
GPS and Relativity - jcr
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html#
======
IvyMike
I seem to remember that the original satellites (which were the first highly
accurate clocks in orbit) had a hedge--if the effects of general relativity
turned out to not be correct the system could drop that part of the
correction. But I'm on janky hotel internet right now so I can't find a
reference.

Edit: The comment from jcr is correct--this was not in GPS, but in an earlier
system. [http://www.leapsecond.com/history/Ashby-
Relativity.htm](http://www.leapsecond.com/history/Ashby-Relativity.htm)

> At the time of launch of the first NTS-2 satellite (June 1977), which
> contained the first Cesium clock to be placed in orbit, there were some who
> doubted that relativistic effects were real. A frequency synthesizer was
> built into the satellite clock system so that after launch, if in fact the
> rate of the clock in its final orbit was that predicted by GR, then the
> synthesizer could be turned on bringing the clock to the coordinate rate
> necessary for operation. The atomic clock was first operated for about 20
> days to measure its clock rate before turning on the synthesizer. The
> frequency measured during that interval was +442.5 parts in 1012 faster than
> clocks on the ground; if left uncorrected this would have resulted in timing
> errors of about 38,000 nanoseconds per day. The difference between predicted
> and measured values of the frequency shift was only 3.97 parts in 1012, well
> within the accuracy capabilities of the orbiting clock. This then gave about
> a 1% validation of the combined motional and gravitational shifts for a
> clock at 4.2 earth radii.

~~~
jcr
From wikipedia, it seems the keeping of accurate time (i.e. known relativistic
effects) was already solved before the first NAVSTAR Global Positioning System
(GPS I) satellites were constructed. What you're possibly remembering is one
of the GPS predecessor systems like Transit or more likely, Timation.

[http://en.wikipedia.org/wiki/Global_Positioning_System#Prede...](http://en.wikipedia.org/wiki/Global_Positioning_System#Predecessors)

------
rzimmerman
GPS receivers also have to correct for things like light traveling slower
through plasma in the ionosphere. Receivers on the ground actually solve for
their positions in 4 dimensions (they need to solve for time!). GPS is so
cool.

~~~
bargl
That's part of what the 4th connected satellite does. Also this is one of the
better descriptions of trilateration I've seen.
[http://gis.stackexchange.com/questions/12866/why-does-gps-
po...](http://gis.stackexchange.com/questions/12866/why-does-gps-positioning-
require-four-satellites)

~~~
nly
Andrew Holme explains a some of these things succinctly on his home made GPS
receiver project page[0]. Search for "Solving for user position", where he
even mentions ionospheric propagation. He also has an appendix showing his
math[1]

[0]
[http://www.aholme.co.uk/GPS/Main.htm](http://www.aholme.co.uk/GPS/Main.htm)
[1]
[http://www.aholme.co.uk/GPS/user_position_solution.pdf](http://www.aholme.co.uk/GPS/user_position_solution.pdf)

------
K2h
$30 for a GPS that will log 15 hours of telemetry[1] I just cant get over how
much cool math, science, engineering and technology can get crammed into a
single concept. in some ways GPS is as revolutionary as the CPU.

[1]
[http://www.adafruit.com/products/790](http://www.adafruit.com/products/790)

------
charriu
By the way, Pogge also has recordings of some of his lectures available as
mp3. Astro162 was especially interesting, and also goes into more detail on
the effects and implications of relativity.

~~~
jcr
Thanks for the info. I totally missed it.

Lecture Recordings: [http://www.astronomy.ohio-
state.edu/~pogge/Ast162/Audio/](http://www.astronomy.ohio-
state.edu/~pogge/Ast162/Audio/)

Lecture Notes: [http://www.astronomy.ohio-
state.edu/~pogge/Ast162/index.html...](http://www.astronomy.ohio-
state.edu/~pogge/Ast162/index.html#lectures)

------
jbert
Does the system rely on knowing the position of the satellites to equivalent
accuracy? i.e. "millimetres" accuracy for differential GPS.

If so, how is this accuracy achieved? (Obviously the satellites themselves
cannot use gps to determine their position...). Measurement from the ground
plus manouvering?

Are there any events (micro debris strike, solar wind?) which cause drift in
our estimate of their position?

~~~
TickleSteve
The orbits of the satellites are known to a certain accuracy allowing
prediction of where the satellite is at any given point. The accuracy of this
almanac & ephemeris data is only valid for a short time in the future (hours
to days) but is continuously updated from measurements of the satellites
actual position. The ephemeris & almanac data is what is transmitted to the
GPS receivers on the ground along with the timing information allowing the
receiver to calculate their position. An assisted GPS (A-GPS) system can
transmit predicted ephemeris for up to a week ahead to a device and store it
allowing very quick start ups (Time-To-First-Fix) presuming that the data is
preloaded (avoids having to wait for an almanac &ephemeris download which can
take up to 13 minutes). In answer to your question, the orbits are affected by
everything from the atmospheric weather which causes deflections in the
signals to phases of the moon and the shape of the earth that it is passing
over causing small deflections in the satellites orbit. Many factors combine
to make orbital predictions _very_ difficult, akin to predicting the weather.

~~~
jbert
Thanks for that, this is really interesting.

So - there are ground-based observatories continuously determining the
absolute position of the satellites?

This seems really hard. The satellites are ~20,000Km up. I think that means a
1 millimetre difference would be a 5 x 10^-11 radians difference (theta ~ tan
theta), or 0.0001 arc seconds - surely this is beyond any telescope
technology?

And even if they could resolve at that level, we're trying for an _absolute_
fix, so we're also trying to measure the alignment of a (moving?) telescope
with 0.0001 arc second precision (hoping no mice cough nearby?)

That can't be right, so what am I missing?

Wikipedia says that there are lots (~13?) stations:
[http://en.wikipedia.org/wiki/Global_Positioning_System#Contr...](http://en.wikipedia.org/wiki/Global_Positioning_System#Control_segment)

Are there potential issues with them being covered by weather etc?

[Ah - found the link to
'[http://en.wikipedia.org/wiki/Kalman_filter'](http://en.wikipedia.org/wiki/Kalman_filter')
\- this is probably the magic?]

~~~
VLM
Two ways to do it

1) You have a defined position of your antenna... make the ephemeris "work"
such that your antenna gets the right signal from the satellite. In a
philosophical sense, where is the satellite? Well... does it really matter?
This ephemeris says your antenna is in the right place, so...

I'm not implying this is how it work or its a good idea, but it certainly is a
good unit test if your "real" method when run thru a test bench implies you're
on the moon instead of at the (note singular) base station...

2) Those numbers are no big deal with doppler / frequency ranging. If you
transmit at 1500 MHz its a little higher as it approaches and lower as it
leaves. Ask a ham radio operator to demonstrate with their 144/440-ish MHz
satellites, the doppler in low earth orbit is maybe 15 KHz or so. Anyway sub-
Hz accuracy measurement (no big deal) of a 1.5e9 Hz signal for a couple
seconds gives you the -11th class of accuracy you're looking for. The absolute
freq would be nice to know, but you can figure out the instant the satellite
passed zenith (or any other elevation relative to your position) as long as
the freq is "short term more or less constant". Of course giant and heavy
earth bound clocks can give you that precise freq you're looking for, which is
also cool.

The doppler of a satellite pass is pleasingly non-linear and they're high up
enough so make for long passes and proper data analysis means you can
downsample maybe 10000 samples to find the theoretical best RMS zenith instant
for all 10000 samples, so oversampling and averaging gives you another couple
orders of magnitude.

Maybe another way to say it, is if you have basically perfect accuracy clocks,
and you sample and literally count every incoming cycle of a 1.5e9 RF signal
for only 100 seconds even if you ignore phase data (why would you? But for the
sake of the argument...) then thats 1.5e11 cycles in a given time, a bit of
division and you have a freq accurate to one cycle or part in 10 to the 11th.

Its more complicated in reality because the GPS signal is not a simple RF
carrier but is a spread spectrum signal so you need a reasonably low noise and
stable PLL to lock onto the SS signal and then you actually measure the SS
signal.

~~~
zb
> the GPS signal is not a simple RF carrier

There is still a simple carrier; the modulation only affects the sidebands
(which contain the broadcast data).

Also, don't forget that GPS is a dual-frequency system (civilian receivers
don't tend to use the L2 band because they can't decode the data it
broadcasts). Finally, the control segment is not limited to passively
listening for signals from the satellite - it has the entire resources of the
USAF available to it.

~~~
VLM
Hmm thats interesting. I've never seen that on a spectrum analyzer. L1 C/A
looks spikey if you zoom out but its really a meg or so wide and only 20 dB or
so above the rest of the spectrum anyway. From what I understand of the
modulator its not possible to output a carrier other than bleed thru probably
60 dB down or equipment failure. BPSK modulation just doesn't work that way.

Maybe you're talking about the L3 signal? I find that part of GPS to be
spooky. Or that experimental L5 stuff that I don't know anything about.
Everything I do know about GPS is just BPSK and the "old" stuff like L1, L2,
etc..

------
nyc111
How come everyone here believes without question the statement in the original
article that "the engineers who designed the GPS system included these
relativistic effects when they designed and deployed the system." The author
gives no evidence for this claim. In fact the research was classified and he
cannot offer evidence even if he tried. See references in this comment
[http://science1.wordpress.com/2010/10/11/if-newton-were-
to-c...](http://science1.wordpress.com/2010/10/11/if-newton-were-to-come-back-
to-earth/#comment-1381) which says that "Nevertheless, in practice, neglect of
relativity does not now contribute measurably to the GPS error budget, as the
OCS software is currently configured. (p.194)" cited in this source GPS AND
RELATIVITY: AN ENGINEERING OVERVIEW Henry F. Fliegel and Raymond S. DiEsposti
[http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf](http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf)

I am always amazed how normally skeptical people suspend their skepticism and
believe anything a physicist or a learned doctor writes. I would be grateful
if you can supply a real evidence that without GR GPS will not work.

------
hoggle
Talk about deployment hell - puts things into perspective:

"to counteract the General Relativistic effect once on orbit, they slowed down
the ticking frequency of the atomic clocks before they were launched"

The mind boggles.

It makes me uneasy that we only have this single system though (the effects of
a GPS failure would be quite severe I guess). Do the people behind GPS
collaborate with the Galileo folks?

Thanks a lot for the submit, now I need to find a good book on the history
behind the GPS!

~~~
timthorn
There are multiple GNSS platforms - not just GPS & Galileo, but also GLONASS,
Compass, IRNSS, and others. Some receivers are multi-system capable, such as:
[http://www.u-blox.com/en/gps-chips/stand-alone-gps-
chips/ubx...](http://www.u-blox.com/en/gps-chips/stand-alone-gps-
chips/ubx-g7020-ctktka.html)

~~~
tomfanning
And the iPhone, Samsung Galaxy and others, at least assisted GPS + GLONASS
[http://en.wikipedia.org/wiki/GLONASS#Receivers](http://en.wikipedia.org/wiki/GLONASS#Receivers)

~~~
CWuestefeld
Given that 4 satellites are necessary for a fix, are such receivers able to
mix-and-match satellites, say, three GPS satellites and one GLONASS satellite?

------
hyperliner
Why does the article say that clocks "appear" to be running differently? Are
they running differently? Or they only appear to do so?

If so, what happens when the two participants get closer? Do clocks start
"getting in sync"?

If we had an atomic clock with a mechanism to self-destruct when not running
at the original "right" time, does the atomic clock self-destruct? Can it
"tell" it is running slower?

In more biological settings (say, a human being) what are the effects of
"aging faster"? Is it possible that the body would "not work correctly" under
certain gravitational forces because of the effects of time? (i.e. maybe the
blood flows faster, just a terrible example, I hope you get the idea).

~~~
acchow
> Why does the article say that clocks "appear" to be running differently? Are
> they running differently? Or they only appear to do so?

Short answer: they are running differently. Complicated answer: I don't think
this question really makes sense in relativity.

> If so, what happens when the two participants get closer? Do clocks start
> "getting in sync"?

No.

> If we had an atomic clock with a mechanism to self-destruct when not running
> at the original "right" time, does the atomic clock self-destruct? Can it
> "tell" it is running slower?

There is no "right" time in relativity, only frames of reference.

> In more biological settings (say, a human being) what are the effects of
> "aging faster"? Is it possible that the body would "not work correctly"
> under certain gravitational forces because of the effects of time? (i.e.
> maybe the blood flows faster, just a terrible example, I hope you get the
> idea).

Relativistic time dilation will have no effect on chemical and biological
reactions. But I'm sure there are aspects to our biology that go beyond
chemical reactions and actually rely on quantum effects - time dilation might
have some effect here? I don't have the answer for this.

~~~
pdonis
_> Relativistic time dilation will have no effect on chemical and biological
reactions._

This is not correct. Relativistic time dilation affects all processes. If you
flew a chemical reaction and a living organism on a GPS satellite, and then
brought them back and compared them with a similar reaction and organism that
stayed behind on Earth, the reaction on the satellite would have proceeded
further and the organism on the satellite would have aged more. (In practice,
the differences would be too small to detect with our current technology, but
if we had accurate enough ways of measuring we could detect them.)

~~~
acchow
Right. That's the actually movement of time changing. The processes themselves
are unchanged and nothing could "go wrong" in your body.

~~~
pdonis
_> That's the actually movement of time changing. The processes themselves are
unchanged_

You can interpret things this way, I suppose, but that doesn't change the fact
that it applies to all processes; from the viewpoint of someone who sees the
processes as moving, _all_ processes are time dilated--the "movement of time
changing" applies to all of them. There's no special exception for certain
quantum effects, or anything else. They're all the same: they all are
unchanged to someone moving with them, and they all are time dilated to
someone not moving with them.

------
mschuster91
Can one build a GPS reciever chip that uses the signals from GPS, GLONASS, EU
and the Chinese navigation satellites?

In theory, there should then, assuming the EU/Chinese navigation systems have
an equal amount of satellites as GPS/GLONASS, be always 24 or more satellites
in view of the user - which should be enough to provide millimetre-precision
positioning in real time.

~~~
gambiting
You can already get a centimetre-precision for rather low money:

[http://hackaday.com/2013/08/05/centimeter-level-precision-
gp...](http://hackaday.com/2013/08/05/centimeter-level-precision-gps-for-500/)

I have a friend who build an automatic lawnmower as his pet project at uni,and
he used two GPS receivers to get <10cm accurancy which allowed the lawnmower
to make automatic turns around the garden.

------
mer10z
Does this mean that the people living on the space station age faster than
people on earth, or does this only affect the atomic clocks?

~~~
deeviant
In there own frame of references, i.e. living near a large gravity well, and
living on a space station, 1 sec = 1 second. Meaning if I experience a second
on earth, then go to a space station, my own person clock will always read 1
second no matter where I am.

The rub is, time is _relative_ , so even though your personal clock always
reads 1 second in your own frame of reference, the clocks of two individual
people in two different frame of references _can disagree_. So, it only really
_looks_ like the person in the space station "ages faster", but if both the
people in both frames lived 100 years, they would be experience 100 years in
their personal reference, but the space station guy might die when the earth
guy is like 99.9999(or something, I didn't do the math here) years old.

This is due to gravitation time dilation, and it's not the only type. For
instance if I went off on a super space ship at a very high fraction of the
speed of light, traveled around the galaxy and returned 10 years later,
situation would be reversed from the space station/earth gravitation scenario,
and while 10 years may have passed ship time, many hundreds of years(once
again, I didn't do the math, it's just more the higher fraction of the speed
of light you are going) may have passed on earth. In this case, it is the
accelerated frame of reference in which time "slows down" relative to the non-
accelerated frame.

~~~
pdonis
_> This is due to gravitation time dilation_

If you're talking about an object in orbit compared to an object at rest on
the Earth's surface, both gravitational time dilation and the other type you
describe come into play, because the objects are in motion relative to each
other as well as being at different altitudes in the Earth's gravitational
field. Many other comments in this thread have addressed this.

 _> In this case, it is the accelerated frame of reference in which time
"slows down" relative to the non-accelerated frame._

Not really. The key difference is not acceleration; it's the fact that the
super space ship is in motion relative to the center of mass of the galaxy,
while the Earth is not. (Strictly speaking, the Earth is too, but its motion
with respect to the galaxy's center of mass is so slow that it can be ignored
in this scenario.) Similarly, if I sit at rest on the Earth's equator and you
move westward around the equator at the same speed as the Earth is rotating
(about 450 meters per second), then when we meet up again, _my_ clock will
have less elapsed time than yours, because you will have been at rest with
respect to the Earth's center of mass, not me (because I am rotating with the
Earth, but you are not).

~~~
deeviant
In the first example, yes, it is the combination both of gravitation and
acceleration based time dilation.

In the spaceship and the earth example, I can't see what your reference of the
galactic center of mass has to do with anything. If you take the space and
earth out of the galaxy into empty space, the result would be very much the
same. You could say there would be some slight differences because of the
extremely minor differences caused by the gravitation effects of the galaxy
and the acceleration due to galactic orbit, but being that relativistic speeds
are require to see the big differences(we were talking about a spaceship
capable of high fractions of C here), I can't see what you were getting at. It
is the accelerated frame in which time is "slower" relative to the rest frame,
it has nothing to do with gravity.

~~~
pdonis
_> I can't see what your reference of the galactic center of mass has to do
with anything_

The galactic center of mass defines a reference frame that is special with
respect to this problem, because that frame is the one that makes manifest the
time translation symmetry of the spacetime. However, I do see that I left out
an important piece of that: see below.

 _> If you take the space and earth out of the galaxy into empty space, the
result would be very much the same_

Yes, because empty space has a similar time translation symmetry, as long as
the Earth is at rest in it. If the galaxy is included, the Earth has to be at
rest relative to the galactic center of mass; I see now that I was implicitly
assuming that it was, without saying so (I did hint at it when I commented
about the Earth also rotating around the galactic center, but too slowly to
make a difference). So you're right that the galaxy itself isn't really
relevant; but the underlying time translation symmetry is.

The point is that what makes the Earth observer in these scenarios have the
longest proper time is the fact that he is the one who is "at rest" with
respect to the underlying time translation symmetry of the spacetime.
Acceleration only comes into it because that is the particular mechanism you
chose to make the space ship move relative to that time translation symmetry.
In flat spacetime (which is essentially the idealization you're adopting
here), accelerating is the _only_ way to move relative to the underlying time
translation symmetry. But this does not generalize: there are plenty of
examples in curved spacetime where unaccelerated observers can be the ones
with shorter elapsed proper time, because they are moving with respect to an
underlying time translation symmetry.

------
agarcia-deniz
A less useful but,perhaps, more interesting example of relativity at work is
the colour of Gold

[http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry#...](http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry#Color_of_gold_and_caesium)

I believe that this has been posted before

------
tgb
I don't understand the problem yet. Presumably all the satellite clocks run
slower at the same rate. The receiver doesn't have a clock on it (or at least
not one of that accuracy) so it can't tell the difference, or can it? Is the
problem with the database or satellite positions?

~~~
maxerickson
The positions of the satellites are tracked by ground stations that also have
atomic clocks. This comment knows more about it than I do:

[https://news.ycombinator.com/item?id=8041620](https://news.ycombinator.com/item?id=8041620)

Those stations have to know the satellite time, so the compensation has to
happen somewhere.

~~~
pdonis
The clocks on board the satellites have their rates corrected so that they run
at the same rate as ground clocks--i.e., the satellite clocks' effective rate
is not the "natural" rate of a clock at their altitude and moving at their
orbital velocity. The ground stations then send corrections to the satellite
clocks to compensate for the fact that the rate correction that's built in to
the clocks on the satellites isn't exactly right, because the satellites are
not in perfectly circular orbits at constant altitude.

------
axilmar
If we can have a common time between two points in space, even if for point A
the time is corrected with relativity, doesn't that mean that we can have a
common time for the universe? i.e. in other words, simultaneity is real for
any two points in space.

------
debrice
GPS Satellites "live" in our future, meaning our present and our future are
real. Whatever you do, you are still free to make your own decision but you
should know that you already made that decision.

~~~
mihai_ionic
Or, as I prefer to think of it, the state of a distant object is undetermined
with respect to your state (in a superposition of all reachable states since
your last interaction) until you actually interact with it, at which point
both get reconciled into a compatible state. Of course, it's slightly more
complicated than that, because this applies to every particle you're made of
individually. And then the particles are actually merely excitations of a
field.

I'll leave the rest to actual physicists. :)

------
elicash
Another way to put this is that we've already built time machines.

------
bernardom
I can't believe nobody posted the obligatory XKCD reference:
[http://xkcd.com/808/](http://xkcd.com/808/)

~~~
tedks
XKCD references don't add to the discussion. Especially since XKCD is itself
mostly just references to things technical people often know, a lot of people
have the courtesy to keep HN clean of its cheap humor-by-association. Note
that the only real connection between this article and the XKCD is that they
both contain the words "relativity" and "gps".

