Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion. Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day. The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!
Drakkith said:
Bjarne said:Do you know where to read about if this is confirmed, and fits with the predictions ?
The confirmation comes in the fact that the GPS system works as designed. Beyond that, I'm sure the service that maintains the GPS system keeps track of clock errors for maintenance reasons and would notice if Relativity was wrong, but I don't think they'd see a value in publishing that data to prove something that is already well proven and accepted.Bjarne said:Do you know where to read about if this is confirmed, and fits with the predictions ?
Bjarne said:Do you know where to read about if this is confirmed, and fits with the predictions ?
George Jones said:Everytime GPS is used is a test that confirms it [edit]as Russ has already noted[/edit]. For a calculation that doesn't split the effect into contributions from special and general relativity, see
https://www.physicsforums.com/showthread.php?p=731738#post731738.
Bill_K said:These effects are pretty easy to calculate. It turns out they both depend on exactly the same quantity, v2/c2 = GM/rc2, where v is the orbital velocity. For the SR effect, the time slowdown is sqrt(1 - v2/c2) ~ - v2/2c2. For the GR effect, the apparent speedup comes from the Schwarzschild metric ds2 = (1-2GM/rc2) dt2, which implies an approximate speedup ~ GM/rc2.
On the face of it, both effects increase as 1/r as you get closer to Earth. However GR loses as you go down, because you need to compare the slowdown in orbit vs the slowdown on the ground, which modifies the answer by an extra factor Δr/r. GR is comparable for the GPS satellites because they are in a very high orbit: 20,000 km, or about three Earth radii. Low Earth orbit would mean an altitude about 50 times less than this, so GR will be 50 times smaller for your average satellite.
The theory of relativity, developed by Albert Einstein, is a fundamental theory in physics that explains the relationship between space and time. It has two main components: the special theory of relativity, which deals with objects moving at a constant velocity, and the general theory of relativity, which includes the effects of gravity.
According to the theory of relativity, time is relative and can be affected by factors such as gravity and velocity. In the case of satellites in orbit, the high speed and weaker gravitational pull result in a slight time dilation, causing time to pass slightly slower for the satellite compared to a stationary observer on Earth.
Satellites are used for a variety of purposes, including communication and navigation. To accurately transmit and receive signals, the precise time measurements of the satellite and ground stations must be synchronized. Failure to account for the effects of relativity can lead to errors in these time measurements, resulting in communication and navigation errors.
The amount of time loss or gain for a satellite in orbit is calculated using the formula: Δt = √(1 - v^2/c^2) - 1, where Δt is the time dilation factor, v is the velocity of the satellite, and c is the speed of light. This formula takes into account the effects of velocity on time dilation in the special theory of relativity.
Yes, the effects of relativity can be observed in many other phenomena, such as the gravitational lensing of light, the redshift of light from distant stars, and the precession of the orbit of Mercury. These observed phenomena provide evidence for the validity of the theory of relativity.