The number may sound like a lot, but it’s actually a pretty small — all the more so if dark matter consists of fairly massive particles. That’s why my alarm bells went off at a New Scientist article that appeared today: “GPS satellites suggest Earth is heavy with dark matter“. Sure, it’s possible that dark matter might clump up a bit around Earth if its constituent particles interact relatively strongly with each other. The effect has to be really tiny, though — we’ve measured the gravitational field around Earth very well, something known as the geoid. (See the image accompanying this post for a neat visualization.) In the absence of such interactions, the density doesn’t increase greatly in the vicinity of Earth or even the Sun. Gravity from those objects concentrates dark matter a little, but because it interacts so weakly with ordinary matter, it won’t comprise a high fraction of the mass of our planet.
So why am I grumpfy about the New Scientist story? My real problem is that it seems to be a very preliminary bit of research announced by at a meeting of the American Geophysical Union, with no reviewed or published paper from its investigator, Ben Harris of the University of Texas at Arlington. Even the story points out that Harris’ calculation is incomplete:
Harris has yet to account for perturbations to the satellites’ orbits due to relativity, and the gravitational pull of the sun and moon. What’s more, preliminary data from NASA’s Juno probe, also presented at the AGU meeting, suggests its speed was as expected as it flew by Earth, casting doubt on the earlier anomalies.
Those aren’t minor problems! The Global Positioning System (GPS) is an incredible work of precision engineering, consisting of a network of satellites that allow very accurate measurement of position on Earth’s surface. To make this system operate, the orbits of the satellites must not only take into account the geoid (which you recall is the fluctuations in Earth’s gravity) and the pull of the Moon, but also the slight difference in the strength of gravity due to general relativity. These effects are tiny, but the necessary precision for GPS requires they be taken into account. In other words, Harris has yet to include some of the details required for GPS to work in the first place, but still wants to draw conclusions about dark matter from his calculations.
Additionally, to make everything work, the dark matter has to be distributed in a very specific way: in a disk “191 kilometres thick and 70,000 km across”. I have no idea why dark matter should be arranged this way, since thin disks like that are generally the result of rapid rotation, while gravity tends to make things spherical. (The dark matter distribution in our galaxy, for example, seems to be a slightly squashed sphere.) Without a paper, though, I don’t know if Harris made an argument for how such a dark matter disk could form.
Ultimately, the question may be moot, again as the New Scientist article itself says. The Juno spacecraft, en route to Jupiter, used Earth’s gravity to give it a boost. If Earth had an extra bit of gravity due to dark matter (not to mention a distortion in the geoid from a disk), Juno would likely have picked it up — yet nothing was measured during the flyby.
I know how it goes at conferences: they’re good opportunities to present ideas that might or might not be publishable in journals. I’ve seen (and even given) talks based on preliminary research that aren’t ready yet, and I suspect this talk fell into that category. When Harris has taken general relativity and the effects of the Sun and Moon into account and if he still sees this phenomenon, then we might have something to talk about. Until then, I think it’s safe to say that there’s no reason to think a disk of dark matter is playing any role in the motion of GPS satellites.
- In numbers, this is 300 MeV/cm3, where MeV stands for mega-electron volt. The mass of an electron is about 0.5 MeV. For details, see Jo Bovy and Scott Tremaine, “On the local dark matter density”. Astrophysical Journal 756, 89 (2012). DOI: 10.1088/0004-637X/756/1/89/ArXiV: 1205.4033.
- See Stephen L. Adler, “Can the flyby anomaly be attributed to earth-bound dark matter?”. Physical Review D 79, 023505 (2009). DOI: 10.1103/PhysRevD.79.023505 / ArXiV: 0805.2895 .