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The Pioneer Anomaly

December 19, 2012

Crookes radiometer

One apparatus that I enjoyed working with as an undergraduate physics major was the Crookes tube, an electric discharge tube that demonstrated the existence of cathode rays long before they were identified as electrons. This tube was invented by William Crookes, who used his prowess with vacuum technology to create the Crookes radiometer, as shown in the figure. The paddle wheel on this radiometer moves when exposed to light, the dark vanes retreating from the light source, so the device functions as a radiometer.

Crookes thought that it was the pressure of light that caused the vanes to move, thus proving a result of Maxwell's theory of electromagnetism. Soon it was found that the paddle wheel of radiometers made with a more perfect vacuum didn't move, and a certain air pressure was needed to produce an optimal motion.

It should have been realized early-on that radiation pressure would cause the paddle wheel to rotate in an opposite direction, since photons would exert more force when bouncing off the reflective surfaces than being absorbed by the dark surfaces. The motion is a thermal effect involving the motion of air molecules, not a radiation effect, although the precise explanation is somewhat involved.[1]

Pressure, of course, is the force applied to an area. Since force is the time derivative of momentum, radiation pressure is connected with the momentum of photons; more specifically, the change in momentum of a body as created by the photon momentum. In fact, the concept of force is not as fundamental as the concept of momentum, since force is its time derivative. That's why we're concerned with conservation of linear momentum, and not conservation of force.

I discussed photon momentum in two previous articles, Photon Momentum (March 15, 2007) and The Yarkovsky Effect (June 12, 2012), the later article being about the use of radiation pressure to steer asteroids away from the Earth. Although photon momentum in a vacuum is well known (it's the energy of the photon divided by the speed of light), one nagging question in physics is the value of the photon momentum in a dielectric medium. It's not known whether it's less than, or greater than, the vacuum momentum, and it might even depend on the type of experiment used to make the measurement.[2-4]

Hermann Minkowski and Max Abraham calculated the photon momentum p by two different methods. According to Minkowski,[5] p = nhk/2π, and according to Abraham,[6] p = hk/2πn where h is Planck's Constant, k is the wave vector, and n is the refractive index. The momentum calculations are different by a factor of n2 when the medium is a dielectric, but they give the same value in a vacuum (n=1).

The radiation pressure that the Sun exerts on an object in a vacuum near Earth's orbit is quite feeble, just 9.2 micropascals on a perfectly reflecting mirror. Even such a small pressure as this is detected in the change it exerts on the orbits of the GPS satellites. The Japanese IKAROS spacecraft was propelled by this pressure through solar sails.

The Yarkovsky effect is the photon momentum effect with a twist - the photons are emitted by an object, rather than impinging upon it. A temperature difference of one side of an object versus the other causes an imbalance in its thermal radiation, and this results in a small force. The anisotropic emission of thermal photons in the Yarkovsky effect has been proposed as a method of steering asteroids away from collision with the Earth.

Pioneer 10 and Pioneer 11 are spacecraft launched in 1972 and 1973, respectively, on trajectory to leave the Solar System. Communication with Pioneer 11 was lost in 1995, but signals were received from Pioneer 10 until 2003. At that point, it was 80 astronomical units from Earth. Analysis of the spacecraft data showed a small, anomalous Doppler frequency drift corresponding to an unexplained sun-wards acceleration of 8.74 ± 1.33 x 10-10 m/s2.

This so-called Pioneer anomaly piqued the interest of many scientists. They likely remembered Michelson's various statements that new physics often can be found in the next decimal place.[7] Most people, however, thought that radiation pressure was the real reason; but the effect is very small, and analysis is complicated by the fact that these spacecraft do not resemble spherical cows (see photograph).

Figure caption

The Pioneer H spacecraft, resident at the National Air and Space Museum.

This is an unflown craft planned for launch after Pioneer 10 and 11.

(Photograph by Cam Wow, via Wikimedia Commons.)

A dedicated group from the California Institute of Technology (Pasadena, California) and the Applied Sciences Laboratory (Baldwin Park, California), has been plugging away at the problem for several years, and 2012 marked their success in explaining the anomaly as a Yarkovsky-type radiation pressure affect.[8-13] The thermal imbalance arises from heat dissipated in the spacecraft electrical circuitry and the onboard radioisotope thermoelectric generators. I discussed such generators in a recent article (Curiosity Rover Power, November 5, 2012)

The thermal imbalance amounts to the same radiation intensity as an automobile's headlamps. In the end, the difference between the computer model and the collected data was just 20%.[13] There are quite a few lengthy articles that describe the analysis, so I direct your attention to the references.[8-13]


  1. Explanation of the motion of a Crookes radiometer, Wikipedia.
  2. Mark Buchanan, "Minkowski, Abraham and the photon momentum," Nature Physics, vol. 3, no. 2 (February, 2007), p. 73.
  3. Berian James, Letter to Nature (Friday, Jan 5 2007).
  4. Peter Bowyer, "The momentum of light in media: The Abraham-Minkowski controversy (24 page PDF File).
  5. H. Minkowski, Nachr. Ges. Wiss. Göttn. Math.-Phys. Kl.(1908), p. 53.
  6. M. Abraham, Rend. Circ. Matem. Palermo vol. 28 (1909), p. 1.
  7. W. Beaty, "Science is at its end, all the important things have already been discovered!" Science Hobbyist.
  8. Slava G. Turyshev and Viktor T. Toth, "The Pioneer Anomaly," arXiv Preprint Server, January 20, 2010 (revised August 19m 2010).
  9. Slava G. Turyshev, Viktor T. Toth, Gary Kinsella, Siu-Chun Lee, Shing M. Lok and Jordan Ellis, "Support for the thermal origin of the Pioneer anomaly," arXiv Preprint Server, April 11, 2012.
  10. F. Francisco, O. Bertolami, P. J. S. Gil, J. Páramos, "Modelling the reflective thermal contribution to the acceleration of the Pioneer spacecraft," arXiv Preprint Server, March 27, 2011 (revised April, 16, 2012).
  11. Slava G. Turyshev, Viktor T. Toth, Gary Kinsella, Siu-Chun Lee, Shing M. Lok and Jordan Ellis, "Support for the Thermal Origin of the Pioneer Anomaly," Phys. Rev. Lett., vol. 108, no. 24 (June 15, 2012), Document No. 241101.
  12. Jia-Rui C. Cook, "Study Finds Heat is Source of Pioneer Anomaly," Jet Propulsion Laboratory Press Release, July 17, 2012.
  13. Viktor T. Toth, Slava G. Turyshev, "Finding the Source of the Pioneer Anomaly," IEEE Spectrum (December, 2012).

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