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Pulsar Signals Could Provide Galactic GPS
KentuckyFC writes "We're all familiar with GPS. It consists of a network of satellites that each broadcast a time signal. A receiver on Earth can then work out its position in three-dimensional space by comparing the arrival times of the signals from at least three satellites. That's handy, but it only works on Earth. Now astronomers say that the millisecond signals from a network of pulsars could allow GPS-style navigation on a galactic scale. They propose using four pulsars that form a rough tetrahedron with the Solar System at its center, and a co-ordinate system with its origin at 00:00 on 1 January 2001 at the focal point of the Interplanetary Scintillation Array, the radio telescope near Cambridge in the UK that first observed pulsars. The additional complexity of working with signals over these distances is that relativity has to be taken into account (which is why the origin is defined as a point in space-time rather than just space). The pulsar GPS system should allow users to determine their position in space-time anywhere in the galaxy to within a few nanoseconds, which corresponds to an accuracy of about a meter." Pulsars slow down over time, and the arXiv paper doesn't seem to mention this. The paper is mainly about establishing a coordinate system and a reference selection of pulsars. Any proposed Galactic Positioning System would have to take the slowing into account, and since it is poorly understood and not completely predictable, this would limit accuracy.
http://en.wikipedia.org/wiki/File:VgrCover.jpg
This is not a new idea. Actually, this idea has been thought about before and dismissed. The researchers referenced propose using millisecond radio pulsars for navigation. This is a poor idea from an engineering standpoint because it requires having a large collecting area of radio dishes in order to get an apporpriate signal level.
A better idea, which is currently being researched, and was suggested four years ago (at least the earliest I recall it being mentioned) was using x-ray pulsars, which require much smaller collecting area. See for example this thesis on the subject.
Actually the closest we have to an inertial reference frame in the solar system is already using this idea. It has been extended to a terrestrial reference frame later. Informative links:
ICRF: http://en.wikipedia.org/wiki/International_Celestial_Reference_Frame
ITRF: http://en.wikipedia.org/wiki/International_Terrestrial_Reference_Frame
The technique used in both cases (which is prettey cool): http://en.wikipedia.org/wiki/VLBI
I would suggest that they use more than four pulsars though to improve accuracy.
There's a whole lot of research and development (and a cost/benefit ratio study) that needs to be done before just throwing out claims like that. If 4 pulsars get you down to 1 meter accuracy, yet 5 only increases it by 10% (and the 6th increases accuracy even less), yet costs millions more dollars to upgrade the probe to handle, then it's of no real benefit to use more than 4.
"People who think they know everything are very annoying to those of us who do."-Mark Twain
The native coordinate system is not a euclidean grid. Think of the pulsars as being clocks that are continuously broadcasting their local time. The 4 spacetime coordinates they define are just the values of those 4 clocks. In order to normalize this, I need to choose a 0 point for each clock, and the authors chose the values of the clocks as observed in Cambridge at the beginning of the millenium. Apparerently, by observing the signals, I can decide how much time (to the nearest 4 ns) had elapsed at each pulsar, at the time it broadcast the signal I'm now receiving. I can then define a transform that maps those 4 numbers into whatever local coordinate system I want. I could convert it to longitude/lattitude/UTC for terrestrial navigation, or some sort of heliocentric system for planetary navigation, or a galactic system for interstellar navigation.
Yes you're absolutely correct. The current GPS system has to incorporate aspects of both special and general relativity in order to be accurate to the meter. ...
General relativity generalizes relativity to arbitrary smooth manifolds...
It makes the problem more complicated, but it does not add error. You don't think the GPS satellites are stationary, do you? The source of error here is uncertainty in the measurements of those positions. And it actually isn't that bad -- start your spacecraft near Sol, with position well enough defined that you know which pulse you're receiving. (When observing, you can only see the relative phasing of the pulsars, unlike GPS satellites which transmit a time base.) Then you need to count pulses as you move. You then know that, relative to your starting point (or, equivalently, the epoch), you've seen X0 pulses from pulsar 0, X1 from pulsar 1, etc. Knowing how many pulses closer to each of the pulsars you are tells you how far you are from your starting point (in spacetime, not just space, obviously). The error bars get larger as you move enough to get parallax effects -- since from Earth we can only measure the distance to a pulsar with modest precision, and its velocity perpendicular to us with even less. If, however, you have a radio telescope that can resolve the position of the pulsar with good precision, you get to add a long baseline parallax measurement to correct for that. Add a timebase transmitter at Earth as well, and the errors basically disappear -- errors of a few nanoseconds should be readily available. And once you're far enough away from Sol to make that transmitter difficult (more than a few lightyears), you'll know the pulsar trajectories well enough it won't matter as much.
Quoting from Wikipedia:
Relative position of the Sun to the center of the Galaxy and 14 pulsars
The radial pattern on the left of the plaque shows 15 lines emanating from the same origin. Fourteen of the lines have corresponding long binary numbers, which stand for the periods of pulsars, using the hydrogen spin-flip transition frequency as the unit. Since these periods will change over time, the epoch of the launch can be calculated from these values.
The lengths of the lines show the relative distances of the pulsars to the Sun. A tick mark at the end of each line gives the Z coordinate perpendicular to the galactic plane.
If the plaque is found, only some of the pulsars may be visible from the location of its discovery. Showing the location with as many as 14 pulsars provides redundancy so that the location of the origin can be triangulated even if only some of the pulsars are recognized.
The data for one of the pulsars is misleading. When the plaque was designed, the frequency of pulsar "1240" (now known as J1243-6423) was known to only three significant decimal digits: 0.388 seconds. The map lists the period of this pulsar in binary to much greater precision: 100000110110010110001001111000. Rounding this off at about 10 significant bits (100000110100000000000000000000) would have provided a hint of this uncertainty. This pulsar is represented by the long line pointing down and to the right.
The fifteenth line on the plaque extends to the far right, behind the human figures. This line indicates the sun's relative distance to the center of the galaxy.
Get off my lawn.
Not really ... it's just a point in space. They can figure out where everything else in the observable universe was, relative to that point. I mean, the reality is, that nothing in space is really all that fixed (since galaxies are spreading apart), but as far as intra-galaxy positioning goes, one point is just as good as another for a standard point of reference. We know where that point was, relative to most other points, at a specific time. That point doesn't complete an orbit of the sun every 12 months, even though the object it was based on does. Small distinction, but it's all that matters. They're going to be measuring position relative to the pulsars, and not measuring it relative to the focal point of a telescope in Cambridge.
Also, there's a bit of silliness in the summary - the braking index of pulsars is fairly well established. It's the causes that aren't really understood, since most pulsars apparently differ from the theoretical index (IANAP). The slowdown also seems to be constant, and gives pulsars a lifespan of 10^6 years. In a modern GPS system, one needs to know two things from each of the satellites Where the signal came from and when (the reality is that you really just need to know when it was sent, and you program the "where" into the receiver-unit in a manner that lets you know where the object would have been at that time). In a modern GPS system, they put really expensive and accurate clocks into the satellites, and the signal they send out encodes the time that the signal was sent. You figure out where you are, by calculating how long it took that signal to get to you, based off of the time received from other satellites
How the hell would a pulsar encode the time it sent its signal? Simple, the period of the signal from each pulsar changes over time... that's your clock. You know what the period was at 0000hrs 1 Jan 2001, and by how much it increases. So, when you receive the signal, you calculate how long, from 0000hrs 1 Jan 2001, it would take for the signal to have a period matching the one you received. You now know when the signal was sent from, and, the information on where it was sent from is programmed into the receiver-unit. Measure the same from the other pulsars and *bam*, there's your location.
Oh god, that woman is John Romero!
> The overall effect of "relativistic time slowing" is tiny and is in the nano-second ballpark, however when calculating positions using GPS a few nano-seconds can mean a few meters...
No, it's in the micro-second ballpark (around 38 microseconds a day) which leads to /kilometers/ of inaccuracy a day, if you do not count in relativity.
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Missing pulses isn't a big deal if you have an accurate clock. Phase locked loops can be tuned to handle lots of missing pulses very, very well. If you're not moving, or know exactly how you're moving, you know when the pulses arrive even if you don't actually look at them. If you're moving, and don't know precisely how, then and only then do you need to be actively counting pulses -- and unless you're accelerating by nontrivial fractions of c in between pulse arrival times, you can still miss lots of pulses before your error in predicted pulse arrival time grows terribly large. Somehow I doubt that will be a problem.