No, dark matter is not messing up GPS measurements

Eastern and western hemisphere geoids: variations of the Earth's gravitational influence, as measured by the GRACE satellites. The lumps and colors both indicate deviations from the average, with blue indicating slightly stronger gravity, and red indicating slightly weaker. [Credit: NASA/EOS]

Eastern and western hemisphere geoids: variations of the Earth’s gravitational influence, as measured by the GRACE satellites. The lumps and colors both indicate deviations from the average, with blue indicating slightly weaker gravity, and red indicating slightly stronger. [Credit: NASA/EOS]

While you sit and read this blog post, dark matter particles are passing through your body, without you ever noticing. Whether you find that creepy or not depends on your mindset, of course; to dark matter, you’re basically transparent. How many particles are passing through you depends on what dark matter’s identity is (whether WIMP, axion, or something else). Nevertheless, thanks to detailed astronomical studies, we have a pretty good idea of what the total density — dark matter mass contained in a given volume — is in the part of the galaxy containing Earth: the equivalent of about 600 electrons in a cube one centimeter across.[1]

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.[2] 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.

Notes

  1. 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.
  2. 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 .
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12 Responses to “No, dark matter is not messing up GPS measurements”


  1. 1 TheTaste January 6, 2014 at 08:53

    Pardon my being off subject and my ignorance, but if dark matter is such a high percentage of matter then wouldn’t light matter accrete around dark matter and not the other way around?

    • 2 Matthew R. Francis January 6, 2014 at 08:57

      You’ve got the idea, yeah! In galaxy formation models, the dark matter slowly gathers first into regions called halos, then attracts atoms into those. The scale of that is pretty huge – dark matter is important for galaxies, but not formation of stars or planets.

      • 3 TheTaste January 6, 2014 at 09:02

        Why not for planets? Gravity is still gravity isn’t it?

      • 4 Matthew R. Francis January 6, 2014 at 09:10

        Gravity is very weak, so to make stuff like stars and planets you need a shock to push stuff together into high enough density to start the process. That’s why stars often form in clumps: something (e.g. a supernova) sent a shock wave through a cloud of gas and forced atoms into close proximity.

        However, that process doesn’t work for dark matter, because dark matter doesn’t respond to pressure (at least not very strongly). That also means you can’t heat it up and you can’t cool it down, both of which are necessary to make planets or stars.

      • 5 TheTaste January 6, 2014 at 09:24

        Thanks!

  2. 6 Marshall Eubanks January 6, 2014 at 11:43

    “Harris has yet to account for perturbations to the satellites’ orbits due to relativity, and the gravitational pull of the sun and moon.”

    That, alone, would make this fail peer review, not to mention that the GPS satellites (which are big and messy and do stationkeeping and get replaced) are not the satellites to use to do this with (the Lageos satellites fit both requirements, being both well monitored and with very low non-gravitational perturbations).

    Note that Adler compared Lageos and LLR estimates of Earth gravity in http://arxiv.org/pdf/0808.0899.pdf and concluded that Earth bound dark matter (outside of the 12,000 km semi major axis of Lageos) is < 4 x 10^-9 Earth masses, much below Harris's 5 x 10^-5 estimate (which is based on a comparison with an ancient IAU determination from the 1960's).

  3. 7 Andrew Laughton January 6, 2014 at 14:22

    The graphic of gravity on our planet shows Blue, stronger gravity over water, with Red, weaker gravity over mountain ranges.
    To a lay person such as myself this appears to be mislabeled, and it also appears to conflict with the scale given.
    Why is this so ?

    • 8 Matthew R. Francis January 6, 2014 at 14:33

      Keep in mind that I’m not an Earth scientist, but my understanding is that Earth’s crust is denser under the ocean than under continents, since it’s primarily volcanic in origin (while dry land has a lot more lighter, sedimentary material).

  4. 9 George kountouris January 7, 2014 at 11:36

    I thing that i agree with the Taste. Gravity is proportional with density of matter (generaly). Density of dark matter is negligible in planetary spatial volume.

    • 10 Walter Hicks January 7, 2014 at 19:44

      The continents are scum floating on a global sea of molten rock. The thickness of that scum is less the 1% of the radius of the planet.

      Another anology comes to mind. If we scale up a C60 fullerene from (10^-9m) to galactic size (10^21m, 10^5 ly) to make a fullerene-wimp halo, the wimp-protons would be 10,000 ly apart with radius of 1 ly. This gives a wimp very low density.

      A mass of 10^30 Gev might be a little bit of a problem. But at a volume of 10^90 protons, the energy density is minute.

      If we applied the same 10^30 scaling to time, in their analogical view, the universe is less than 1 picosecond old. Apply the scaling to temperature, and these wimps are very very cold.

      A very cold, diffuse object 1ly across, 5000 ly away – why should you be able to detect it?

      QM calculations involving such a disparity of wave scale will come out nearly zero.

      I am available for consultation on grant applications. Usual terms. Happy New Year.

  5. 11 Andrew Laughton January 7, 2014 at 22:39

    http://en.wikipedia.org/wiki/Gravity_of_Earth

    Explains this quite well, your labels are wrong, mountain ranges do not reduce gravity, however measuring gravity from a mountain range coincidentally means that you are further from the center of earth, and for this reason gravity will be slightly less. If gravity is measured from a uniform height above sea level, mountain ranges will have a slightly more gravity.


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