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Dark Matter May Explain the Puzzling Change in Earth-Sun Distance

If the sun sweeps up dark matter as it moves through the galaxy, how would that affect the orbit of the planets?

In the last five years or so, astronomers have noticed a puzzling change in the astronomical unit, the distance of the Earth’s from the sun. Various measurements indicate that this distance (or at least the length of the Earth’s semimajor axis) is increasing at the rate of 15 cm per year (plus or minus 4 cm).

Why that should be, nobody knows. But today, Lorenzo Iorio at the National Institute of Nuclear Physics in Pisa, Italy, says dark matter could be to blame.

Astronomers have long assumed that dark matter must fill the universe. In fact, the motion of the Milky Way implies that there ought to be some 10^-25 grams of the stuff in every cubic centimeter of the galaxy. And the density ought to be even higher near massive bodies such as stars, whose gravity would attract a halo of dark matter. Around the sun, the density of dark matter should be about 10^-19 g/cm^3.

Not only that, but the sun ought to sweep up dark matter as it moves through the galaxy. Iorio says it should have encountered about 200 times its own mass in dark matter during its travels. That means the density of dark matter in the Solar System should be increasing.

Iorio quite naturally asks what effect this might have on the orbits of the planets. The answer is that the orbits ought to shrink as the density of dark matter increases. One curious side effect of this for elliptical orbits is that “the osculating semimajor axis of a gradually shrinking trajectory around a mass-increasing central body gets larger.”

Iorio calculates that the rate of the sun’s dark matter accumulation at the moment ought to cause the Earth’s semi-major axis to increase by about 7 cm per year (plus or minus 5 cm). That’s a good enough match to the measured value to give pause for thought.

Iorio goes on to say that dark matter has important implications for the fate of the planets. We know that Earth will one day be swallowed by the sun as it expands into a red giant. But Iorio calculates that dark mater will cause the Earth’s orbit to shrink by half in this time scale.

And if that’s true, the end could be much nearer than we think.

Ref:arxiv.org/abs/1001.1697: Effect of Planet-Bound DarkMatter on Satellite Dynamics in the Solar System

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