From: "Lorenzo U."
Date: 7 Oct 2008
Q Do we measure any gravitational effect of dark matter in our solar system? Are the orbits of our planets influenced by dark matter? If there are no gravitational effects of dark matter in the solar system, why do we observe them in the galaxies? Is dark matter not uniformly distributed into space?
A These are excellent questions! Here are my answers (somewhat out of order):
Dark matter should have gravitational effects on the planets orbits and on space probes, but we are so far unable to detect them. This is not surprising, however, because they are hidden by bigger effects: the gravitational pulls of the sun and planets are much, much larger.
The average density of dark matter near the solar system is approximately 1 proton-mass for every 3 cubic centimeters, which is roughly 6x10-28 kg/cm3. The actual density might be a little lower or higher, but this is the right order of magnitude.
Based on this number, we can work out the total mass of dark matter within the radius of Earth's orbit around the sun: for an orbital radius of 100 million km, we get a total of 2.3x1012 kg of dark matter within the Earth's orbit. This sounds like a lot, but the sun's mass is 2x1030 kg. All of that dark matter only weighs 10-18 as much as the sun does, so we cannot detect the tiny pull of dark matter upon the Earth's orbit. The same story is true all over the solar system: the gravitational pulls of the sun and planets are always much larger than that of the dark matter.
Now consider the effect of dark matter upon the orbit of the sun around the galactic center. Let's suppose that the density of the dark matter is the same everywhere in the galaxy; this is NOT true (the density is much higher near the galactic center), so the dark matter mass will really be higher than we calculate.
The radius of the sun's orbit is about 2.5x1017 km, so the total mass of dark matter within that orbit is 6x1040 kg. This is the mass of 3x1010 (30 billion) stars like the sun! The entire galaxy only contains ~100 billion stars, so the dark matter does have a significant effect on the sun's orbit through the galaxy. For objects farther out near the edge of the galaxy, the dark matter is actually the main thing keeping them in their orbits. This is more or less how dark matter was discovered by astronomer Vera Rubin and others: the orbital speeds of galactic stars and gas clouds don't match our expectations from the visible matter.
In other words, a galaxy is much lower in density than the solar system, so the small dark matter density becomes much more important.
Dark matter is not distributed uniformly in space. The galaxy is embedded in a large cloud of dark matter, and gravity makes this cloud denser in the center than at the edges. The density varies slowly over many light years, though some theories suggest that there could be "clumps" on smaller scales than that.
Hope that helps, and thanks again for the questions.
Particle Cosmology Group
University of California - Berkeley