |title=Mystery remains: Rosetta fails to observe swingby anomaly |publisher=ESA}}</ref>
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| {| class="wikitable" border="1"
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| |-
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| ! Quantity
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| ! [[Galileo (spacecraft)|Galileo I]]
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| ! [[Galileo (spacecraft)|Galileo II]]
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| ! [[NEAR Shoemaker|NEAR]]
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| ! [[Cassini–Huygens|Cassini]]
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| ! [[Rosetta (spacecraft)|Rosetta]]-I
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| ! [[MESSENGER|Messenger]]
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| ! [[Rosetta (spacecraft)|Rosetta]]-II
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| ! [[Rosetta (spacecraft)|Rosetta]]-III
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| ! [[Juno (spacecraft)|Juno]]
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| |-
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| | Date
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| | 12/8/1990
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| | 12/12/1992
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| | 01/23/1998
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| | 08/18/1999
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| | 03/04/2005
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| | 08/02/2005
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| | 11/13/2007
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| | 11/13/2009
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| | 10/9/2013
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| |-
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| | Speed at infinity, km/s
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| | 8.949
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| | 8.877
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| | 6.851
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| | 16.01
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| | 3.863
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| | 4.056
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| |-
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| | Speed at [[perigee]], km/s
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| | 13.738
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| | ---
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| | 12.739
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| | 19.03
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| | 10.517
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| | 10.389
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| | 12.49
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| | 13.34
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| |-
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| | [[Impact parameter]], km
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| | 11261
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| | 12850
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| | 8973
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| | 22680.49
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| | 22319
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| |-
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| | Minimal [[altitude]], km
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| | 956
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| | 303
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| | 532
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| | 1172
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| | 1954
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| | 2336
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| | 5322
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| | 2483
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| |-
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| | Spacecraft [[mass]], kg
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| | 2497.1
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| | 730.40
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| | 4612.1
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| | 2895.2
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| | 1085.6
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| | 2895
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| | 2895
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| |-
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| | [[Inclination#Orbits|Trajectory inclination to equator]], degrees
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| | 142.9
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| | 138.9
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| | 108.8
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| | 25.4
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| | 144.9
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| | 133.1
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| |-
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| | Deflection angle, degrees
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| | 47.46
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| | 51.1
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| | 66.92
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| | 19.66
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| | 99.396
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| | 94.7
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| |-
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| | Speed increment at infinity, mm/s
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| | 3.92±0.08
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| | -4.60± 1.00
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| | 13.46±0.13
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| | −2±1
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| | 1.82±0.05
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| | 0.02±0.01
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| |-
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| | Speed increment at [[perigee]], mm/s
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| | 2.56±0.05
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| | 7.21±0.07
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| | −1.7±0.9
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| | 0.67±0.02
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| | 0.008±0.004
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| | ~0
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| | −0.004±0.044
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| |-
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| | Gained energy, J/kg
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| | '''35.1±0.7'''
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| | '''92.2±0.9'''
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| | '''7.03±0.19'''
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| |}
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| In November 2009, ESA's [[Rosetta (spacecraft)|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.<ref name="ESA"/>
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| ==Future research==
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| Upcoming missions with Earth flybys include [[BepiColombo]].
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| Some missions designed to study gravity, such as [[STE-QUEST]] or [[STEP (satellite)|STEP]], will make extremely accurate gravity measurement and may shed some light on the anomaly.<ref>{{cite web |title=Probing the Flyby Anomaly with the future STE-QUEST mission |url=http://arxiv.org/abs/1210.7333}}</ref>
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| ===Proposed equation===
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| An empirical equation for the anomalous flyby velocity change was proposed by J.D. Anderson et al.:
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| :<math> \frac{dV}{V} = \frac{2 \omega_e R_e (\cos \varphi_i - \cos \varphi_o)}{c}</math>
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| where ''ω<sub>e</sub>'' is the [[angular frequency]] of the Earth, ''R<sub>e</sub>'' is the Earth radius, and ''φ<sub>i</sub>'' and ''φ<sub>o</sub>'' are the inbound and outbound equatorial angles of the spacecraft.<ref>{{Citation|author=Anderson, et al.|title=Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth|journal=Phys. Rev. Lett.|date=7 March 2008|url=http://virgo.lal.in2p3.fr/NPAC/relativite_fichiers/anderson_2.pdf|postscript=.}}</ref>
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| ==Possible explanations==
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| Possible explanations of the flyby anomaly include
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| *Unaccounted [[Transverse Doppler effect]]—i.e. the redshift of light source with zero radial and non-zero tangential velocity.<ref>{{cite arxiv|author=J. P. Mbelek|title=Special relativity may account for the spacecraft flyby anomalies|year=2008|eprint=0809.1888|postscript=<!--none-->|bibcode=2008arXiv0809.1888M|class=gr-qc}}</ref> However, this cannot explain the similar anomaly in the ranging data;
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| *A [[dark matter]] halo around the Earth;<ref>{{citation|author=S.L.Adler|title=Can the flyby anomaly be attributed to Earth-bound dark matter?|year=2008|arxiv=0805.2895|postscript=<!--none-->|bibcode=2009PhRvD..79b3505A|doi=10.1103/PhysRevD.79.023505|journal=Physical Review D|volume=79|issue=2 }}</ref>
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| *A Modification of Inertia resulting from a Hubble-scale [[Casimir effect]] ([[MIHsC]]);<ref>{{citation|author=M.E. McCulloch|title=Modelling the flyby anomalies using a modification of inertia|journal=MNRAS Letters|volume=389 |issue=1|pages=L57–L60|doi=10.1111/j.1745-3933.2008.00523.x|year=2008|postscript=<!--none-->|bibcode=2008MNRAS.389L..57M|arxiv=0806.4159}}</ref>
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| *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:<ref>{{citation|author=L. Iorio|title= The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly|journal=Scholarly Research Exchange|volume=2009|doi=10.3814/2009/807695|id=807695|year=2009|pages=1|postscript=<!--none-->|bibcode=2009ScReE2009.7695I|arxiv=0811.3924}}</ref> it turns out to be unable to account for the flyby anomaly;
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| *The anomaly may be due to the rotation of the Earth. This rotation induces an azimuthally symmetric gravitational field.<ref>{{cite arxiv|author1=G. G. Nyambuya|author=G. G. Nyambuya|title=Are Flyby Anomalies and the Pioneer Effect an ASTG Phenomenon?|eprint=0803.1370|year=2010|postscript=<!--none-->|bibcode=2008arXiv0803.1370N|class=physics.gen-ph}}</ref>
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| ==See also==
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| {{div col|colbreak=2}}
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| * [[General relativity]]
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| * [[List of unsolved problems in physics]]
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| * [[Modified Newtonian dynamics]]
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| * [[Pioneer anomaly]]
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| {{div col end}}
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| ==References==
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| {{Reflist}}
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| * {{Citation |author1=P.G. Antreasian |author2=J.R. Guinn |contribution=Investigations into the unexpected delta-v increase during the Earth Gravity Assist of GALILEO and NEAR |contribution-url=http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/20322/1/98-1237.pdf |id=paper no. 98-4287 |title=AIAA/AAS Astrodynamics Specialist Conf. and Exhibition |location=Boston |year=1998 |postscript=<!--none-->}}
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| * {{Citation |author1=J.D. Anderson |author2=J.G. Williams |title=Long-range tests of the equivalence principle |journal=[[Classical and Quantum Gravity|Class. Quantum Grav.]] |volume=18 |issue=13 |pages=2447–2456 |year=2001 |doi=10.1088/0264-9381/18/13/307 |postscript=<!--none-->|bibcode = 2001CQGra..18.2447A }}
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| * {{Citation |author1=C. Lämmerzahl |author2=O. Preuss |author3=H. Dittus |title=Is the physics within the Solar system really understood? |journal=Proceedings of the 359th WE-Heraeus Seminar on "Lasers, Clocks, and Drag-Free: Technologies for Future Exploration in Space and Tests of Gravity" |year=2006 |postscript=<!--none-->}}, Preprint at {{arxiv|gr-qc/0604052}}. [http://cgc.pmo.ac.cn/Center-for-Gravitation-and-Cosmology/ppt/ASTROD2006-Laemmerzahl.pdf Associated presentation slides]
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| * {{Citation |author1=J.D. Anderson |author2=J.K. Campbell |author3=M.M. Nieto |title=The Energy Transfer Process in Planetary Flybys |arxiv=astro-ph/0608087 |year=2006 |postscript=<!--none-->|bibcode = 2007NewA...12..383A |doi = 10.1016/j.newast.2006.11.004 |journal=New Astronomy |volume=12 |issue=5 |pages=383 }}
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| *[http://www.space.com/scienceastronomy/080229-spacecraft-anomaly.html NASA Baffled by Unexplained Force Acting on Space Probes], at [[Space.com]]
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| * {{Citation |author1=J.D. Anderson |author2=J.K. Campbell |author3=J.E. Ekelund |author4=J. Ellis |author5=J.F. Jordan |title=Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth |url=http://www2.phys.canterbury.ac.nz/editorial/Anderson2008.pdf |doi=10.1103/PhysRevLett.100.091102 |journal=[[Physical Review Letters|Phys. Rev. Lett.]] |volume=100 |issue=91102 |year=2008 |pages=091102 |postscript=<!--none--> |bibcode=2008PhRvL.100i1102A}}
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| * [http://www.economist.com/science/displaystory.cfm?story_id=10804075 Wanted: Einstein Jr], at [http://www.economist.com Economist.com]
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| * {{cite arxiv |author=K. Svozil |title=Microphysical analogues of flyby anomalies |eprint=0804.2198 |year=2008 |postscript=<!--none-->|bibcode = 2008arXiv0804.2198S |class=quant-ph }}
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| ==External links==
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| * Claus Lämmerzahl, University of Bremen:[http://www.zarm.uni-bremen.de/fileadmin/images/laemmerzahlDatei/Pioneer_Utrecht.pdf The Pioneer Anomaly or Do We Really Understand the Physics With the Solar System?] (PDF file; 6.25 MB, 139 pages
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| * Andreas Aste, University of Basel:[http://phys-merger.physik.unibas.ch/~aste/flyby.pdf Spacecraft Anomalies: An Update](PDF file; 9.8 MB, talk/slides)
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| {{DEFAULTSORT:Flyby Anomaly}}
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| [[Category:Unsolved problems in physics]]
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| [[Category:Gravitation]]
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