gps and theory of relativity

GPS and Relativity – Department of Astronomy

Real-World Relativity: The GPS Navigation System. GPS was developed by the United States Department of Defense to provide a satellite-based navigation system for the U.S. military. It was later put under joint DoD and Department of Transportation control to provide for both military and civilian navigation uses,

Special Relativity · The Machinery of Night · General Relativity

Why does GPS depend on relativity? – Stack Exchange

GPS satellite navigation system doesn’t use, doesn’t need and doesn’t prove Einstein’s General Relativity. The GPS satellites use classical (Newtonian) relativistic principles to work. These are the same relativistic principles that make sense in the everyday world, that most people equate with ‘common sense’.

Error margin for position predicted by GPS is $15\text{m}$. So GPS system must keep time with accuracy of at least $15\text{m}/c$ which is roughly $50\text{ns}$. So $50\text{ns}$ error in timekeeping corresponds to $15\text{m}$ error in distance prediction.
Hence, for $38\text{μs}$ error in timekeeping corresponds to $11\text{km}$ error in distance prediction. If we do not apply corrections using GR to GPS then $38\text{μs}$ error in timekeeping is introduced per day . You can check it yourself by using following formulas $T_1 = \frac{T_0}{\sqrt{1-\frac{v^2}{c^2}}}$ clock runs relatively slower if it is moving at high velocity. $T_2 = \frac{T_0}{\sqrt{1-\frac{2GM}{c^2 R}}}$ clock runs relatively faster because of weak gravity. $T_1$ = 7 microseconds/day $T_2$ = 45 microseconds/day $T_2 – T_1$ = 38 microseconds/day use values given in this very good article . And for equations refer to HyperPhysics . So Stephen Hawking is right! :-)Best answer · 53
There’s the article from Ohio State University which explains quite well why the clocks on a GPS satellite are faster by about 38 microseconds every day. The article then claims that not compensation for these 38 microseconds per day would cause a GPS to be off by about 11 km per day, plainly unusable, and claims that this (the fact that we need to compensate for the 38 microseconds to get GPS working) is proof for General Relativity. The problem is that while the clocks are indeed off by 38 microseconds per day and General Relativity is all fine, we wouldn’t actually have to compensate for it. The GPS in your car or your phone doesn’t have an atomic clock. It doesn’t have any clock precise enough to help with GPS. It doesn’t measure how long the signal took to get from satellite A to GPS. It measures the difference between the signal from satellite A and the signal from satellite B (and two more satellites). This works if the clocks are fast: As long as they are all fast by the exact same amounts, we still get the right results. That is, almost. Satellites don’t stand still. So if we rely on a clock that is 38 microseconds fast per day, we do the calculations based on the position of a satellite that is off by 38 microseconds per day. So the error is not (speed of light times 38 microseconds times days), it is (speed of satellite times 38 microseconds times day). This is about 15 cm per day. Well, satellite positions get corrected once a week. I hope nobody thinks we could predict the position of a satellite for long time without any error. Back to the original assumption, that without compensation the error would be 11km per day: The satellite clocks are multiplied by a factor just shy of 1 so that they go at the correct speed. But that wouldn’t work. The effect that produces 38 microseconds per day isn’t constant. When the satellite flies over an ocean, gravity is lower. The satellite speed changes all the time because the satellite doesn’t fly on a perfect circle around a perfectly round earth made of perfectly homogenous material. If GR created an error of 11km per day uncompensated, then it is quite unconceivable that a simple multiplication of the clock speed would be good enough to reduce this to make GPS usable.32You can find out about this in great detail in the excellent summary over here: What the Global Positioning System Tells Us about Relativity? In a nutshell: General Relativity predicts that clocks go slower in a higher gravitational field. That is the clock aboard the GPS satellites “clicks” faster than the clock down on Earth. Also, Special Relativity predicts that a moving clock is slower than the stationary one. So this effect will slow the clock compared to the one down on Earth. As you see, in this case the two effects are acting in opposite direction but their magnitude is not equal, thus don’t cancel each other out. Now, you find out your position by comparing the time signal from a number of satellites. They are at different distance from you and it then takes different time for the signal to reach you. Thus the signal of “Satellite A says right now it is 22:31:12” will be different from what you’ll hear Satellite B at the same moment ). From the time difference of the signal and knowing the satellites positions (your GPS knows that) you can triangulate your position on the ground. If one does not compensate for the different clock speeds, the distance measurement would be wrong and the position estimation could be hundreds or thousands of meters or more off, making the GPS system essentially useless.29The effect of gravitational time dilation can even be measured if you go from the surface of the earth to an orbit around the earth. Therefore, as GPS satellites measure the time it’s messages take to reach you and come back, it is important to account for the real time that the signal takes to reach the target.3GPS satellite navigation system doesn’t use, doesn’t need and doesn’t prove Einstein’s General Relativity. The GPS satellites use classical (Newtonian) relativistic principles to work. These are the same relativistic principles that make sense in the everyday world, that most people equate with ‘common sense’. GPS calculates positions based on geometric principles. The atomic clocks on the satellites have their rates preset in order to match experimentally observed effects. No General Relativity is used or needed. The website dedicated by the USA government to the GPS system,, has a lot of information for those who want to know how GPS works, but does not put forward anything about General Relativity (GR). The equations used by the GPS system are based on geometry and classical relativity. They dont include compensations for GR effects. The satellite simply sends out a signal at regular intervals with some information. The receiving device does all the required calculations with the signals it receives. You can check out the basics at When the clocks of each satellite were set, the rate of each clock was adjusted according to previously observed effects. Experimental observations over decades, showed how speed and altitude affected the rate of ticking of atomic clocks. It had been experimentally observed that atomic clocks speed up at higher altitudes. It was also observed that the speed of the clock also affects the rate of ticking. Based on these experimental observations, the GPS engineers had to adjust the rate of the atomic clocks based on what had been observed – regardless of what any theory said. The engineers knew how the clocks would be affected in orbit because of experimental observations. Not the theory of general relativity. Supporters of Einsteins GR had to make sure their theory fits these observations. The GPS engineers didnt use GR to work out how much to change the clocks. More detail: www. /focus/chat/1025790/posts “In the 1990’s, he [Van Flandern] worked as a special consultant to the Global Positioning System (GPS), a set of satellites whose atomic clocks allow ground observers to determine their position to within about a foot. Van Flandern reports that an intriguing controversy arose before GPS was even launched. Special Relativity gave Einsteinians reason to doubt whether it would work at all. In fact, it works fine.” “At high altitude, where the GPS clocks orbit the Earth, it is known that the clocks run roughly 46,000 nanoseconds (one-billionth of a second) a day faster than at ground level, because the gravitational field is thinner 20,000 kilometers above the Earth. The orbiting clocks also pass through that field at a rate of three kilometers per second — their orbital speed. For that reason, they tick 7,000 nanoseconds a day slower than stationary clocks.
To offset these two effects, the GPS engineers reset the clock rates, slowing them down before launch by 39,000 nanoseconds a day. They then proceed to tick in orbit at the same rate as ground clocks, and the system “works.” Ground observers can indeed pin-point their position to a high degree of precision.” “in Einstein’s theory the relevant speed is always speed relative to the observer, it was expected that continuously varying relativistic corrections would have to be made to clock rates. This in turn would have introduced an unworkable complexity into the GPS. But these corrections were not made. Yet “the system manages to work, even though they use no relativistic corrections after launch,” Van Flandern said.” “The presence of Special and General Relativity effects has no bearing on the accuracy of GPS operation. In summary, it wouldn’t matter whether clocks aboard GPS satellites ran faster or slower than Earth’s clocks or even changed their speed each day. Just so long as the satellites’ clocks remained synchronised with each other and the time-difference relative Earth’s clocks didn’t become too large, GPS receivers would continue to calculate their correct position.” The following articles make the claim that GPS requires General Relativity, but in error. They refer to the initial clock rate presets as being due to GR, when the reality is that these presets had to be done, theory or not, because of experimental observations. This article is cited in many articles and publications that are supportive of the theory of general relativity, inclucing wikipedia references. Yet, it is just opinion. In it, Richard W. Pogge makes these 2 claims without supporting them in the text. The references cited at the end of this article dont refer to relativity at all – they link to the GPS FAQ at the FAA. 1 “However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.”
2 “For example, to counteract the General Relativistic effect once on orbit, they slowed down the ticking frequency of the atomic clocks before they were launched so that once they were in their proper orbit stations their clocks would appear to tick at the correct rate as compared to the reference atomic clocks at the GPS ground stations.” Wandera asks: In an article that claims GPS as a real world example for relativity, why doesnt the author back up such important claims? The firt claim isnt even explained, and isnt backed up at all. The second claim labels the effect G Relativistic, but this is another unsupported opinion. www.aticourses. com/global_positioning_system.htm “The corrections that must be applied include signal propagation delays caused by the ionosphere and the troposphere, the space vehicle clock error, and the user’s receiver clock error.”
“Other error sources and modeling errors continue to be investigated. For example, a recent modification of the Kalman filter has led to improved performance. Studies have also shown that solar radiation pressure models may need revision and there is some new evidence that the earth’s magnetic field may contribute to a small orbit period variation in the satellite clock frequencies.”
The precision of GPS measurements is so great that it requires the application of Albert Einstein’s special and general theories of relativity for the reduction of its measurements.” Wandera says: The claim about general relativity isnt true and the article makes no attempt to back up this claim. Its nothing but opinion.
Lorenz created the theory of slowing clocks prior to Einstein, not Einstein in a GR theory. My understanding of GPS is that it is calculated by the one-way time of flight of radiation from satellite-to-receiver. The synchronization of the clocks of the two is essential. But, just because a clock slows down or speeds up does not mean that time is changing, only that the shape of the atom is changing (as Lorenz postulated). The Cesium atoms are being compressed as they move through the ether. So, the equations are pure time-of-flight equations, and the clocks are adjusted and the pre-adjustments (i.e. intentional slowing of the satellite clocks) matches the equations of Lorenz.
In response to David van Driessche, GPS does depend on adjustment of clocks and so LET relativity, but it does not depend on GR. GR is an as yet unproven theory. It’s most often cited success is that it was used the predict the precession of the planet Mercury. Unfortunately, more recent calculations of Mercury’s orbit, using only Newtonian mechanics, shows that there is close to zero precession. Therefore, the precession of Mercury disproves GR, itis not predicted by GR.[i.e. in science, a theory is put aside when it does not predict correctly].

GPS Satellite – Special Relativity – Physics Stack Exchange
How are GPS corrected for special/general relativity

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Top 4 Reasons Why GPS Doesn’t Need Einstein’s Relativity

Explanation of GPS’s special consultant. Scientists should stop calling it that. (GPS, Relativity, and pop-Science Mythology ). A physics professor said that given Einstein’s status as a popular icon, there are countless people who wish to prove him wrong, even among scientists with degrees to their names.

How is the theory of relativity used in GPS? – Quora

Sep 26, 2018 · GPS is affected by special relativity because the satellites used travel in high speed orbits around the Earth. Special relativity shows that a faster moving object will experience time slower relative to a ‘stationary’ object. For GPS satellites, this slight difference in time is around 7.2 microseconds per day.

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How Your GPS Uses Einstein’s Relativity – Scientific American

How Your GPS Uses Einstein’s Relativity. This is a modal window. Caption Settings Dialog Beginning of dialog window. Escape will cancel and close the window. This is a modal window. This modal can be closed by pressing the Escape key or activating the close button. Time flows slightly faster on the Global Positioning System satellites

GPS, Relativity, and pop-Science Mythology

Relativity theory predicts the clocks aboard the GPS satellites will run faster than clocks on Earth by about 38 microseconds a day. This inaccuracy would grow steadily larger each day, e.g. after 10 days the inaccuracy would have grown to 110 km.

8 Ways You Can See Einstein’s Theory of Relativity in Real

Profound implications. Relativity is one of the most famous scientific theories of the 20th century, …


GPS AND RELATIVITY: AN ENGINEERING OVERVIEW. Henry F. Fliegel and Raymond S. DiEsposti GPS Joint Program Offlce The Aerospace Corporation El Segundo, California 09245, USA. Abstract. We give and explain in detail the fonnuh for the re&fivisfic corwtiona to be implemented in.

Theory of relativity – Wikipedia

Theory of relativity. It introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions,

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