View source for Physics:Flyby anomaly

{{short description|Unexplained observed excessive energy during Earth flybys of spacecraft}}
{{unsolved|physics|What causes the unexpected change in [[Physics:Acceleration|acceleration]] for flybys of spacecraft?}}

The '''flyby anomaly''' is a discrepancy between current scientific models and the actual increase in speed (i.e. increase in ''[[Physics:Kinetic energy|kinetic energy]]'') observed during a [[Astronomy:Gravity assist|planetary flyby]] (usually of Earth) by a spacecraft. In multiple cases, spacecraft have been observed to gain greater speed than scientists had predicted, but thus far no convincing explanation has been found. This anomaly has been observed as shifts in the [[Astronomy:S band|S-band]] and [[Physics:X band|X-band]] [[Physics:Doppler effect|Doppler]] and ranging [[Telemetry|telemetry]].  The largest discrepancy noticed during a flyby has been 13&nbsp;mm/s.<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>

==Observations==
Gravitational assists are valuable techniques for [[Astronomy:Timeline of Solar System exploration|Solar System exploration]]. Because the success of such flyby maneuvers depends on the exact geometry of the [[Physics:Trajectory|trajectory]], the position and velocity of a spacecraft during its encounter with a planet is continually tracked with great precision by the Deep Space Network (DSN).

[[Image:AntreasianGuinn199803b.jpg|thumb|upright=1.35|Range residuals during the Earth flyby of NEAR]]
[[File:Mdis depart anot.ogv|thumb|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&nbsp;mHz shift, which corresponds to a velocity increase of 3.92&nbsp;mm/s at [[Astronomy:Apsis|perigee]]. Investigations of this effect at the [[Organization:Jet Propulsion Laboratory|Jet Propulsion Laboratory]] (JPL), the [[Organization:Goddard Space Flight Center|Goddard Space Flight Center]] (GSFC) and the University of Texas have not yielded a satisfactory explanation.

No such anomaly was detected after the second Earth flyby of ''Galileo'' in December 1992, where the measured velocity decrease matched that expected from atmospheric drag at the lower altitude of 303&nbsp;km.  However, the drag estimates had large error bars, and so an anomalous acceleration could not be ruled out.<ref name="GAL2">{{cite report |title=Tracking Galileo at Earth-2 Perigee Using The Tracking and Data Relay Satellite System |first1=C. |last1=Edwards |first2=J |last2=Anderson |first3=P |last3=Beyer |first4=S. |last4=Bhaskaran |first5=J. |last5=Borders |first6=S. |last6=DiNardo |first7=W. |last7=Folkner |first8=R. |last8=Haw |first9=S. |last9=Nandi |first10=F. |last10=Nicholson |first11=C. |last11=0ttenhoff |first12=S. |last12=Stephens |date=1993-08-16 |citeseerx=10.1.1.38.4256 |hdl=2014/34792 |url=https://trs.jpl.nasa.gov/bitstream/handle/2014/34792/93-0165.pdf |archive-url=https://web.archive.org/web/20220418090852/https://trs.jpl.nasa.gov/bitstream/handle/2014/34792/93-0165.pdf |archive-date=2022-04-18 |url-status=live  }}.  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±4.0 mm/s [5], clearly consistent with the observed velocity change. By 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.</ref>

On 23 January 1998 the Near Earth Asteroid Rendezvous (NEAR) spacecraft experienced an anomalous velocity increase of 13.46&nbsp;mm/s after its Earth encounter. ''[[Astronomy:Cassini–Huygens|Cassini–Huygens]]'' gained around 0.11&nbsp;mm/s in August 1999, and ''Rosetta'' gained 1.82&nbsp;mm/s after its Earth flyby in March 2005.

An analysis of the ''[[Astronomy:MESSENGER|MESSENGER]]'' spacecraft (studying [[Astronomy: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.

In November 2009, ESA's [[Engineering: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"/><ref>{{cite news |url=https://www.nav.ei.tum.de/fileadmin/w00bkq/layout/colloquium_biele_slides.pdf |title=Navigation of the interplanetary Rosetta and Philae spacecraft and the determination of the gravitational field of comets and asteroids - (DLR) @ TU München, 2012 |author=J. Biele |date=2012 |accessdate=2014-11-18 |url-status=dead |archiveurl=https://web.archive.org/web/20141129054256/https://www.nav.ei.tum.de/fileadmin/w00bkq/layout/colloquium_biele_slides.pdf |archivedate=2014-11-29 }}</ref>

The 2013 flyby of Juno on the way to Jupiter yielded no anomalous acceleration.<ref name="JUNO">{{cite conference |author1=Thompson, Paul F. |author2=Matthew Abrahamson |author3=Shadan Ardalan |author4=John Bordi |title=Reconstruction of Earth flyby by the Juno spacecraft. |publisher=AAS |conference=24th AAS/AIAA Space Flight Mechanics Meeting |location=Santa Fe, NM |date=2014 |pages=14–435 |url=https://ntrs.nasa.gov/search.jsp?R=20160008163}}</ref>

In 2018, a careful analysis of the trajectory of the presumed interstellar asteroid [[Astronomy:ʻOumuamua|ʻOumuamua]] revealed a small excess velocity as it receded from the Sun. Initial speculation suggested that the anomaly was due to outgassing, though none had been detected.<ref>[http://www.ifa.hawaii.edu/info/press-releases/Oumuamua-06-2018/ Is the Interstellar Asteroid Really a Comet?]</ref>

Summary of some Earth-flyby spacecraft is provided in table below.<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 |archiveurl=https://web.archive.org/web/20091223041138/http://webservices.esa.int/blog/post/5/916 |archivedate=2009-12-23}}</ref><ref name="Anderson">{{citation |doi=10.1016/j.newast.2006.11.004 |last=Anderson |first=John D. |author2=James K. Campbell |author3=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 |bibcode=2007NewA...12..383A|s2cid=15913052 }}</ref>

{| class="wikitable" border="1"
|-
! {{Diagonal split header|Data|Craft}}
! [[Engineering:Galileo (spacecraft)|''Galileo'' I]]
! [[Engineering:Galileo (spacecraft)|''Galileo'' II]]
! [[Astronomy:NEAR Shoemaker|NEAR]]
! [[Astronomy:Cassini–Huygens|''Cassini'']]
! [[Engineering:Rosetta (spacecraft)|''Rosetta'']]-I
! ''[[Astronomy:MESSENGER|MESSENGER]]''
! ''[[Engineering:Rosetta (spacecraft)|Rosetta]]''-II
! ''[[Engineering:Rosetta (spacecraft)|Rosetta]]''-III
! ''[[Engineering:Juno (spacecraft)|Juno]]''
! ''[[Astronomy:Hayabusa2|Hayabusa2]]''
! [[Astronomy:OSIRIS-REx|OSIRIS-REx]]<ref>{{cite web |title=OSIRIS-REx asteroid mission receives gravitational boost from planet Earth |date=September 22, 2017 |author=Stephen Clark |publisher=Spaceflight Now |url=https://spaceflightnow.com/2017/09/22/osiris-rex-earth-gravity-assist/}}</ref>
! ''[[Astronomy:BepiColombo|BepiColombo]]''<ref>{{cite web |url=https://www.cosmos.esa.int/web/bepicolombo-flyby/earth-flyby |title=BEPICOLOMBO EARTH FLYBY}}</ref>
|-
| Date
| 1990-12-08
| 1992-12-08
| 1998-01-23
| 1999-08-18
| 2005-03-04
| 2005-08-02
| 2007-11-13
| 2009-11-13
| 2013-10-09
| 2015-12-03
| 2017-09-22
| 2020-04-10
|-
| Speed at infinity, km/s
| 8.949
| 8.877
| 6.851
| 16.01
| 3.863
| 4.056
|
|
|
| 4.7
|
|
|-
| Speed at perigee, km/s
| 13.738
| 8.877
| 12.739
| 19.03
| 10.517
| 10.389
| 12.49
| 13.34
| 14.93
| 10.3
| 8.5
|
|-
| [[Physics:Impact parameter|Impact parameter]], km
| 11261
|
| 12850
| 8973
| 22680.49
| 22319
|
|
|
|
|
| 19064
|-
| Minimal [[Altitude|altitude]], km
| 956
| 303
| 532
| 1172
| 1954
| 2336
| 5322
| 2483
| 561<ref>[http://www.universetoday.com/105451/nasas-juno-spacecraft-returns-1st-flyby-images-of-earth-while-sailing-on-to-jupiter/ NASA’S JUNO SPACECRAFT RETURNS 1ST FLYBY IMAGES OF EARTH WHILE SAILING ON TO JUPITER]</ref>
| 3090<ref>[http://global.jaxa.jp/press/2015/12/20151214_hayabusa2.html Hayabusa2 Earth Swing-by Result]</ref>
| 17237
| 12677
|-
| Spacecraft [[Physics:Mass|mass]], kg
| 2497.1
| 2223.0
| 730.40
| 4612.1
| 2895.2
| 1085.6
| 2895
| 2895
| ~2720
| 590
|
|4000
|-
| Trajectory inclination to equator, degrees
| 142.9
| 138.9
| 108.0
| 25.4
| 144.9
| 133.1
|
|
|
|
|
|
|-
| Deflection angle, degrees
| 47.46
| 51.1
| 66.92
| 19.66
| 99.396
| 94.7
| 
|
|
| 80
|
|
|-
| 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
| 0±0.8<ref name="JUNO"/>
| ?
| ?
| ?
|-
| Speed increment at perigee, mm/s
| 2.560±0.050
| -9.200±0.600
| 7.210±0.0700
| −1.700±0.9000
| 0.670±0.0200
| 0.008±0.004
| ~0.000±0.000
| −0.004±0.044
| 
| ?
| ?
| ?
|-
| Gained energy, J/kg
| '''35.1±0.7'''
|
| '''92.2±0.9'''
|
| '''7.03±0.19'''
|
|
|
|
| ?
| ?
| ?
|}

== Anderson's empirical relation ==
An empirical equation for the anomalous flyby velocity change was proposed in 2008 by J. D. Anderson et al.:<ref>{{cite journal |author=Anderson |title=Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth |journal=Physical Review Letters |volume=100 |issue=9 |pages=091102 |date=7 March 2008 |url=http://virgo.lal.in2p3.fr/NPAC/relativite_fichiers/anderson_2.pdf |doi=10.1103/physrevlett.100.091102 |pmid=18352689 |bibcode=2008PhRvL.100i1102A |display-authors=0}}</ref>

<math display="block"> \frac{dV}{V} = \frac{2 \omega_\text{E} R_\text{E} (\cos \varphi_\text{i} - \cos \varphi_\text{o})}{c}, </math>

where {{math|{{var|ω}}{{sub|E}}}} is the [[Physics:Angular frequency|angular frequency]] of the Earth, {{math|{{var|R}}{{sub|E}}}} is the Earth radius, and {{math|{{var|φ}}{{sub|i}}}} and {{math|{{var|φ}}{{sub|o}}}} are the inbound and outbound equatorial angles of the spacecraft. This formula was derived later by Jean Paul Mbelek from special relativity, leading to one of the possible explanations of the effect.<ref name="mbelek"/> This does not, however, consider the SSN residuals – see "Possible explanations" below.

==Possible explanations==
There have been a number of proposed explanations of the flyby anomaly, including:

* A postulated consequence of the assumption that the speed of light is isotropic in all frames, and invariant in the method used to measure the velocity of the space probes by means of the Doppler effect.<ref>{{cite journal |last1=Greaves |first1=Eduardo D. |last2=Bracho |first2=Carlos |last3=Mikoss |first3=Imre |title=A Solution to the Flyby Anomaly Riddle |journal=Progress in Physics |date=2020 |volume=16 |issue=1 |page=49}}</ref> The inconsistent anomalous values measured: positive, null or negative are simply explained relaxing this assumption. During flyby maneuvers the velocity components of the probe in the direction of the observer {{math|{{var|V}}{{sub|o}}}} are derived from the relative displacement {{math|d{{var|f}}}} of the radiofrequency {{mvar|f}} transmitted by the probe, multiplied by the local speed of the light {{mvar|{{prime|c}}}} by the Doppler effect: {{math|1={{var|V}}{{sub|o}} = (d{{var|f}} / {{var|f}}) {{var|{{prime|c}}}}}}. According to the Céspedes-Curé hypothesis,<ref>{{cite book |last1=Cespedes-Cure |first1=Jorge |title=Einstein on Trial or Metaphysical Principles of Natural Philosophy |date=2002 |publisher=et al. Organization |location=Venezuela |isbn=0-9713873-0-3 |edition=1st}}</ref> the movement through variable gravitational energy density fields produces slight variations of the refractive index {{mvar|{{prime|n}}}} of space and therefore of the speed of light {{mvar|{{prime|c}}}} which leads to unaccounted corrections of the Doppler data that are based on an invariant {{mvar|c}}. This leads to incorrect estimates of the speed or energy change in the flyby maneuver on the Earth's frame of reference.
* Unaccounted-for [[Physics:Transverse Doppler effect|transverse Doppler effect]]—i.e. the redshift of light source with zero radial and non-zero tangential velocity.<ref name="mbelek">{{cite arXiv |last=Mbelek |first=J. P. |eprint=0809.1888 |title=Special relativity may account for the spacecraft flyby anomalies |class=qr-qc |date=2009}}</ref> However, this cannot explain the similar anomaly in the ranging data.
* A dark-matter halo around Earth.<ref>{{citation |first=S. L. |last=Adler |title=Can the flyby anomaly be attributed to Earth-bound dark matter? |year=2009 |arxiv=0805.2895 |bibcode=2009PhRvD..79b3505A |doi=10.1103/PhysRevD.79.023505 |journal=Physical Review D |volume=79 |issue=2 |pages=023505|s2cid=13152802 }}</ref>
* The impact of [[Physics:General relativity|general relativity]], in its weak-field and linearized form yielding gravitomagnetic phenomena like [[Physics:Frame-dragging|frame-dragging]], has been investigated as well:<ref>{{cite journal |first=L. |last=Iorio |title=The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly |journal=Scholarly Research Exchange |date=2009 |volume=2009 |page=7695 |doi=10.3814/2009/807695 |arxiv=0811.3924 |bibcode=2009ScReE2009.7695I |doi-access=free }}</ref> it turns out to be unable to account for the flyby anomaly.
* The classical time-retarded gravity explanation proposed by [[Biography:Joseph C. Hafele|Joseph C. Hafele]].<ref>{{cite journal |url=http://www.ptep-online.com/2013/PP-33-01.PDF |title=Causal Version of Newtonian Theory by Time-Retardation of the Gravitational Field Explains the Flyby Anomalies |journal=Progress in Physics |first=Joseph C. |last=Hafele |volume=2 |date=April 2013 |issue=2 |page=3 |bibcode=2013PrPh....9b...3H |issn=1555-5534}}</ref>[[Image:Graph of the SSN range residuals in the 1998 NEAR flyby with lag.jpg|thumb|SSN range residuals for the NEAR flyby with range, delay]]
* Range-proportional excess delay of the telemetry signal revealed by the United States Space Surveillance Network range data in the NEAR flyby.<ref>{{cite conference |first1=Peter G. |last1=Antreasian |first2=Joseph R. |last2=Guinn |title=Investigations into the Unexpected Delta-V Increase During the Earth Gravity Assist of GALILEO and NEAR |url=https://trs.jpl.nasa.gov/bitstream/handle/2014/20322/98-1237.pdf |id=AIAA 98-4287 |conference=AIAA/AAS Astrodynamics Specialist Conference and Exhibition |location=Boston, Massachusetts |publisher=AIAA |date=1998-08-10 |accessdate=2017-05-06 |citeseerx=10.1.1.613.5871 |hdl=2014/20322 |archive-url=https://web.archive.org/web/20220119191845/https://trs.jpl.nasa.gov/bitstream/handle/2014/20322/98-1237.pdf?sequence=1&isAllowed=y |archive-date=2022-01-19 |url-status=live }}</ref> 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.<ref>{{cite journal |first=V. |last=Guruprasad |title=Observational evidence for travelling wave modes bearing distance proportional shifts |doi=10.1209/0295-5075/110/54001 |journal=EPL |volume=110 |issue=5 |date=2015 |pages=54001 |arxiv=1507.08222 |bibcode=2015EL....11054001G|s2cid=42285652 }}</ref>
* The action of a topological torsion current predicting flyby anomalies in retrograde direction, but null-effect when spacecraft approach the planet in prograde direction with respect to the planetary sense of rotation.<ref>{{cite journal |first=Mario J. |last=Pinheiro |title=Some effects of topological torsion currents on spacecraft dynamics and the flyby anomaly |url=https://academic.oup.com/mnras/article-abstract/461/4/3948/2608696/Some-effects-of-topological-torsion-currents-on?rss=1 |doi=10.1093/mnras/stw1581 |journal=[[Organization:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society]] |volume=461 |issue=4 |date=2016 |pages=3948–3953 |arxiv=1606.00691 |bibcode=2016MNRAS.461.3948P}}</ref>
* The analysis of the ''Juno'' flyby looked at analysis errors that could potentially mimic the flyby anomaly.  They found that a [[Physics:Geopotential model#The deviations of Earth's gravitational field from that of a homogeneous sphere|high-precision gravity field]] of at least 50×50 coefficients was needed for accurate flyby predictions.  Use of a lower-precision gravity field (such as a model with 10×10 coefficients, sufficient for launch analysis), would yield a 4.5&nbsp;mm/s velocity error.<ref name="JUNO"/>

==Related research==
Some missions designed to study gravity, such as [[Physics:MICROSCOPE|MICROSCOPE]] and [[Physics:STEP (satellite)|STEP]], are designed to make extremely accurate gravity measurements and may shed some light on the anomaly.<ref>{{cite journal |title=Probing the Flyby Anomaly with the future STE-QUEST mission |journal=Planetary and Space Science |volume=79-80 |pages=76–81 |issn=0032-0633 |arxiv=1210.7333 |doi=10.1016/j.pss.2013.02.005 |year=2013 |last1=Páramos |first1=Jorge |last2=Hechenblaikner |first2=G. |bibcode=2013P&SS...79...76P |s2cid=119287334 }}</ref> However, MICROSCOPE has completed its mission, finding nothing anomalous,<ref>{{cite journal |last1=Touboul |first1=P. |last2=Métris |first2=G. |last3=Rodrigues |first3=M. |last4=Bergé |first4=J. |last5=Robert |first5=A. |last6=Baghi |first6=Q. |last7=André |first7=Y. |last8=Bedouet |first8=J. |last9=Boulanger |first9=D. |last10=Bremer |first10=S. |last11=Carle |first11=P. |display-authors=6 |year=2022 |title=MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle |journal=Physical Review Letters |volume= 129 |issue=12 |pages=121102 |doi=10.1103/PhysRevLett.129.121102 |pmid=36179190 |arxiv=2209.15487 |bibcode=2022PhRvL.129l1102T |s2cid=252468544 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.121102 }}</ref> and STEP is yet to fly.

==See also==
* [[Physics:List of unsolved problems in physics|List of unsolved problems in physics]]
* [[Astronomy:Modified Newtonian dynamics|Modified Newtonian dynamics]]
* [[Astronomy:Pioneer anomaly|Pioneer anomaly]]

==References==
{{Reflist}}

==Literature==
* {{Citation |author1=J. D. Anderson |author2=J. G. Williams |title=Long-range tests of the equivalence principle |journal=[[Physics:Classical and Quantum Gravity|Class. Quantum Grav.]] |volume=18 |issue=13 |pages=2447–2456 |date=2001 |doi=10.1088/0264-9381/18/13/307 |bibcode=2001CQGra..18.2447A|s2cid=250861959 }}.
* {{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" |date=2006 |arxiv=gr-qc/0604052 |bibcode=2006gr.qc.....4052L}}.
* {{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=2007 |bibcode=2007NewA...12..383A |doi=10.1016/j.newast.2006.11.004 |journal=New Astronomy |volume=12 |issue=5 |pages=383–397|s2cid=15913052 }}.
*[http://www.space.com/scienceastronomy/080229-spacecraft-anomaly.html NASA Baffled by Unexplained Force Acting on Space Probes] (2008), at Space.com.
* {{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=[[Physics:Physical Review Letters|Phys. Rev. Lett.]] |volume=100 |issue=91102 |date=2008 |pages=091102 |bibcode=2008PhRvL.100i1102A |pmid=18352689 |url-status=dead |archiveurl=https://web.archive.org/web/20081016172147/http://www2.phys.canterbury.ac.nz/editorial/Anderson2008.pdf |archivedate=2008-10-16 }}.
* [http://www.economist.com/science/displaystory.cfm?story_id=10804075 Wanted: Einstein Jr] (2008), at [http://www.economist.com Economist.com].
* {{cite journal |author=K. Svozil |title=Microphysical analogues of flyby anomalies |journal=New Astronomy |volume=12 |issue=5 |pages=383–397 |arxiv=0804.2198 |date=2007 |bibcode=2007NewA...12..383A |doi=10.1016/j.newast.2006.11.004|s2cid=15913052 }}

==External links==
* {{cite web |first=Claus |last=Lämmerzahl |publisher=University of Bremen |url=http://www.zarm.uni-bremen.de/fileadmin/images/laemmerzahlDatei/Pioneer_Utrecht.pdf |title=The Pioneer Anomaly or Do We Really Understand the Physics With the Solar System? |format=pdf; 6.25 MB, talk/slides |pages=123 |date=2008 |work=Center for Applied Space Technology and Microgravity}}
* {{cite web |first=Andreas |last=Aste |publisher=University of Basel |url=http://phys-merger.physik.unibas.ch/~aste/flyby.pdf |title=Spacecraft Anomalies: An Update |format=pdf; 9.8 MB, talk/slides |pages=29 |date=2008 |work=Department of Physics |access-date=2009-10-01 |archive-url=https://web.archive.org/web/20161107090438/http://phys-merger.physik.unibas.ch/%7Easte/flyby.pdf |archive-date=2016-11-07 |url-status=dead }}

{{DEFAULTSORT:Flyby Anomaly}}
[[Category:Unsolved problems in physics]]
[[Category:Gravity]]
[[Category:Unexplained phenomena]]

{{Sourceattribution|Flyby anomaly}}