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Newton’s second law, F=ma, is one of the bedrocks of modern physics. Or at least it was until the early 1980s, when astronomers noticed that stars orbiting spiral galaxies don’t obey it.

Here’s the problem. By Newton’s law, more distant objects should orbit a central massive object more slowly. That’s exactly what happens in the solar system. But the stars in spiral galaxies orbit far more quickly than Newton’s law predicts.

Astronomers have proposed two solutions to this conundrum. Most think that there must be a halo of invisible matter pulling the stars in some unseen way. Others think that Newton’s law must somehow break down for the tiny accelerations that stars feel in galaxies. These guys have spent the 20 years since then exploring the implications of Modified Newtonian Dynamics, or MOND, led by Mordehai Milgrom from the Weizmann Institute Center for Astrophysics, in Israel, who dreamed up the idea in 1983.

The trouble is that MOND only kicks into action when the acceleration is tiny–so small that no experiment on Earth has been able to distinguish its effects from Newton’s law. And measurements on stars in distant galaxies are difficult to make, so it has been hard for astronomers to find evidence for or against it.

But today, Milgrom says that he has calculated a new effect of MOND that should be measurable for planets and comets in the solar system.

The new effect is a quadropole force that repels objects in the space above and below the plane of the solar system while attracting objects that lie within the plane. Milgrom says that this should produce an effect on the precession of the perihelion of planets in the solar system.

He says that the current measurements are not yet precise enough to see or constrain this effect, but the appropriate precision seems to be within reach.

Interestingly, last year astronomers found that the precession of the perihelion of Saturn does not quite fit with predictions.

Could this be the smoking gun that Milgrom is looking for?

Ref: arxiv.org/abs/0906.4817: MOND effects in the inner solar system

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