http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.htmlBecause 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)!
russ_watters said:GPS Satellites orbit unusually high - 20,000 km - and slow - 14,000 km/h - compared with 240 km and 27,000 km/h for most normal satellites and real astronauts. I suspect, but don't really know, that the SR correction would be the bigger factor for astronauts. They'd age slower.
yogi said:When a clock is in orbit, the slow-down due to velocity is always going to be less than the greater rate required to adjust for the height assuming the reference is taken as the non-moving Earth centered frame.
russ_watters said:GPS Satellites orbit unusually high - 20,000 km - and slow - 14,000 km/h - compared with 240 km and 27,000 km/h for most normal satellites and real astronauts. I suspect, but don't really know, that the SR correction would be the bigger factor for astronauts. They'd age slower.
Yogi, I'm not sure if Sorry!'s teacher was talking about real astronauts or the hypothetical ones from the twins paradox...
I wouldn't say "always" - there is an orbital velocity that corresponds to sea level, afterall. So the question is, is the altitude below which the SR correction is bigger than the GR correction high enough to be above the atmosphere? Jorrie seems to have calculated that that altitude is somewhere above LEO.yogi said:When a clock is in orbit, the slow-down due to velocity is always going to be less than the greater rate required to adjust for the height assuming the reference is taken as the non-moving Earth centered frame.
You're right - I confused my prefixes (micro with mili). I thought 14 seconds seemed awfully large.Jorrie said:BTW, I think you made a typo in a previous post - an uncorrected GPS satellite clock would gain about 14 ms/year relative to a ground clock, not 14 seconds.
russ_watters said:I wouldn't say "always" - there is an orbital velocity that corresponds to sea level, afterall. So the question is, is the altitude below which the SR correction is bigger than the GR correction high enough to be above the atmosphere? Jorrie seems to have calculated that that altitude is somewhere above LEO.
russ_watters said:Jorrie seems to have calculated that that altitude is somewhere above LEO.
Jorrie said:It is now easy to spot that [itex]d\tau_0/dt = d\tau_1/dt [/itex] when r = 1.5R, giving an altitude of ~3190 km above MSL. Below this altitude uncorrected satellite clocks lose time and above it they gain time relative to a terrestrial clock.
russ_watters said:GPS Satellites orbit unusually high - 20,000 km - and slow - 14,000 km/h - compared with 240 km and 27,000 km/h for most normal satellites and real astronauts.
russ_watters said:The reference is in the first post i made...5 years ago. Couldn't you have googled that or checked my reference in the meantime! Sheesh.
So, I guess they are pretty high.The SPACE segment consists of 24 operational satellites in six orbital planes (four satellites in each plane). The satellites operate in circular 20,200 km (10,900 nm) orbits at an inclination angle of 55 degrees and with a 12-hour period. The position is therefore the same at the same sidereal time each day, i.e. the satellites appear 4 minutes earlier each day.
FrankMak said:GPS clocks do not show time-of-day, they provide a precise cyclic rate.
"The U.S. Naval Observatory (USNO) monitors the timing of the GPS to provide a reliable and stable coordinated time reference for the satellite navigation system."
U.S. Naval Observatory
If you brought a GPS clock to earth, it would have a cyclic rate that is different from the earth-based GPS reference. It was launched with this difference to compensate for the orbital altitude difference.
"To account for this, the frequency standard onboard each satellite is given a rate offset prior to launch, making it run slightly more slowly than the desired frequency on Earth; specifically, at 10.22999999543 MHz instead of 10.23 MHz."
http://www.gpsfleetsolutions.com/GPS_Technology_Technical.php
GPS TIME STEERING
GPS time is automatically steered to UTC(USNO) on a daily basis to keep system time within one microsecond of UTC(USNO), but during the last several years has been within a few hundred nanoseconds. The rate of steer being applied is +/-1.0E-19 seconds per second squared.
nternational Atomic Time (TAI, from the French name Temps atomique international)[1] is a high-precision atomic coordinate[2] time standard based on the notional passage of proper time on Earth's geoid. It is the basis for Coordinated Universal Time (UTC), which is used for civil timekeeping all over the Earth's surface, and for Terrestrial Time, which is used for astronomical calculations. Since 30 June 2012 when the last leap second was added,[3] TAI has been exactly 35 seconds ahead of UTC. The 35 seconds results from the initial difference of 10 seconds at the start of 1972, plus 25 leap seconds in UTC since 1972.
The accuracy of GPS clocks does not change over time. They are designed to be highly precise and maintain their accuracy for extended periods of time.
The relativistic effect on GPS clocks is caused by time dilation due to the high speeds and gravitational fields experienced by the satellites. This effect must be accounted for in order for the clocks to maintain accurate time on Earth's surface.
The adjustment of GPS clocks after one year is necessary to account for the relativistic effects mentioned above. Without this adjustment, the clocks would drift from their intended accuracy and result in incorrect GPS positioning data.
GPS clocks are accurate to within nanoseconds after one year. This level of accuracy is necessary for the precise measurements required for GPS positioning and navigation.
The adjustment of GPS clocks after one year is a complex process that involves precise calculations and constant monitoring of the satellites in orbit. It requires a thorough understanding of relativity and advanced technology to ensure the accuracy of the clocks and the GPS system as a whole.