The discussion centers on the time loss or gain experienced by satellites in orbit due to the effects of Special Relativity (SR) and General Relativity (GR). Participants explore the implications of these relativistic effects on satellite clocks, particularly in the context of GPS systems, and consider whether the direction of orbit (clockwise vs. anti-clockwise) has any impact.
Participants generally agree on the existence of relativistic effects impacting satellite clocks, but there is no consensus on the specifics of these effects or their implications for celestial mechanics, particularly regarding Mercury's orbit and the concept of relativistic resistance.
Some mathematical relationships and assumptions are discussed, but there are unresolved questions about the implications of these effects in different orbital scenarios and the specific contributions of SR and GR to time dilation.
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.