Flyby anomaly

Last updated October 06, 2024

Unsolved problem in physics:

What causes the unexpected change in 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 kinetic energy ) observed during a 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 S-band and X-band Doppler and ranging telemetry. The largest discrepancy noticed during a flyby is tiny, 13.46 mm/s.^[1]

Observations

Gravitational assists are valuable techniques for Solar System exploration. Because the success of such flyby maneuvers depends on the exact geometry of the trajectory, the position and velocity of a spacecraft during its encounter with a planet is continually tracked with great precision by earth telemetry, e.g. via the Deep Space Network (DSN).

Range residuals during the Earth flyby of NEAR AntreasianGuinn199803b.jpg — 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. Investigations of this effect at the Jet Propulsion Laboratory (JPL), the 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 km. However, the drag estimates had large error bars, and so an anomalous acceleration could not be ruled out.^[2]

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 around 0.11 mm/s in August 1999, and Rosetta gained 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.^[3]^[4]

The 2013 flyby of Juno on the way to Jupiter yielded no anomalous acceleration.^[5]

In 2018, a careful analysis of the trajectory of the presumed interstellar asteroid 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.^[6]

Summary of some Earth-flyby spacecraft is provided in table below.^[3]^[7]

Craft Data	Galileo I	Galileo II	NEAR	Cassini	Rosetta-I	MESSENGER	Rosetta -II	Rosetta -III	Juno	Hayabusa2	OSIRIS-REx ^[8]	BepiColombo ^[9]
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
Impact parameter, km	11261		12850	8973	22680.49	22319						19064
Minimal altitude, km	956	303	532	1172	1954	2336	5322	2483	561^[10]	3090^[11]	17237	12677
Spacecraft 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^[5]	?	?	?
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.:^[12]

${\frac {dV}{V}}={\frac {2\omega _{\text{E}}R_{\text{E}}(\cos \varphi _{\text{i}}-\cos \varphi _{\text{o}})}{c}},$

where $ω E$ is the angular frequency of the Earth, $R E$ is the Earth radius, and $φ i$ and $φ o$ 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.^[13] 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.^[14] 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 $V o$ are derived from the relative displacement $d f$ of the radiofrequency $f$ transmitted by the probe, multiplied by the local speed of the light $c'$ by the Doppler effect: $V o = (d f / f) c'$ . According to the Céspedes-Curé hypothesis,^[15] the movement through variable gravitational energy density fields produces slight variations of the refractive index $n'$ of space and therefore of the speed of light $c'$ which leads to unaccounted corrections of the Doppler data that are based on an invariant $c$ . This leads to incorrect estimates of the speed or energy change in the flyby maneuver on the Earth's frame of reference.
Unaccounted-for transverse Doppler effect—i.e. the redshift of light source with zero radial and non-zero tangential velocity.^[13] However, this cannot explain the similar anomaly in the ranging data.
A dark-matter halo around Earth.^[16]
The impact of general relativity, in its weak-field and linearized form yielding gravitomagnetic phenomena like frame-dragging, has been investigated as well:^[17] it turns out to be unable to account for the flyby anomaly.
The classical time-retarded gravity explanation proposed by Joseph C. Hafele.^[18]

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.^[19] 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.^[20]
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.^[21]
The analysis of the Juno flyby looked at analysis errors that could potentially mimic the flyby anomaly. They found that a 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 mm/s velocity error.^[5]

Related research

Some missions designed to study gravity, such as MICROSCOPE and STEP, are designed to make extremely accurate gravity measurements and may shed some light on the anomaly.^[22] However, MICROSCOPE has completed its mission, finding nothing anomalous,^[23] and STEP is yet to fly.

Related Research Articles

In astronomy, dark matter is a hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravitational effects which cannot be explained by general relativity unless more matter is present than can be observed. Such effects occur in the context of formation and evolution of galaxies, gravitational lensing, the observable universe's current structure, mass position in galactic collisions, the motion of galaxies within galaxy clusters, and cosmic microwave background anisotropies.

Pioneer 11 is a NASA robotic space probe launched on April 5, 1973, to study the asteroid belt, the environment around Jupiter and Saturn, the solar wind, and cosmic rays. It was the first probe to encounter Saturn, the second to fly through the asteroid belt, and the second to fly by Jupiter. Later, Pioneer 11 became the second of five artificial objects to achieve an escape velocity allowing it to leave the Solar System. Due to power constraints and the vast distance to the probe, the last routine contact with the spacecraft was on September 30, 1995, and the last good engineering data was received on November 24, 1995.

<span class="mw-page-title-main">Redshift</span> Change of wavelength in photons during travel

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

Near Earth Asteroid Rendezvous – Shoemaker, renamed after its 1996 launch in honor of planetary scientist Eugene Shoemaker, was a robotic space probe designed by the Johns Hopkins University Applied Physics Laboratory for NASA to study the near-Earth asteroid Eros from close orbit over a period of a year. It was the first spacecraft to orbit an asteroid and land on it successfully. In February 2000, the mission closed in on the asteroid and orbited it. On February 12, 2001, Shoemaker touched down on the asteroid and was terminated just over two weeks later.

A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.

In physics, there are four observed fundamental interactions that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative theories have proposed a fifth force to explain various anomalous observations that do not fit existing theories. The characteristics of this fifth force depend on the hypothesis being advanced. Many postulate a force roughly the strength of gravity with a range of anywhere from less than a millimeter to cosmological scales. Another proposal is a new weak force mediated by W′ and Z′ bosons. Some physicists speculate that a form of dark energy called quintessence could be a fifth force.

Rosetta was a space probe built by the European Space Agency launched on 2 March 2004. Along with Philae, its lander module, Rosetta performed a detailed study of comet 67P/Churyumov–Gerasimenko (67P). During its journey to the comet, the spacecraft performed flybys of Earth, Mars, and the asteroids 21 Lutetia and 2867 Šteins. It was launched as the third cornerstone mission of the ESA's Horizon 2000 programme, after SOHO / Cluster and XMM-Newton.

Peculiar motion or peculiar velocity refers to the velocity of an object relative to a rest frame—usually a frame in which the average velocity of some objects is zero.

MESSENGER was a NASA robotic space probe that orbited the planet Mercury between 2011 and 2015, studying Mercury's chemical composition, geology, and magnetic field. The name is a backronym for "Mercury Surface, Space Environment, Geochemistry, and Ranging", and a reference to the messenger god Mercury from Roman mythology.

<span class="mw-page-title-main">Mass concentration (astronomy)</span> Region of a planet or moons crust that contains a large positive gravitational anomaly

In astronomy, astrophysics and geophysics, a mass concentration is a region of a planet's or moon's crust that contains a large positive gravity anomaly. In general, the word "mascon" can be used as a noun to refer to an excess distribution of mass on or beneath the surface of an astronomical body, such as is found around Hawaii on Earth. However, this term is most often used to describe a geologic structure that has a positive gravitational anomaly associated with a feature that might otherwise have been expected to have a negative anomaly, such as the "mascon basins" on the Moon.

The Pioneer anomaly, or Pioneer effect, was the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about 20 astronomical units (3×10⁹ km; 2×10⁹ mi) on their trajectories out of the Solar System. The apparent anomaly was a matter of much interest for many years but has been subsequently explained by anisotropic radiation pressure caused by the spacecraft's heat loss.

Redshift-space distortions are an effect in observational cosmology where the spatial distribution of galaxies appears squashed and distorted when their positions are plotted as a function of their redshift rather than as a function of their distance. The effect is due to the peculiar velocities of the galaxies causing a Doppler shift in addition to the redshift caused by the cosmological expansion.

<span class="mw-page-title-main">Martin Tajmar</span>

Martin Tajmar is a physicist and professor for Space Systems at the Dresden University of Technology. He has research interests in advanced space propulsion systems, FEEP thrusters, breakthrough propulsion physics and possible connections between gravity and superconductivity.

Any planet is an extremely faint light source compared to its parent star. For example, a star like the Sun is about a billion times as bright as the reflected light from any of the planets orbiting it. In addition to the intrinsic difficulty of detecting such a faint light source, the light from the parent star causes a glare that washes it out. For those reasons, very few of the exoplanets reported as of January 2024 have been observed directly, with even fewer being resolved from their host star.

Gravitational waves are transient displacements in a gravitational field – generated by the motion or acceleration of gravitating masses – that radiate outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic waves. In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime.

<span class="mw-page-title-main">Doppler spectroscopy</span> Indirect method for finding extrasolar planets and brown dwarfs

Doppler spectroscopy is an indirect method for finding extrasolar planets and brown dwarfs from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star. As of November 2022, about 19.5% of known extrasolar planets have been discovered using Doppler spectroscopy.

Vyacheslav Gennadievich Turyshev is a Russian physicist now working in the US at the NASA Jet Propulsion Laboratory (JPL). He is known for his investigations of the Pioneer anomaly, affecting Pioneer 10 and Pioneer 11 spacecraft, and for his attempt to recover early data of the Pioneer spacecraft to shed light on such a phenomenon.

The gravity of Mars is a natural phenomenon, due to the law of gravity, or gravitation, by which all things with mass around the planet Mars are brought towards it. It is weaker than Earth's gravity due to the planet's smaller mass. The average gravitational acceleration on Mars is 3.72076 m/s² and it varies.

<span class="mw-page-title-main">Long Range Reconnaissance Imager</span> Telescope aboard the New Horizons spacecraft for imaging

Long Range Reconnaissance Imager (LORRI) is a telescope aboard the New Horizons spacecraft for imaging. LORRI has been used to image Jupiter, its moons, Pluto and its moons, and Arrokoth since its launch in 2006. LORRI is a reflecting telescope of Ritchey-Chrétien design, and it has a main mirror diameter of 208 mm across. LORRI has a narrow field of view, less than a third of a degree. Images are taken with a CCD capturing data with 1024 × 1024 pixels. LORRI is a telescopic panchromatic camera integrated with the New Horizons spacecraft, and it is one of seven major science instruments on the probe. LORRI does not have any moving parts and is pointed by moving the entire New Horizons spacecraft.

References

↑ "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 2024-08-11.
↑ Edwards, C.; Anderson, J; Beyer, P; Bhaskaran, S.; Borders, J.; DiNardo, S.; Folkner, W.; Haw, R.; Nandi, S.; Nicholson, F.; 0ttenhoff, C.; Stephens, S. (1993-08-16). Tracking Galileo at Earth-2 Perigee Using The Tracking and Data Relay Satellite System (PDF) (Report). CiteSeerX 10.1.1.38.4256 . hdl:2014/34792. Archived (PDF) from the original on 2022-04-18.{{cite report}}: CS1 maint: numeric names: authors list (link). 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.
1 2 "Mystery remains: Rosetta fails to observe swingby anomaly". ESA. Archived from the original on 2009-12-23.
↑ 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). Archived from the original (PDF) on 2014-11-29. Retrieved 2014-11-18.
1 2 3 Thompson, Paul F.; Matthew Abrahamson; Shadan Ardalan; John Bordi (2014). Reconstruction of Earth flyby by the Juno spacecraft. 24th AAS/AIAA Space Flight Mechanics Meeting. Santa Fe, NM: AAS. pp. 14–435.
↑ Is the Interstellar Asteroid Really a Comet?
↑ 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, S2CID 15913052
↑ Stephen Clark (September 22, 2017). "OSIRIS-REx asteroid mission receives gravitational boost from planet Earth". Spaceflight Now.
↑ "BEPICOLOMBO EARTH FLYBY".
↑ NASA’S JUNO SPACECRAFT RETURNS 1ST FLYBY IMAGES OF EARTH WHILE SAILING ON TO JUPITER
↑ Hayabusa2 Earth Swing-by Result
↑ Anderson; et al. (7 March 2008). "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" (PDF). Physical Review Letters. 100 (9): 091102. Bibcode:2008PhRvL.100i1102A. doi:10.1103/physrevlett.100.091102. PMID 18352689. Archived from the original (PDF) on 4 June 2016. Retrieved 15 February 2011.
1 2 Mbelek, J. P. (2009). "Special relativity may account for the spacecraft flyby anomalies". arXiv: 0809.1888 [qr-qc].
↑ Greaves, Eduardo D.; Bracho, Carlos; Mikoss, Imre (2020). "A Solution to the Flyby Anomaly Riddle". Progress in Physics. 16 (1): 49.
↑ Cespedes-Cure, Jorge (2002). Einstein on Trial or Metaphysical Principles of Natural Philosophy (1st ed.). Venezuela: et al. Organization. ISBN 0-9713873-0-3.
↑ Adler, S. L. (2009), "Can the flyby anomaly be attributed to Earth-bound dark matter?", Physical Review D, 79 (2): 023505, arXiv: 0805.2895 , Bibcode:2009PhRvD..79b3505A, doi:10.1103/PhysRevD.79.023505, S2CID 13152802
↑ Iorio, L. (2009). "The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly". Scholarly Research Exchange. 2009: 7695. arXiv: 0811.3924 . Bibcode:2009ScReE2009.7695I. doi: 10.3814/2009/807695 .
↑ Hafele, Joseph C. (April 2013). "Causal Version of Newtonian Theory by Time-Retardation of the Gravitational Field Explains the Flyby Anomalies" (PDF). Progress in Physics. 2 (2): 3. Bibcode:2013PrPh....9b...3H. ISSN 1555-5534.
↑ Antreasian, Peter G.; Guinn, Joseph R. (1998-08-10). Investigations into the Unexpected Delta-V Increase During the Earth Gravity Assist of GALILEO and NEAR (PDF). AIAA/AAS Astrodynamics Specialist Conference and Exhibition. Boston, Massachusetts: AIAA. CiteSeerX 10.1.1.613.5871 . hdl:2014/20322. AIAA 98-4287. Archived (PDF) from the original on 2022-01-19. Retrieved 2017-05-06.
↑ Guruprasad, V. (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. S2CID 42285652.
↑ Pinheiro, Mario J. (2016). "Some effects of topological torsion currents on spacecraft dynamics and the flyby anomaly". Monthly Notices of the Royal Astronomical Society . 461 (4): 3948–3953. arXiv: 1606.00691 . Bibcode:2016MNRAS.461.3948P. doi: 10.1093/mnras/stw1581 .
↑ Páramos, Jorge; Hechenblaikner, G. (2013). "Probing the Flyby Anomaly with the future STE-QUEST mission". Planetary and Space Science. 79–80: 76–81. arXiv: 1210.7333 . Bibcode:2013P&SS...79...76P. doi:10.1016/j.pss.2013.02.005. ISSN 0032-0633. S2CID 119287334.
↑ Touboul, P.; Métris, G.; Rodrigues, M.; Bergé, J.; Robert, A.; Baghi, Q.; et al. (2022). "MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle". Physical Review Letters. 129 (12): 121102. arXiv: 2209.15487 . Bibcode:2022PhRvL.129l1102T. doi:10.1103/PhysRevLett.129.121102. PMID 36179190. S2CID 252468544.

Literature

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, S2CID 250861959 .
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", arXiv: gr-qc/0604052 , Bibcode:2006gr.qc.....4052L .
J. D. Anderson; J. K. Campbell; M. M. Nieto (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, S2CID 15913052 .
NASA Baffled by Unexplained Force Acting on Space Probes (2008), 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" (PDF), Phys. Rev. Lett. , 100 (91102): 091102, Bibcode:2008PhRvL.100i1102A, doi:10.1103/PhysRevLett.100.091102, PMID 18352689, archived from the original (PDF) on 2008-10-16.
Wanted: Einstein Jr (2008), at Economist.com.
K. Svozil (2007). "Microphysical analogues of flyby anomalies". New Astronomy. 12 (5): 383–397. arXiv: 0804.2198 . Bibcode:2007NewA...12..383A. doi:10.1016/j.newast.2006.11.004. S2CID 15913052.

External links

Lämmerzahl, Claus (2008). "The Pioneer Anomaly or Do We Really Understand the Physics With the Solar System?" (pdf; 6.25 MB, talk/slides). Center for Applied Space Technology and Microgravity. University of Bremen. p. 123.
Aste, Andreas (2008). "Spacecraft Anomalies: An Update" (PDF). Department of Physics. University of Basel. p. 29. Archived from the original (pdf; 9.8 MB, talk/slides) on 2016-11-07. Retrieved 2009-10-01.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Rosetta-1] "ESA's Rosetta spacecraft may help unravel cosmic mystery". European Space Agency. November 12, 2009. Retrieved 2024-08-11.

[GAL2-2] Edwards, C.; Anderson, J; Beyer, P; Bhaskaran, S.; Borders, J.; DiNardo, S.; Folkner, W.; Haw, R.; Nandi, S.; Nicholson, F.; 0ttenhoff, C.; Stephens, S. (1993-08-16). Tracking Galileo at Earth-2 Perigee Using The Tracking and Data Relay Satellite System (PDF) (Report). CiteSeerX 10.1.1.38.4256 . hdl:2014/34792. Archived (PDF) from the original on 2022-04-18.{{cite report}}: CS1 maint: numeric names: authors list (link). 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.

[ESA-3] 1 2 "Mystery remains: Rosetta fails to observe swingby anomaly". ESA. Archived from the original on 2009-12-23.

[4] 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). Archived from the original (PDF) on 2014-11-29. Retrieved 2014-11-18.

[JUNO-5] 1 2 3 Thompson, Paul F.; Matthew Abrahamson; Shadan Ardalan; John Bordi (2014). Reconstruction of Earth flyby by the Juno spacecraft. 24th AAS/AIAA Space Flight Mechanics Meeting. Santa Fe, NM: AAS. pp. 14–435.

[6] Is the Interstellar Asteroid Really a Comet?

[Anderson-7] 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, S2CID 15913052

[8] Stephen Clark (September 22, 2017). "OSIRIS-REx asteroid mission receives gravitational boost from planet Earth". Spaceflight Now.

[9] "BEPICOLOMBO EARTH FLYBY".

[10] NASA’S JUNO SPACECRAFT RETURNS 1ST FLYBY IMAGES OF EARTH WHILE SAILING ON TO JUPITER

[11] Hayabusa2 Earth Swing-by Result

[12] Anderson; et al. (7 March 2008). "Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" (PDF). Physical Review Letters. 100 (9): 091102. Bibcode:2008PhRvL.100i1102A. doi:10.1103/physrevlett.100.091102. PMID 18352689. Archived from the original (PDF) on 4 June 2016. Retrieved 15 February 2011.

[mbelek-13] 1 2 Mbelek, J. P. (2009). "Special relativity may account for the spacecraft flyby anomalies". arXiv: 0809.1888 [qr-qc].

[14] Greaves, Eduardo D.; Bracho, Carlos; Mikoss, Imre (2020). "A Solution to the Flyby Anomaly Riddle". Progress in Physics. 16 (1): 49.

[15] Cespedes-Cure, Jorge (2002). Einstein on Trial or Metaphysical Principles of Natural Philosophy (1st ed.). Venezuela: et al. Organization. ISBN 0-9713873-0-3.

[16] Adler, S. L. (2009), "Can the flyby anomaly be attributed to Earth-bound dark matter?", Physical Review D, 79 (2): 023505, arXiv: 0805.2895 , Bibcode:2009PhRvD..79b3505A, doi:10.1103/PhysRevD.79.023505, S2CID 13152802

[17] Iorio, L. (2009). "The Effect of General Relativity on Hyperbolic Orbits and Its Application to the Flyby Anomaly". Scholarly Research Exchange. 2009: 7695. arXiv: 0811.3924 . Bibcode:2009ScReE2009.7695I. doi: 10.3814/2009/807695 .

[18] Hafele, Joseph C. (April 2013). "Causal Version of Newtonian Theory by Time-Retardation of the Gravitational Field Explains the Flyby Anomalies" (PDF). Progress in Physics. 2 (2): 3. Bibcode:2013PrPh....9b...3H. ISSN 1555-5534.

[19] Antreasian, Peter G.; Guinn, Joseph R. (1998-08-10). Investigations into the Unexpected Delta-V Increase During the Earth Gravity Assist of GALILEO and NEAR (PDF). AIAA/AAS Astrodynamics Specialist Conference and Exhibition. Boston, Massachusetts: AIAA. CiteSeerX 10.1.1.613.5871 . hdl:2014/20322. AIAA 98-4287. Archived (PDF) from the original on 2022-01-19. Retrieved 2017-05-06.

[20] Guruprasad, V. (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. S2CID 42285652.

[21] Pinheiro, Mario J. (2016). "Some effects of topological torsion currents on spacecraft dynamics and the flyby anomaly". Monthly Notices of the Royal Astronomical Society . 461 (4): 3948–3953. arXiv: 1606.00691 . Bibcode:2016MNRAS.461.3948P. doi: 10.1093/mnras/stw1581 .

[22] Páramos, Jorge; Hechenblaikner, G. (2013). "Probing the Flyby Anomaly with the future STE-QUEST mission". Planetary and Space Science. 79–80: 76–81. arXiv: 1210.7333 . Bibcode:2013P&SS...79...76P. doi:10.1016/j.pss.2013.02.005. ISSN 0032-0633. S2CID 119287334.

[23] Touboul, P.; Métris, G.; Rodrigues, M.; Bergé, J.; Robert, A.; Baghi, Q.; et al. (2022). "MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle". Physical Review Letters. 129 (12): 121102. arXiv: 2209.15487 . Bibcode:2022PhRvL.129l1102T. doi:10.1103/PhysRevLett.129.121102. PMID 36179190. S2CID 252468544.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]