Calculations made by a physicist in Italy suggest that the observable changes to Earth's orbit could be caused by the Sun's appetite for dark matter. This latest research predicts that over the next few billion years the orbits of the planets should shrink considerably, with the Earth to Sun distance halving over this timescale.

Physicists believe that some 23% of the mass-energy content of the universe is made up of dark matter, a non-luminous substance that interacts gravitationally with ordinary matter. This dark matter is spread throughout the universe but clumps together at higher densities in the vicinity of visible bodies, thereby forming a "halo" around the Milky Way. Some researchers also believe that the solar system is home to an especially dense lump of dark matter.

Accreting since birth

The Italian physicist Lorenzo Iorio calculated the effects of this dark matter on the orbits of the planets. To do this he assumed that between 2 and 5% of the Sun's mass is in the form of dark matter, an upper limit imposed by measurements of properties such as solar luminosity and energy flux, and that the Sun accumulated this dark matter continuously over its 4.5 billion year history as it moved through the galactic halo. These assumptions lead to a fractional increase in the Sun's mass of about one part in 1012 each year.

First, Iorio calculated how much further out the planets would have been at the birth of the solar system 4.5 billion years ago. The outermost planets, he concluded, would have been the furthest removed from their present positions, the orbital radius of Neptune, for example, being greater by up to 10 astronomical units (1 au is approximately equal to the Earth's semi-major axis, some 150 million kilometres). Earth, in contrast, would have been no more than 0.32 au further out.

Iorio also worked out how much the planetary orbits will have shrunk by the time the Sun is expected to reach its maximum size as a red giant star, in some 7.5 billion years' time. He calculated that Neptune could be some 16 au closer in, while the Earth's radius could be halved. Given that there is currently disagreement between astronomers over whether or not the Earth's orbit will be engulfed by the expanding Sun, Iorio says that the effect of solar dark matter would be to increase the probability of this encroachment.

Just about consistent with observations

One counterintuitive effect of the Earth's orbital shrinkage, according to Iorio's modelling, is that the Earth's semi-major axis will actually increase by some 2–5 cm per year. He says that this is possible because the solar dark matter causes the trajectory of the Earth's orbit to continually shrink and therefore only approximate an ellipse. So while the distance of closest approach of the Earth to the Sun in each cycle decreases, the distance taken to be the semi-major axis can increase. In fact, this conclusion is just about consistent with observations, combined from a variety of different sources, showing an increase in the astronomical unit of between 5 and 9 cm per year.

Iorio also calculated how planetary accretion of dark matter would affect the motion of the planetary satellites but found this to be negligible – with the Moon's orbital radius a mere 160 m greater at the beginning of the solar system. In fact, this mechanism is not able to explain a number of observed changes in the orbits of planetary satellites, including different variations in the orbital periods of some of the moons of Jupiter and a decrease in the semi-major axis of the Earth's artificial satellite LAGEOS.

Indeed, Iorio emphasizes that his work does depend on a number of assumptions about the nature of dark matter, in particular the rate at which it might accrete within the solar system. Philippe Jetzer, an astrophysicist at the University of Zurich points out that the situation is further complicated by the fact that the Sun and the planets can also accrete ordinary matter. "With our present knowledge one cannot conclude that dark matter is accumulating at any significant rate within the solar system," he says.

The research is reported at arXiv:1001.1697.