# GPS satellites; relativity correction for solar gravity variation?
**URL:** https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776
**Category:** Factual Questions
**Created:** [December 18, 2023, 2:24pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776 "2023-12-18T14:24:11Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)
#### Post date: [December 18, 2023, 2:24pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/1 "2023-12-18T14:24:11Z")
Plenty of discussions of relativity and time dilation lately, so here’s another one.
The global positioning system features corrections for general and special relativity due to the movement of the satellites relative to any given GPS receiver, and also due to their different height in the earth’s gravity well:
> **[Error analysis for the Global Positioning System | Relativity](https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity)**
>
> The theory of relativity introduces several effects that need to be taken into account when dealing with precise time measurements. According to special relativity, time passes differently for objects in relative motion. That is known as kinetic time dilation: in an inertial reference frame, the faster an object moves, the slower its time appears to pass
> (as measured by the frame's clocks). General relativity takes into account also the effects that gravity has on the passage of time. In the cont...
What about the effect of solar gravity on GPS satellites? When any given satellite is on the daylight side of Earth, it must be moving a bit faster than average due to having been accelerated by the sun’s gravity as it transitioned from the night side of the earth to the day side; conversely, when any given satellite is on the night side of Earth, it must be moving a bit slower than average. The satellites must also be subjected to slightly differing gravitational accelerations on the day and night side of the earth, due to the variation in solar gravitational acceleration as a function of distance from the sun.
Is it necessary to apply relativity corrects to compensate for these effects? Or are they too small to bother?
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### Author:  [@Dorjan](https://boards.straightdope.com/u/Dorjan)
#### Post date: [December 18, 2023, 2:34pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/2 "2023-12-18T14:34:32Z")
The general consensus seems to be “too small to bother”. Some link I’ve found that address the issue:
> **[GPS, Gravitational Influences, and Measuring Time](https://futurism.com/gps-gravitational-influences-and-measuring-time)**
>
> Like the GPS satellites around the other planets in our solar system must have varying levels of velocity and gravitational time dilation as they orbit closer and further from the sun, is there an equation? How is time on Mars different than on...
> **[Effect of Sun’s gravity on time dilation of atomic clocks.](https://mdashf.org/2011/11/03/effect-of-suns-gravity-on-time-dilation-of-atomic-clocks/)**
>
> This is an original research work of Manmohan Dash, published here, 3rd November 2011, 8:10 am. What are the effect of Sun’s gravity, on time dilation, of atomic clocks, on GPS satellite and …
The 2nd is specific to atomic clocks, but it’s really the same problem.
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### Author:  [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)
#### Post date: [December 18, 2023, 2:53pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/3 "2023-12-18T14:53:15Z")
> [@Machine\_Elf](#):
>
> Is it necessary to apply relativity corrects to compensate for these effects? Or are they too small to bother?
The GPS satellites and other objects in Earth’s orbit are in the Earth’s sphere of influence, which is strong enough it dwarfs the tiny gradient of the solar gravitational field. On the other hand, periodic corrections do need to be made for the Moon’s influence because it is much closer and pulling in different directions, which does have a tiny but cumulatively significant effect on GPS satellites. These are not relativistic corrections, though; just classical gravitational perturbations.
Stranger
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### Author:  [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)
#### Post date: [December 18, 2023, 3:05pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/4 "2023-12-18T15:05:56Z")
> [@Dorjan](#):
>
> The general consensus seems to be “too small to bother”.
> [@Stranger\_On\_A\_Train](#):
>
> The GPS satellites and other objects in Earth’s orbit are in the Earth’s sphere of influence, which is strong enough it dwarfs the tiny gradient of the solar gravitational field.
Yeah, I thought that might be the case. Thanks for the confirmation.
> [@Stranger\_On\_A\_Train](#):
>
> On the other hand, periodic corrections do need to be made for the Moon’s influence because it is much closer and pulling in different directions, which does have a tiny but cumulatively significant effect on GPS satellites. These are not relativistic corrections, though; just classical gravitational perturbations.
So these corrections just account for gravitationally induced discrepancies in the positions/movements of the GPS satellites due to lunar gravity, correct?
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### Author:  [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)
#### Post date: [December 18, 2023, 3:20pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/5 "2023-12-18T15:20:22Z")
> [@Machine\_Elf](#):
>
> So these corrections just account for gravitationally induced discrepancies in the positions/movements of the GPS satellites due to lunar gravity, correct?
Yes, the varying position of Earth’s Moon will cause slight but cumulative affects on the ephemerides of satellites. These are generally neglected because the influence is slight, and over the operational timespan (especially in LEO) they don’t have any functional impact for communications, Earth observation, et cetera, but because of the unique function of GPS (and presumably other GNSS constellations) these corrections are occasionally required.
Stranger
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### Author:  [@RitterSport](https://boards.straightdope.com/u/RitterSport)
#### Post date: [December 18, 2023, 3:35pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/6 "2023-12-18T15:35:07Z")
> [@Stranger\_On\_A\_Train](#):
>
> (especially in LEO)
Just a nitpick that GPS is really not in LEO, it’s in half-GEO, 12.5k miles up, vs. 400-500 for LEO.
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### Author:  [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)
#### Post date: [December 18, 2023, 4:13pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/7 "2023-12-18T16:13:36Z")
> [@RitterSport](#):
>
> Just a nitpick that GPS is really not in LEO,…
I wasn’t suggesting that the GPS constellation was in LEO; rather that satellites in LEO generally have short enough operational lifespans (months to decades) that perturbations from Lunar influence are insignificant and overshadowed by variations in the Earth’s gravitational field. Satellites at the very high end of LEO and above can remain in orbit for many centuries or even millennia, and so changes in ephemerides due to Lunar perturbations will accumulate, but will still be small enough to not affect the performance of most satellite functions (assuming you could build a satellite that would remain functional for centuries or longer). A GPS satellite is uniquely sensitive to tiny changes in ephemeris because of how it functions and the precision required for geodesic measurement from space. It is the only ‘practical’ application I know of (excluding astrophysical observations, deep space spacecraft positioning, and other ‘pure science’ applications) where effects due to General Relativity actually have to be accounted for.
I once worked on an unsolicited proposal for what was essentially a solar orbiting interplanetary spacecraft positioning and telemetry relay system (PlaTePoS) where we spent a bunch of time trying to figure out a scheme for performing relativistic corrections, only to discover that except for a very narrow set of experimental applications (at about the orbit of Mercury) we could just use the JPL Planetary and Lunar Ephemerides database with some very minor SR corrections and no GR corrections because we had such a wide parallax baseline and the current _ad hoc_ methods for positioning using the ground-based Deep Space Network were more than adequate for high precision spacecraft navigation. So, for anything not involving synchronizing atomic clocks in orbit or the slight frame-dragging effects of the Sun, we just don’t need Einstein gravity. Thanks for nothing, Albert!
Stranger
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### Author:  [@Voyager](https://boards.straightdope.com/u/Voyager)
#### Post date: [December 18, 2023, 6:24pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/8 "2023-12-18T18:24:18Z")
> [@RitterSport](#):
>
> Just a nitpick that GPS is really not in LEO, it’s in half-GEO, 12.5k miles up, vs. 400-500 for LEO.
When researching this for a book chapter I found that the reason for the orbit chosen was a compromise between reducing the number of satellites needed and the ability of lift vehicles available at the time to boost the satellites into a higher orbit.
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### Author:  [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)
#### Post date: [December 18, 2023, 6:36pm UTC](https://boards.straightdope.com/t/gps-satellites-relativity-correction-for-solar-gravity-variation/994776/9 "2023-12-18T18:36:12Z")
There are a few other reasons for selecting those orbits for the GPS constellation but yes, the primary consideration was getting a sufficient number of satellites at an orbit reachable by the Atlas E/F SLV from Vandenberg and Delta II-6925 from the Cape. A higher orbit would mean better coverage with fewer satellites (and also more difficult for an opponent to destroy) but would have required the far more expensive Titan III (C, E, or 34D) which were also needed for surveillance satellites and Defense Satellite Communication System launches.
Stranger