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Anomalies and Their Uses

Anomalies in scientific data can sometimes lead to a richer understanding of the underlying principles involved. Einstein was able to explain the difference between the Newtonian description of Mercury’s orbit and subsequent observations by applying his developing theory of General Relativity. Add the curvature of spacetime to the Newtonian picture and the problem of a tiny discrepancy in Mercury’s perihelion precession can be resolved.


This anomaly briefly changed our view of the Solar System. Originally, the astronomer Urbain Le Verrier had thought it could be explained by the presence of another planet — Vulcan — closer than Mercury to the Sun, but reported sightings of Vulcan were found to be spurious. Einstein’s work solved the precession problem. In a letter to his close friend Michele Angelo Besso, Einstein would write: “In these last months I had great success in my work. Generally covariant gravitation equations. Perihelion motions explained quantitatively… you will be astonished.”

Image: Urbain Le Verrier ((1811 – 1877). Misreading an anomaly in Mercury’s orbit caused him to believe in a planet that didn’t exist. But his prediction of the existence of Neptune showed him to be a master of Newtonian celestial mechanics. Portrait by Felix Henri Giacomotti.

Astonished indeed, but that’s General Relativity for you. As for anomalies, whether they’re a window into revised physical principles or something completely mundane, they’re well worth studying. A new paper by John Anderson (JPL) and Michael Martin Nieto (Los Alamos National Laboratory) looks at four anomalies that have grown out of astrometry, the precise measurement of the position of objects in space. All may have conventional explanations, but we need to investigate to find out whether or not we need to tweak our theories.

The four anomalies:

  • Earth Flyby: Earth flybys of the Galileo spacecraft in 1990 and 1992 seem to indicate an anomalous acceleration whose effects were also traced by the Near Earth Asteroid Rendezvous (NEAR) mission during its Earth gravity assist in 1998. And again in 2005 an anomalous acceleration was observed during an Earth flyby by the Rosetta spacecraft. A 2007 Earth flyby by Rosetta, however, produced no reported detection of such an anomaly. Is the effect related to distance? The second Rosetta flyby may have been too far from Earth (5322 kilometers) to produce it. Usefully, we’ll have the chance to study this again, for Rosetta makes a third trip past Earth in November of this year at a much closer range, a gravity assist maneuver that could produce more evidence of the apparent effect.
  • The Astronomical Unit: The distance between the Earth and the Sun can be measured down to a level of three meters, making it what the authors call “…the most accurately determined constant in all of astronomy.” The anomalous effect is that, according to at least one 2004 study, the AU appears to be increasing, whereas it should be decreasing. An increase in the Sun’s mass could explain the anomalous result, but it would involve too much mass to be likely, the mass of some 40,000 comets with a mean radius of 2000 meters. If the reported AU increase withstands further scrutiny, it is intriguing indeed.
  • The Pioneer Anomaly: This best-known of the four oddities involves an anomalous acceleration that appears to be acting on both the Pioneer spacecraft, an acceleration directed approximately toward the Sun. Possible explanations involve radiant heat from the spacecraft themselves, and Anderson, who has noted this possibility in earlier papers, seems to suspect that it’s the case. But the paper notes other possibilities, from drag from dark matter to a modification of inertia.
  • The Moon’s Orbit: Studies of Lunar Laser Ranging data from 1970 to 2008 show slight changes in the eccentricity of the Moon’s orbit. The anomalous change is not yet understood.

We study such phenomena in hopes of learning one of two things. If any of the these anomalies helps us unlock a new principle, we’ve obviously expanded our understanding of the universe, with benefits to our expansion into space. If we learn that any or all of them can be explained by currently understood physics, we’ve then added to the solidity of those theories and can feel renewed confidence in applying them. Either way, we win, but only future studies will tell us which results apply here.

The paper is Anderson and Nieto, “Astrometric Solar-System Anomalies,” to be published in Proceedings of the IAU Symposium 261 and available online.


Comments on this entry are closed.

  • Adam August 5, 2009, 5:42

    Hi Paul

    The arxiv-blog also points out the weird anomalies of Saturn’s orbit. I do wonder if there’s not sizeable dark matter planets whizzing around.

  • Michael Spencer August 5, 2009, 6:44

    An increase in the AU? hmm.

    Three parts in 150 billion is some pretty fancy measurin’, I would say.

    I never understood how universal expansion could solely affect intergalactic space–perhaps it doesn’t.

  • george scaglione August 6, 2009, 9:36

    michael, i agree. also sometimes i think we are just argueing “how many angels can dance on the head of a pin”!!!!!!!!!? sometimes it is true (for good or ill),”the more things change the more they remain the same”.hope we hear alot more on this subject though.your friend george ps the distance between the earth and the sun can be accurately measured down to 3 meters! (about 9 feet!) wow!!!!!! sounds like something out of star trek!!! good to know. again,thanks your friend george

  • ljk August 6, 2009, 10:53

    The perihelion precession of Saturn, planet X/Nemesis and MOND

    Authors: Lorenzo Iorio

    (Submitted on 27 Jul 2009 (v1), last revised 5 Aug 2009 (this version, v2))

    Abstract: We show that the retrograde perihelion precession of Saturn \Delta\dot\varpi, recently estimated by different teams of astronomers by processing ranging data from the Cassini spacecraft and amounting to some milliarcseconds per century, can be explained in terms of a localized, distant body X, not yet directly discovered.

    From the determination of its tidal parameter K = GM_X/r_X^3 as a function of its ecliptic longitude \lambda_X and latitude \beta_X, we calculate the distance at which X may exist for different values of its mass, ranging from the size of Mars to that of the Sun. The minimum distance would occur for X located perpendicularly to the ecliptic, while the maximum distance is for X lying in the ecliptic.

    We find for rock-ice planets of the size of Mars and the Earth that they would be at about 80-150 au, respectively, while a Jupiter-sized gaseous giant would be at approximately 1 kau.

    A typical brown dwarf would be located at about 4 kau, while an object with the mass of the Sun would be at approximately 10 kau, so that it could not be Nemesis for which a solar mass and a heliocentric distance of about 88 kau are predicted.

    If X was directed towards a specific direction, i.e. that of the Galactic Center, it would mimick the action of a recently proposed form of the External Field Effect (EFE) in the framework of the MOdified Newtonian Dynamics (MOND).

    Comments: LaTex2e, 13 pages, no figures, no tables. Some typos fixed and reference updated

    Subjects: General Relativity and Quantum Cosmology (gr-qc); Earth and Planetary Astrophysics (astro-ph.EP); Space Physics (physics.space-ph)

    Cite as: arXiv:0907.4514v2 [gr-qc]

    Submission history

    From: Lorenzo Iorio [view email]

    [v1] Mon, 27 Jul 2009 15:30:56 GMT (9kb)

    [v2] Wed, 5 Aug 2009 09:30:23 GMT (9kb)


  • Erik Anderson August 10, 2009, 1:16


    Thanks for posting this. I had not heard of the “A.U. anomaly” before. Anderson’s & Nieto’s use of the word “astrometry” in their title, however, is misleading. The first 3 of the 4 anomalies featured in this paper are wholly based upon Doppler radar ranging. Thus, the A.U. anomaly entails the same common denominator as the Pioneer anomaly and the Earth-flyby anomalies: blueshift in the radio signals.

    I would be interested to know if similar precision could be attained for a truly astrometric measurement of Earth’s orbital distance (e.g., timings of conjunctions and occultations between stars and planets). If the necessary precision could be achieved, I would not expect the A.U. anomaly to show up in such a test.

  • bigdan201 August 11, 2009, 21:45

    I agree that anomalies in data can be important, as theyre often clues that lead to bigger processes and events we may not be aware of.

    and urbain le verrier should definitely get the credit for neptune.

  • James M Rotenberry August 12, 2009, 18:05


    I think some of the comments about this article suggest that there are misunderstandings about spacecraft navigation.

    Disclaimer: I worked at JPL with John Anderson in the 1980’s.

    I know of four methods used to determine the trajectory of a spacecraft: ranging, Doppler measurements, VLBI, and optical navigation.

    Ranging uses the round-trip transit time to estimate the distance. Doppler measurements provide an estimate of the velocity along the line of sight. VLBI measures the angular distance from extragalactic radio sources such as quasars. (Note that VLBI provides information that is perpendicular to the line-of-sight). Optical navigation is the technique of using onboard imaging to determine the position of the spacecraft relative to “nearby” planets or moons using the fixed star background.

    For a more detailed discussion see http://descanso.jpl.nasa.gov/Monograph/series1/Descanso1_all.pdf

  • Administrator August 12, 2009, 21:30

    James, thanks very much for the link to the “Radiometric Tracking Techniques for Deep – Space Navigation” monograph. Helpful indeed!

  • Torbjörn Larsson, OM August 15, 2009, 10:05

    Three parts in 150 billion is some pretty fancy measurin’

    Indeed. Without knowing anything about the particulars of these cases, it has always been the tendency of so called “anomalies” found when measuring to greater precision to go away at even greater precision.

    One recent example, connected to astronomy, was the apparent periodical extinctions that were found when surveying more comprehensive sets of fossils of, say, bivalves. Which was then tied to astronomical hypotheses of passing galactic arms, or plane, and what not.

    But recently (last year IIRC) the progress in paleontology had enabled so much data that these statistic “anomalies” disappeared at greater resolution of the fossil record. [Dunno the name of the paper at the moment, but it should be googeable.] Mundane but satisfying results. Not that the “my theory is interesting, your’s is boring” people appears to have taken notice. ;-)

    The way to bet is that these things goes away eventually. :-/

    And then again, we have once or twice in a century or so, these extraordinary anomalies that doesn’t, that will take extra-ordinary evidence to be confirmed, and likely turn out to have extra-ordinary mechanisms. Last time it was perhaps the acceleration of cosmological expansion, the time before that perhaps the CMB discovery, … . Exciting! :-o

  • Torbjörn Larsson, OM August 15, 2009, 10:06

    D’oh! Sorry about the failed blockquote in my previous comment.

  • ljk August 17, 2009, 13:20

    On the gravitational origin of the Pioneer Anomaly

    Authors: I. A. Siutsou, L. M. Tomilchik

    (Submitted on 12 Aug 2009)

    Abstract: From Doppler tracking data and data on circular motion of astronomical objects we obtain a metric of the Pioneer Anomaly. The metric resolves the issue of manifest absence of anomaly acceleration in orbits of the outer planets and extra-Pluto objects of the Solar system.

    However, it turns out that the energy-momentum tensor of matter, which generates such a gravitational field in GR, violates energy dominance conditions. At the same time the equation of state derived from the energy-momentum tensor is that of dark energy with $w=-1/3$. So the model proposed must be carefully studied by “Grand-Fit” investigations.

    Subjects: General Relativity and Quantum Cosmology (gr-qc); Earth and Planetary Astrophysics (astro-ph.EP)

    Cite as: arXiv:0908.1644v1 [gr-qc]

    Submission history

    From: Ivan Siutsou [view email]

    [v1] Wed, 12 Aug 2009 08:54:42 GMT (103kb)


  • ljk August 18, 2009, 11:31

    Modeling the flyby anomalies with dark matter scattering

    Authors: Stephen L. Adler

    (Submitted on 17 Aug 2009)

    Abstract: We continue our exploration of whether the flyby anomalies can be explained by scattering of spacecraft nucleons from dark matter gravitationally bound to Earth.

    We formulate and analyze a simple model in which inelastic and elastic scatterers populate shells generated by the precession of circular orbits with normals tilted with respect to Earth’s axis. Good fits to the data published by Anderson et al. are obtained.

    Comments: Latex, 17 pages

    Subjects: Earth and Planetary Astrophysics (astro-ph.EP)

    Cite as: arXiv:0908.2414v1 [astro-ph.EP]

    Submission history

    From: Stephen Adler [view email]

    [v1] Mon, 17 Aug 2009 19:30:59 GMT (13kb)


  • ljk August 20, 2009, 12:06

    Serendipity in Astronomy

    Authors: A.C. Fabian (University of Cambridge, UK)

    (Submitted on 19 Aug 2009)

    Abstract: Astronomy is an observationally-led subject where chance discoveries play an important role. A whole range of such discoveries is continually made, from the trivial to the highly significant.

    What is generally needed is for luck to strike someone who is prepared, in the sense that they appreciate that something novel has been seen. “Chance favours the prepared mind” in the words of Pasteur, 1854.

    Comments: 12 pages with 10 figures. To be published in Serendipity (eds Mark de Rond and Iain Morley), CUP

    Subjects: Popular Physics (physics.pop-ph); Cosmology and Extragalactic Astrophysics (astro-ph.CO); Galaxy Astrophysics (astro-ph.GA)

    Cite as: arXiv:0908.2784v1 [physics.pop-ph]

    Submission history

    From: A.C. Fabian [view email]

    [v1] Wed, 19 Aug 2009 16:37:44 GMT (3782kb)


  • ljk August 20, 2009, 22:17

    Peculiar Velocity Anomaly from Forces Beyond Gravity?

    Authors: Youness Ayaita, Maik Weber, Christof Wetterich

    (Submitted on 20 Aug 2009)

    Abstract: We address recently reported anomalously large bulk flows on scales of 100 Mpc/h and beyond. These coherent motions of galaxies challenge the standard LCDM concordance model as well as a large class of competitive models of dark energy and modified gravity.

    If confirmed, they may support alternative models that include extra forces enhancing the growth of perturbations on large scales. In such scenarios, current observational constraints on structure formation favor an onset of the extra forces in recent times, as predicted, e.g., in growing neutrino models. For the illustration of the main effects, we employ intuitive phenomenological parameterizations.

    Comments: 4 pages, 4 figures

    Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO)

    Cite as: arXiv:0908.2903v1 [astro-ph.CO]

    Submission history

    From: Maik Weber [view email]

    [v1] Thu, 20 Aug 2009 11:12:25 GMT (20kb)


  • ljk October 12, 2009, 1:24

    Spacecraft calorimetry as a test of the dark matter scattering model for flyby anomalies

    Authors: Stephen L. Adler

    (Submitted on 8 Oct 2009)

    Abstract: In previous papers we have shown that scattering of spacecraft nucleons from dark matter gravitationally bound to the earth gives a possible explanation of the flyby velocity anomalies.

    In addition to flyby velocity changes arising from the average over the scattering cross section of the collision-induced nucleon velocity change, there will be spacecraft temperature increases arising from the mean squared fluctuation of the collision-induced velocity change.

    We give here a quantitative treatment of this effect, and suggest that careful calorimetry on spacecraft traversing the region below 70,000 km where the flyby velocity changes take place could verify, or at a minimum place significant constraints, on the dark matter scattering model.

    Comments: Latex, 7 pages; also submitted in single spaced format as a white paper to the NAS decadal review on biological and physical sciences in space

    Subjects: Space Physics (physics.space-ph); Earth and Planetary Astrophysics (astro-ph.EP); High Energy Physics – Phenomenology (hep-ph); Instrumentation and Detectors (physics.ins-det)

    Cite as: arXiv:0910.1564v1 [physics.space-ph]

    Submission history

    From: Stephen Adler [view email]

    [v1] Thu, 8 Oct 2009 18:15:52 GMT (6kb)


  • ljk October 27, 2009, 13:05

    Seven questions that keep physicists up at night

    New Scientist Oct. 23, 2009

    What is reality really? How does complexity happen? What is everything made of? These were among the questions discussed at the Perimeter Institute last week….


  • ljk November 3, 2009, 23:50

    A new crisis for astronomical research: why has the rate of fundamental new discoveries collapsed so dramatically?

    In an earlier blog on Cosmic Diary I published my personal list of the 25 greatest discoveries in astronomy of the 20th century. See my article of 18 June at:

    http://cosmicdiary.org/blogs/john_hearnshaw/?p=96 on this topic.

    In that article I listed my choice of the 25 major discoveries of the last century, and broke the list down into 42 key papers. These papers represented fundamental discoveries of new phenomena, or new types of object, each of which resulted in the development of a major new field of investigation or branch of astronomy.

    Certainly much subjectivity went into the selection, but I suspect many others who go through this exercise would choose many of the same groundbreaking discoveries, perhaps in a slightly different order.

    Attached to these discoveries I have now selected 49 key papers (originally I chose just 42, but in the last few months I have added a few more papers associated with the same 25 discoveries) and these were published by 62 authors.

    You can see a spreadsheet giving details of these papers and their authors by downloading an Excel file from this website:


    Full article here:


    To quote:

    My explanation for the startling drop off in the fraction of new papers reporting fundamental ground-breaking discoveries is that astronomers are running out of new types of object or new phenomena to discover. This is not such a bizarre concept. The idea that the number of fundamentally different types of phenomena that exist in the observable universe might be finite seems quite reasonable. Since about 1980 the vast majority of papers are simply adding detail to our knowledge of existing phenomena or types of object.

  • ljk November 30, 2009, 0:48

    November 23, 2009

    Mystery of the Flyby Anomaly Endures

    Written by Nancy Atkinson

    The weird mystery of the flyby anomaly just got even weirder. Since the early 1990’s scientists and mission controllers have noticed that some spacecraft experience unexpected changes in speed during Earth-flybys.

    The unexplained variation is extremely small and has occurred as either speed gained or lost, but this variant is not predicted by fundamental physics.

    The anomaly doesn’t happen to every spacecraft but scientists were hoping to gain more insight into the anomaly when the Rosetta spacecraft swung by Earth on Nov. 13 to pick up a gravitational boost for its journey to rendezvous with a comet in 2014.

    However, in a major disappointment – which had deepened the mystery — the Rosetta spacecraft did not experience the flyby anomaly during this swingby of Earth, even though the same spacecraft did experience the anomaly when it flew by Earth 2005, but didn’t in 2007.

    Full article here:


  • ljk January 3, 2010, 1:29

    The exploration of the unknown

    Authors: K.I. Kellermann, J.M. Cordes, R.D. Ekers, J. Lazio, P. Wilkinson

    (Submitted on 22 Dec 2009)

    Abstract: The discovery of cosmic radio emission by Karl Jansky in the course of searching for the source of interference to telephone communications and the instrumental advances which followed, have led to a series of new paradigm changing astronomical discoveries.

    These discoveries, which to a large extent define much of modern astrophysical research were the result of the right people being in the right place at the right time using powerful new instruments, which in many cases they had designed and built. They were not the result of trying to test any particular theoretical model or trying to answer previously posed questions, but they opened up whole new areas of exploration and discovery.

    Rather many important discoveries came from military or communications research; others while looking for something else; and yet others from just looking.

    Traditionally, the designers of big telescopes invariably did not predict what the telescopes would ultimately be known for. The place in history of the next generation of telescopes will not likely be found in the science case created to justify their construction, but in the unexpected new phenomena, new theories, and new ideas which will emerge from these discoveries.

    It is important that those who are in a position to filter research proposals and plans not dismiss as butterfly collecting, investigations which explore new areas without having predefined the result they are looking for.

    Progress must also allow for new discoveries, as well as for the explanation of old discoveries. New telescopes need to be designed with the flexibility to make new discoveries which will invariably raise new questions and new problems.

    Comments: Paper presented at Special Session 5, IAU General Assembly XXVII, Rio de Janerio, August 11, 2009. To be published in Proceedings of Science

    Subjects: Instrumentation and Methods for Astrophysics (astro-ph.IM)

    Cite as: arXiv:0912.4441v1 [astro-ph.IM]

    Submission history

    From: Kenneth Kellermann [view email]

    [v1] Tue, 22 Dec 2009 16:34:33 GMT (93kb,X)