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MOND and Planet Nine

November 27, 2023

In writing these blog articles, I provide links to keywords, most often to Wikipedia, to give interested readers a way to better understand the topics. When I first started doing this, I found that I needed to be careful about such links, since the same word can mean a different thing to different people. One easy example of this is antenna, which is a device (antenna) for radio communications to electrical engineers, but an insect body part (antenna) to a biologist. To Germans, Mond is the word for Moon. To physicists, MOND is the acronym for Modified Newtonian dynamics.

Newtonian gravitation quite accurately defines the gravitational attraction of matter over an interaction range from laboratory scale (as in the Cavendish experiment) to the orbits of planets in our Solar System out to the farthest planet, Neptune, at 30 astronomical units. That's a range of one meter to 4.5 x 1012 meters. Since gravitation is so weak, the gravitational constant (6.67408±0.00031x10-11 m3 kg-1 s-2) is the least precisely measured physical constant, with a relative uncertainty of 47 parts per million.[1]

In the 1970s, Vera Rubin (1928-2016) and Kent Ford (1931-2023) discovered that the rotations of galaxies would only conform to Newtonian gravitation is they contained about six times as much dark mass as visible mass. This led to the theory that dark matter is the principal constituent of matter in the universe. To add to the confusion, there's dark energy, which is the dominant component of the universe, contributing about twice the total energy of the universe as dark matter and ordinary matter combined.

Constituents of the universe

Things were simpler in my childhood, when Pluto was still a planet, and the universe consisted of just ordinary matter.

Here's our present view of the constituents of the universe. The percentages don't add to 100 because of observational uncertainty.

(Portion of a Wikimedia Commons image by NASA/WMAP Science Team. Click for larger image.)

Theorizing the existence of dark matter was quite a leap of faith. Another leap of faith that explains observations is the idea that gravitation behaves differently at distances much larger than the scale of our Solar System. Our Milky Way galaxy is about 87,500 light years in diameter, which is much larger than the 0.00095 light years approximate diameter of Neptune's orbit. Modified Newtonian dynamics (MOND) describes how Newton's law of universal gravitation must be modified to account for gravitation at galactic distance scales. So, which is the greatest leap of faith, dark matter, or MOND?

MOND was proposed in 1982, shortly after the discovery of the anomalous gravitation of galaxies. MOND differs from Newtonian gravitation only at extremely small gravitational accelerations, such as those arising from forces between galaxies, which are far below anything encountered in the Solar System or in a laboratory. MOND has been modified over the decades as it's been tested by subsequent observations.

While gravitation is considered to be one of the fundamental forces of nature, there's another theory of gravitation known as entropic gravity that explains MOND. In entropic gravity, gravity is viewed as an emergent phenomenon that arises from the quantum entanglement of small bits of spacetime information. At a threshold of gravitational acceleration of approximately 1.2x10-10 m-sec-2, gravitational strength starts to vary inversely with distance, rather than the Newtonian inverse square of distance. This threshold is just 12x10-12 the strength of gravity at Earth's surface.

Pluto, the former ninth planet, was demoted from planetary status in 2006, but a potential successor, called Planet Nine, was conjectured to exist in 2014, less than a decade later.[2] I discussed Planet Nine in two previous articles (Planet Nine, June 27, 2016 and Farfarout, April 19, 2021). Planet Nine is proposed to be in a highly elliptical orbit at a distance from the Sun of about 40 billion to 140 billion miles (400-1500 astronomical units).[2] Because of its distance and orbital peculiarity, it's been proposed that Planet Nine is a captured exoplanet.[3] Planet Nine has never been imaged, but its mass is supposed to be ten times the mass of the Earth.[3]

Orbits of Kuiper Belt objects and the conjectured Planet Nine.

It's thought that the closely spaced orbits of the most distant objects discovered in the Kuiper Belt are a consequence of the gravity of Planet Nine. (Wikimedia Commons image by MagentaGreen. Click for larger image.)

While the mass of Planet Nine might be ten Earth masses, it might also be zero; that is, Planet Nine might not exist, observational evidence of its gravitational influence on other Kuiper Belt objects notwithstanding.[4] A recent paper in The Astronomical Journal by Katherine Brown of Hamilton College (Clinton, New York) and Harsh Mathur of Case Western Reserve University (Cleveland, Ohio) proposes that modified Newtonian dynamics (MOND) provides an alternative explanation for the anomalies in the orbits of the Kuiper Belt objects (KBOs) with semimajor axes greater than 250 astronomical units.[5]

Orbits of six KBOs of the Sedna family showing alignment with orientations towards the galactic center

Orbits of six Kuiper Belt objects of the Sedna family projected onto the ecliptic plane. The major axes of the orbits are seen to align with the direction to the center of the galaxy, with the aphelion oriented towards the galactic center.

(Figure 3 of ref. 5, released under a Creative Commons license. Click for larger image.)

According to The Astronomical Journal paper, the orbits of these Solar System outliers should have high eccentricity and a tendency for the minor axes of their orbits to be perpendicular to the direction to the center of the galaxy.[5] All of these features are exhibited in support of the MOND hypothesis; so, MOND might be observable in the outer Solar System.[5] Says study coauthor, Harsh Mathur,

"MOND is really good at explaining galactic-scale observations... but I hadn't expected that it would have noticeable effects on the outer Solar System... the alignment was striking."[6-7]

MOND appears to predict the observed clustering of orbits. As a mechanism, it's conjectured that the orbits of objects in the outer solar system would be dragged into alignment with the galaxy's own gravitational field over the course of millions of years.[7] However, the researchers note that the current dataset is too small to draw reliable conclusions.[7-8]


  1. Chao Xue, Jian-Ping Liu, Qing Li, Jun-Fei Wu, Shan-Qing Yang, Qi Liu, Cheng-Gang Shao, Liang-Cheng Tu, Zhong-Kun Hu, and Jun Luo, "Precision measurement of the Newtonian gravitational constant," National Science Review, vol. 7, no. 12 (December, 2020), pp. 1803-1817, https://doi.org/10.1093/nsr/nwaa165.
  2. Chadwick A. Trujillo and Scott S. Sheppard, "A Sedna-like body with a perihelion of 80 astronomical units," Nature, vol. 507, no. 7493 (March 27, 2014), pp. 471-474, doi:10.1038/nature13156.
  3. Alexander J. Mustill, Sean N. Raymond, and Melvyn B. Davies, "Is there an exoplanet in the Solar system?" MNRAS Letters, vol. 460, no. 1 (July 21, 2016), pp. L109-L113.
  4. Michael E. Brown and Konstantin Batygin, "The Orbit of Planet Nine," The Astronomical Journal, vol. 162, no. 5 (October 28, 2021), pp. 1-16, DOI 10.3847/1538-3881/ac2056. Also at arXiv.
  5. Katherine Brown and Harsh Mathur, "Modified Newtonian Dynamics as an Alternative to the Planet Nine Hypothesis," The Astronomical Journal, vol. 166, no. 4 (September 22, 2023), DOI 10.3847/1538-3881/acef1e. This is an open access paper with a PDF file here. Also at arXiv.
  6. Andrew Griffin, "'Planet Nine' hidden world at the edge of our solar system could actually be something else, scientists say," Independent (UK), October 6, 2023.
  7. Outer reaches of solar system could harbor another planet—or evidence modifying laws of gravity, Case Western Reserve University Press Release, October 5, 2023.
  8. Brown Publishes Study on MOND, Planet Nine Hypothesis, Hamilton College Press Release, September 28, 2023 .

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