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I've read this answer about satellites synchronizing their clocks with the Earth frame with adjustments for special and general relativity for speed and gravity. There are some satellites and ICBMs that make use of the GPS satellites to navigate. These might be following right behind the GPS satellites and so have no relative motion; they might be in an opposite orbit and so have really fast relative motion; or they might be crossing at various angles so have any number of different levels of relative motion. Is it correct that all of these other satellites and ICBMs have their clocks set relative to the Earth frame? If so, how can they possibly work with GPS satellites? Wouldn't their navigation fail because of the special relativity effects of relative motion between them and the GPS satellites?

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    $\begingroup$ I find it unlikely that an ICBM would pay attention to GPS satellites. Too slow to update and too likely to be spoofed. $\endgroup$
    – Jon Custer
    Commented Dec 12, 2023 at 1:54
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    $\begingroup$ @JonCuster I haven't a clue, but 1) with spoofing detection (signal strength & direction of each signal and simultaneous processing of multiple GNSS constellations, and 2) constant comparison to inertial navigation and other info, I would be surprised if at least some newer ICBM technology didn't incorporate "total GNSS awareness" into its algorithm somehow, thought not relying on it. If we only had a "Warfare and Military Technology SE" site, we could explore the question further. $\endgroup$
    – uhoh
    Commented Dec 12, 2023 at 3:22
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    $\begingroup$ If you can't rely on it, why bother wasting the mass to include it? ICBM navigation was a solved problem 60 years ago and is more than good enough. Perhaps one of the 'rogue' nations would incorporate it if they assumed they would launch first. $\endgroup$
    – Jon Custer
    Commented Dec 12, 2023 at 14:08
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    $\begingroup$ "These might be following right behind the GPS satellites and so have no relative motion" To add context to this: ICBMs typically won't go above 4500km altitude, where a GPS satellite is above 20,000 km. ICBM's can move roughly 24,000km/h, GPS satellites move roughly 11,000km/h. You can fit a whole Earth between the two orbital paths. $\endgroup$
    – David S
    Commented Dec 12, 2023 at 19:42
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    $\begingroup$ I think producers of commercial GPS systems are not allowed to build a GPS that will work in an ICBM. It should detect height and speed and turn itself off. Military can obviously ignore these regulations I assume. $\endgroup$
    – gnasher729
    Commented Dec 12, 2023 at 20:02

3 Answers 3

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Is it correct that all of these other satellites and ICBMs have their clocks set relative to the Earth frame?

The beauty of the GPS system is that the receiver does not need an accurate clock at all. There is no dependence on any sort of super-accurate clock on the vehicle.

Now the time delivered by the GPS solution may drift from some other clock on the vehicle. You may need to decide if that drift is acceptable, or if they need to be synchronized for some other reason. But that doesn't affect the navigation solution from the processor.


The answer below seems to say that it doesn't matter, because the clock on the receiver does not need to be accurate. I'd believe that for an earth bound, slow moving receiver like in my car. But I have trouble believing it for a receiver moving at 4k/s, with a relative speed to the GPS of 8k/s.

I never said a standard consumer GPS would work on orbit. But the changes to make it work don't include a fantastic clock.

Basically it's because the receiver doesn't need any sort of TOD clock to decipher the signal. It just needs the correlators to be able to handle the doppler shift of the signals. At a high enough speed, that would be out of spec, but that's got nothing to do with relativistic corrections. A receiver to work in space will ensure that the increased doppler space is accommodated.

Once the signals from enough sats are received, the combination of the signals tells you what time it is right now at your position. If you synced an oscillator to that time, you would recover the GPS clock.

If you're in orbit and you have the need of precise timing of a second, then the uncorrected GPS clock may not be sufficient.

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  • $\begingroup$ If you look at a satellite in opposite orbit to the GPS satellite, then in a very few days its clocks would be off by a whole bunch compared to the GPS satellite. Are you saying that it doesn't matter if it is off, even by this large amount? $\endgroup$ Commented Dec 11, 2023 at 22:55
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    $\begingroup$ What clock would be off? I don't know if it matters if it's off by a bunch or not. That depends on the mission. But it doesn't affect the performance of the GPS receiver. That will still produce a solution (assuming all the other requirements are met) $\endgroup$
    – BowlOfRed
    Commented Dec 11, 2023 at 23:04
  • $\begingroup$ "in a very few days its clock would be off by a whole bunch". I disagree. The difference is tiny. In fact I suspect that unless you have an atomic clock on your satellite, you don't have the precision to tell the difference at all. $\endgroup$
    – BowlOfRed
    Commented Dec 11, 2023 at 23:12
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    $\begingroup$ The GPS transmitter needs an accurate clock. The GPS receiver does not. $\endgroup$
    – BowlOfRed
    Commented Dec 11, 2023 at 23:31
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    $\begingroup$ @foolishmuse are you familiar with the idea that you need at least 4 satellites locked to get a 3D fix? That's because the fourth variable is time. A receiver that had a hyper-accurate clock could get a 3D fix from 3 satellites, but one that can see 4 satellites doesn't need an independent clock at all; the receiver solves for position and time simultaneously. $\endgroup$
    – hobbs
    Commented Dec 12, 2023 at 8:12
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The time reported by a GPS receiver is an extrapolation of TAI, which is a geocentric coordinate time. It is not the relativistic proper time of the receiver.

The coordinate time is usually what you want to know when you ask what time it is.

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  • $\begingroup$ Just curious; does "geocentric time" mean at the center of the Earth or at the WGS84 surface? $\endgroup$
    – uhoh
    Commented Dec 12, 2023 at 1:03
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    $\begingroup$ @uhoh TAI is defined to be synchronous with proper time measured by a clock on the geoid. There is also a specific definition of Geocentric Coordinate Time (note capitals), based on an assumed gravitational potential at the center of the Earth. $\endgroup$
    – John Doty
    Commented Dec 12, 2023 at 2:01
  • $\begingroup$ You have pointed out the whole issue. The satellite is set to an Earth frame, and I assume with its own adjustments for altitude and speed. But it is communicating with the GPS satellite. Where is the special relativistic effect taken into account? The answer below seems to say that it doesn't matter, because the clock on the receiver does not need to be accurate. I'd believe that for an earth bound, slow moving receiver like in my car. But I have trouble believing it for a receiver moving at 4k/s, with a relative speed to the GPS of 8k/s. $\endgroup$ Commented Dec 12, 2023 at 2:58
  • $\begingroup$ @uhoh TAI is defined as a scaled version of TCG. See physics.stackexchange.com/a/791753/123208 $\endgroup$
    – PM 2Ring
    Commented Dec 12, 2023 at 3:04
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    $\begingroup$ Well, for example, on NICER on the ISS, each group of eight detectors has a low-stability clock. Every recorded photon gets a time stamp from that clock with a precision of 40 ns. However, the same machinery also records GPS time once per second. Thus, we have a precise record of the relationship of our instrument clocks to GPS time. From there, we can use relativity to predict the relationship of our measured time to any clock in a known state of motion. We can thus track pulsar phases to ±1µs over years. $\endgroup$
    – John Doty
    Commented Dec 12, 2023 at 3:21
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If so, how can they possibly work with GPS satellites? Wouldn't their navigation fail because of the special relativity effects of relative motion between them and the GPS satellites?

Like other answers have said, GPS receivers do not typically have atomic clock on board. Therefore they can't even detect that their local clock would undergo time dilation.

Receivers simply track the time signal from GPS satellite, which is in Earth frame. It wouldn't really matter even if the GPS satellite clocks were sped up or slowed down, as long as all 4+ GPS satellites used for navigation solution are synchronized. Earth frame is simply the easiest frame to use for synchronization.

That said, large relative speed between receiver and satellites does introduce another problem: Doppler effect. The receiver used for high velocity vehicles must have an algorithm that can compensate for high Doppler shifts in the received signal. Even normal GPS receivers must do Doppler compensation, but they know the satellite speeds from orbit data and can assume close-to-zero speed for themselves. Fortunately, like time dilation, the Doppler effect is well understood and can be calculated away.

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  • $\begingroup$ Is it really true that "receiver used for high velocity vehicles must have an algorithm that can compensate for high Doppler shifts" which is above and beyond the algorithms used to correct for everyday doppler shift of 100's of meters per second (mostly Earth rotation and satellites low in the west) Why isn't it the same algorithm? It's true high velocity vehicles need special GPS units, but that's primarily the altitude and velocity limits set in firmware? Current situation with CoCom regulations and GPS receivers for balloons and cubesats $\endgroup$
    – uhoh
    Commented Dec 12, 2023 at 10:10
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    $\begingroup$ @uhoh On Earth, the Doppler shift will consist of Earth rotation (up to 460 m/s) and satellite orbital velocity (4000 m/s, but due to geometry about 500 m/s Doppler shift on ground). For ICBM, it would additionally have ICBM orbital velocity (6000 m/s) and due to geometry larger part of the satellite orbital velocity. So in total about 10x higher shift. Many on-ground GPS receivers assume zero speed to get initial guess for Doppler, see e.g. GNSS-SDR. $\endgroup$
    – jpa
    Commented Dec 12, 2023 at 11:58
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    $\begingroup$ @uhoh I guess with modern chips, you could just scan a large Doppler range for each satellite, even though that takes a lot more computation. I would assume that high-velocity receivers would take into account the receiver velocity - after all it is quite easy to do, you just need a way to tell the receiver rough information about where you are going and how fast. It will make signal capture faster and more reliable. $\endgroup$
    – jpa
    Commented Dec 12, 2023 at 14:10
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    $\begingroup$ Yeah, I guess with the better line-of-sight from high up, you could get away with using only satellites traveling at similar speed.. at least if you aren't going with retrograde orbit. $\endgroup$
    – jpa
    Commented Dec 12, 2023 at 14:26
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    $\begingroup$ A "cold" GPS receiver start in orbit can take some time, tens of minutes, to scan for satellite frequencies before it can lock. But you rarely have to start cold. Usually, the GPS receiver knows about what time it is, and has good ephemerides for your spacecraft and the GPS constellation. Thus, it knows the doppler to good accuracy before scanning, and that makes it quick. $\endgroup$
    – John Doty
    Commented Dec 12, 2023 at 16:12

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