What If GPS Stood for “Galactic Positioning System”?(spectrum.ieee.org)
spectrum.ieee.org
What If GPS Stood for “Galactic Positioning System”?
https://spectrum.ieee.org/tech-talk/aerospace/space-flight/what-if-gps-stood-for-galactic-positioning-system
62 comments
Agreed that the explanation is a bit lacking. This uses the phase difference between the signals of multiple pulsars, as indeed the individual pulses are not marked with a timestamp like in GPS.
Imagine you have two pulsars each with a 1ms signal, that don't move relative to you and emit signals that are in sync at their source. If the tops of both signals overlap at your location, you are in one one of many possible circles that are centered around the line between the pulsars, where the difference in distance to the pulsars is N times 300 km (distance light travels in 1 ms). By adding additional pulsars, you reduce your possible position to a set of points, and finally a single point.
To generalize this to a set of pulsars with different timings and for whom you don't know the exact location, you need to know the phase difference for all signals at a given reference point in space and time. The same procedure will then give you your current position and time relative to the reference point.
Imagine you have two pulsars each with a 1ms signal, that don't move relative to you and emit signals that are in sync at their source. If the tops of both signals overlap at your location, you are in one one of many possible circles that are centered around the line between the pulsars, where the difference in distance to the pulsars is N times 300 km (distance light travels in 1 ms). By adding additional pulsars, you reduce your possible position to a set of points, and finally a single point.
To generalize this to a set of pulsars with different timings and for whom you don't know the exact location, you need to know the phase difference for all signals at a given reference point in space and time. The same procedure will then give you your current position and time relative to the reference point.
If you go on, the article addresses this: measuring the peak of a pulsar signal places you on an infinite set of spheres centered on the pulsar, because you don't know "which" peak you measured (i.e. when it was emitted). Since the pulsar emits a peak every millisecond or so, these spheres are separated by one light-millisecond each. If you repeat the procedure with several pulsars, you should be able to find that there is only one point in space that lies in the intersection between a sphere of each pulsar.
It’s [a little bit] bullshit. The light emitted from a pulsar is only a sphere if you live in a universe that contains only you and the pulsar.
Spacetime is curved by every mass in it. The distance light travels is subtly changed by what is between you and the source.
If four observers cannot agree on what was your exact location at time n (without a perfect model of the entire universe) then how would you be able to determine your location by observing four other objects?
Edit: You can get the right neighborhood, but if you’re moving at relativistic speeds it will be problematic. And if you’re in the middle of nowhere and not moving at relativistic speeds you’re probably gonna die anyway...
Spacetime is curved by every mass in it. The distance light travels is subtly changed by what is between you and the source.
If four observers cannot agree on what was your exact location at time n (without a perfect model of the entire universe) then how would you be able to determine your location by observing four other objects?
Edit: You can get the right neighborhood, but if you’re moving at relativistic speeds it will be problematic. And if you’re in the middle of nowhere and not moving at relativistic speeds you’re probably gonna die anyway...
Er, can you characterize which post-Newtonian correction/s is or are of non-negligible order here for Milky-way millisecond pulsars? Where do they enter, if not extremely close to the pulsars themselves? I'm curious, because we use them to test, among other things, |\alpha_3| in the PPN formalism alpha-zeta notation. Along the way you necessarily get a very good characterization of the transforms available on local arrival times in different coordinate systems and can probe other PPN parameters. (cf. Kramer, sec 4 and 5.1 free version: http://arxiv.org/abs/astro-ph/0405178v2).
More generally, do you object to systems of coordinates that are in-practice recoverable by a wide variety of observers? We sure aren't Eulerian observers of the Milky Way, but does it really seem parochial or idiosyncratic to take a Eulerian approach to its matter?
> If four observers cannot agree on what was your exact location at time n
Find four observers who see the CMB (and matter in the bulk) as isotropic and homogeneous, who measure the same temperature of the relic photons, and who have a direct line of sight (with improbably good telescopes) into the relevant part of the Milky Way, and they can agree very precisely on your location in a cosmological frame constructed like the standard one used in this tiny patch of spacetime. The tricky part is that the light travel times are long compared to chaotic movements of individual humans, and the choice of gauge has to be agreed and the observations shared.
> If you're in the middle of nowhere and not moving at relativistic speeds
Where in spacetime is the middle of nowhere?
What's materially different for a relativistic observer moving through the same general curved spacetime (especially if "the middle of nowhere" is, say, a large region of extremely-close-to-Minkowski spacetime) as a non-relativistic one? While you're there, what's different for an accelerated observer in the same region? Are you saying that something more than a Lorentz transform would be needed?
More generally, do you object to systems of coordinates that are in-practice recoverable by a wide variety of observers? We sure aren't Eulerian observers of the Milky Way, but does it really seem parochial or idiosyncratic to take a Eulerian approach to its matter?
> If four observers cannot agree on what was your exact location at time n
Find four observers who see the CMB (and matter in the bulk) as isotropic and homogeneous, who measure the same temperature of the relic photons, and who have a direct line of sight (with improbably good telescopes) into the relevant part of the Milky Way, and they can agree very precisely on your location in a cosmological frame constructed like the standard one used in this tiny patch of spacetime. The tricky part is that the light travel times are long compared to chaotic movements of individual humans, and the choice of gauge has to be agreed and the observations shared.
> If you're in the middle of nowhere and not moving at relativistic speeds
Where in spacetime is the middle of nowhere?
What's materially different for a relativistic observer moving through the same general curved spacetime (especially if "the middle of nowhere" is, say, a large region of extremely-close-to-Minkowski spacetime) as a non-relativistic one? While you're there, what's different for an accelerated observer in the same region? Are you saying that something more than a Lorentz transform would be needed?
I guess my point is that if you’re going to call it Galactic Positioning, it better work someplace else than on the surface of the earth, and I am not seeing how.
We are all so ‘close’ that you can find a near exact distance between telescopes but that’s different than plotting your current distance to Tau Ceti.
We are all so ‘close’ that you can find a near exact distance between telescopes but that’s different than plotting your current distance to Tau Ceti.
And indeed this is how the golden record on the Voyager spacecraft potentially informs any aliens of the location of Earth.
Ahh, I missed that it was a large set of spheres. Thanks.
You'd calibrate the timing of the pulsars before launch.
Which means that you would have to keep track of each pulse, if you have a comparatively inaccurate clock. Does not seem practical.
EDIT: On second thought, using an accurate clock would be a tiny fraction of the cost of the whole system, so it's a solved problem.
EDIT: On second thought, using an accurate clock would be a tiny fraction of the cost of the whole system, so it's a solved problem.
There’s a washing machine sized pulsar detector bolted to the International Space Station that is successfully locating itself with pulsars.
https://www.nasa.gov/sites/default/files/atoms/files/session...
https://www.nasa.gov/sites/default/files/atoms/files/session...
TIL using multiple pulsars to create a galactic positioning system "is a solved problem."
Though it's useful, you don't even need an accurate clock. You can observe the relative phases of several pulsars to recover your clock.
You can know the current time if the decay rate of the pulsars is characterizable and you have a reference rate->time (eg: on date X pulsar was 1.45266363mhz and decays 1.6ns/hr)
Interesting, this is probably the right approach to searching for the aliens civilizations. These guys should have globally visible intergalactic GPS, we just have to imagine how and where they would put the searchlights, the most effective places.
What if these pulsars are their 'GPS satellites'?
There should be some logic. Someone should create a project of this imaginary galactic GPS infrastructure, taking into a count all the details - potentially limited resources needed to build it, maximum visibility, distances coverage and then compare it to the map of these pulsars. And if there is bingo or sort of, we could get the space points where to rearrange our radio telescopes to listen to.
I can imagine some kind of optimization problem, the solution for which would be the ideal locations for these bodies.
Unfortunately I do not understand enough physics to give a concrete problem.
Unfortunately I do not understand enough physics to give a concrete problem.
From the end of TFA:
Indeed, it’s so incredible that some might see in this accomplishment hints that there could be more at work than nature here. Even before these measurements were taken by NICER, a group of researchers at the Free University of Brussels led by Clément Vidal explored whether these x-ray millisecond pulsars could have been arrayed around the galaxy on purpose. In a preprint titled “Pulsar Positioning System: A quest for evidence of extraterrestrial engineering,” they examine that albeit remote possibility.
Indeed, it’s so incredible that some might see in this accomplishment hints that there could be more at work than nature here. Even before these measurements were taken by NICER, a group of researchers at the Free University of Brussels led by Clément Vidal explored whether these x-ray millisecond pulsars could have been arrayed around the galaxy on purpose. In a preprint titled “Pulsar Positioning System: A quest for evidence of extraterrestrial engineering,” they examine that albeit remote possibility.
There probably would be no need to build anything, since we already can use pulsars for that (XNAV; what this article is about) and the achievable resolution should be more than good enough to be able to use it for navigation inside our solar system (couple km iirc).
My point was not that we need to build something, but that if we would need to build it , we build it in the same locations.
They say it took 8 hours, what's the cause of this? Does it take that time to locate and measure the pulsars? Or is it more signal processing time?
Also - the idea of a pulsar spinning a thousand times a second is just incredible.
Also - the idea of a pulsar spinning a thousand times a second is just incredible.
How quickly, on an astronomical scale, do pulsars slow down? I'd imagine that eventually the changes in rotation would throw off the positioning, and require recalibration. And of course eventually they'll stop being useful altogether.
One would hope a civilization is able to create artificial pulsars by that time, however...
One would hope a civilization is able to create artificial pulsars by that time, however...
Wikipedia mentions a life span of about 10 million years. If they slow down in a predictable way (exponentially?), navigation system could just calculate that in. And when some pulsars die out, new one have probably emerged in the meantime, allowing a smart-enough system to gradually switch sources.
The M1 (Crab Nebula) pulsar slows by 38 ns per day. But it is very new, less than 1000 years old.
https://en.m.wikipedia.org/wiki/Crab_Pulsar
https://en.m.wikipedia.org/wiki/Crab_Pulsar
Thats almost 1.6ns/hour. If you have a stable oscillator you can compare them to compute the time/date.
Wouldn't it depend on what happens to show up in the accretion disk? Including the life cycle of any companion stars? I would imagine that it's normally stable but less predictable perturbations can't be strictly ruled out.
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In theory this is a much better approach than Earth satellites: the farther away an object is, the smaller its motion will appear. With hundreds or even thousands of "fixed" data points incoming, it should be possible to develop an incredibly accurate model for position in space.
This is exactly what is already done! On Earth at least. Radio telescopes around the world observe (mostly) quasars to perform geodesy. This is the main method used to measure the Earth Orientation Parameters which is need for keeping GPS/GNSS calibrated.
With it, you can measure distances of several thousand km with a precision on the order of a few millimetres. The problem is that it's really expensive compared to GPS: at each site you need a reasonably size telescope, atomic clock, some serious storage, and a way to ship all the data to a central cluster.
With it, you can measure distances of several thousand km with a precision on the order of a few millimetres. The problem is that it's really expensive compared to GPS: at each site you need a reasonably size telescope, atomic clock, some serious storage, and a way to ship all the data to a central cluster.
I suspect the latency might kill this idea.
What latency?
They're talking about measuring millisecond pulsars, there's no latency
They're talking about measuring millisecond pulsars, there's no latency
Indeed.
But if you're travelling significant distances, you're not going to be able to assume the space between you and all your beacons is flat.
For good accuracy you'd need a predictive spacetime curvature map for the entire galaxy, and that might not be an easy thing to generate.
But if you're travelling significant distances, you're not going to be able to assume the space between you and all your beacons is flat.
For good accuracy you'd need a predictive spacetime curvature map for the entire galaxy, and that might not be an easy thing to generate.
it would probably be an advantage to measure the shift effect from multiple sources as you travel whatever fraction of the speed of light, giving both your position and derivatives such as velocity
Not at all, if you take it into account.
Would you be happy to wait for tens of minutes to get a position lock?
One wouldn't be transmitting to pulsars and awaiting a response, but treating them as what they are: always-on beacons. The signals would always be present.
Not even GPS transmits to the satellites, it only relies on observations of what the satellites sent.
And pulsars are quite a bit further away than tens of light minutes :) Mars is currently 14 light minutes from Earth. PSR J2144-3933 is one of the nearest known pulsars, and it's some 587 light years away.
And pulsars are quite a bit further away than tens of light minutes :) Mars is currently 14 light minutes from Earth. PSR J2144-3933 is one of the nearest known pulsars, and it's some 587 light years away.
Yes but if we're using it as a beacon the distance is irrelevant, isn't it? It's been "transmitting" for much longer than 587 years, we're already receiving a signal, and that's what we're using?
Exactly. The post I replied to said "One wouldn't be transmitting to pulsars and awaiting a response", and I expanded on that. The whole subthread of https://news.ycombinator.com/item?id=16288955 doesn't make much sense because nobody defined what they mean by "latency" and people are talking about different things.
Tens of minutes to get a position lock for your location in the entire Galaxy? Yes, that sounds completely reasonable.
Of course, if that was the best I could do.
People will happily spend an entire day becoming unlost if they're lost.
As long as they have the means to survive, they'll be willing to spend much longer than that.
People will happily spend an entire day becoming unlost if they're lost.
As long as they have the means to survive, they'll be willing to spend much longer than that.
Likely, after the first calibration you could keep moving around and updating your location, so as long as the system doesn't go down you always know your (relative) position as you travel through the galaxy.
Regular GPS does this, too. It takes about 12 minutes to download the list of currently active satellites and their attributes. The data is part of the signal from the satellites.
Most GPS units do this in the background. But if you leave it unpowered for too long, it will need to update itself before it begins to work properly. The GPS in my dad's car used to have a flaky ROM, and it would show the car flying across the wilderness at over 400mph while it was updating.
Most GPS units do this in the background. But if you leave it unpowered for too long, it will need to update itself before it begins to work properly. The GPS in my dad's car used to have a flaky ROM, and it would show the car flying across the wilderness at over 400mph while it was updating.
I thought of this as well. After the first lock, you can use inertial navigation.
If I can then keep the lock indefinitely, I don't see much of a downside.
Yes, especially if it’s just to occasionally recalibrate an inertial guidance system.
... And here I was thinking all you needed was six points of reference, and seventh point for the origin
Had to enable too much 3rd party scripts and other resources to read it.
htetm;dr? Had to enable too much; didn't read?
htetm;dr? Had to enable too much; didn't read?
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edit: Not to be cryptic:
> "Open In Reader View" adds a new context menu item to the page and link context menu to let you open webpages and urls directly in the reader view mode to strip away all of the clutter.
Ignore the domain name, there's versions for Chrome and Opera too!
could we use this on earth in the future?
Just a guess: In priciple, yes, but it wouldn't be very practial. Because of noise sources on earth, one would need very big antennas pointing to the pulsars to get good s/n ratios.
Additionally, as x-rays are blocked by the atmosphere, one would be limited to longer-wavelength pulsars, again increasing the size of the antennas.
Given that, using GPS, we already have a positioning system much more accurate, I don't see why one would use pulsars for positioning on earth.
It does, perhaps, have the advantage of not needed a satellite fleet to work. So therefore isn’t at the whim of said fleet’s owner, or someone with anti-satellite missiles.
(Granted that the antenna size problem might be a killer)
(Granted that the antenna size problem might be a killer)
Star trackers do exactly this, providing relatively accurate positioning without GPS:
https://en.wikipedia.org/wiki/Star_tracker
https://en.wikipedia.org/wiki/Star_tracker
Was going to say this, and in use by things like submarines and ships since the 60’s
I was about to suggest the use of a sextant for this. As far as I know, navigators are still trained to operate them in this day. Of course, the same operational principle can be integrated into a dedicated device.
I thought this was more of a thought experiment for galactic travel, that would make the most sense. However navigation by star triangulation is much less complicated and historically proven ever since ships were sailed. Star trackers are on many satellites and rovers for positioning.
Even some military aircraft like the SR-71: http://www.thedrive.com/the-war-zone/17207/sr-71s-r2-d2-coul...
Does star navigation work once you’re far beyond locations where we’ve previously been able to map stars from? Or put another way, is our "3D" map of the stars sufficiently accurate, or is it more of a "2D" map.
Perhaps you could update the map as you move (SLAM?)
Does star navigation work once you’re far beyond locations where we’ve previously been able to map stars from? Or put another way, is our "3D" map of the stars sufficiently accurate, or is it more of a "2D" map.
Perhaps you could update the map as you move (SLAM?)
Am I missing something here? It doesn't seem like you can know the time emitted if you don't know your position.