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Winston001
Something I've stumbled across on the net which leaves me very confused. I've always thought for a satellite orbiting (or geosynchronous) with the Earth, time passes more slowly. Ergo the satellite clock loses time relative to its earthbound mate. I do know that satellite clocks have to be readjusted.

But..but...now I read that the satellite clock ticks faster -

"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."

and slower and huh.gif

"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."

Obviously I'm missing something. Anybody help?

http://www.astronomy.ohio-state.edu/~pogge.../Unit5/gps.html
Ed Wood
Special Relativity -7 microseconds per day speed

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.


General relativity +45 microseconds per day curvature difference

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 difference +38 micro seconds 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)!
brucep
QUOTE (Winston001+Nov 14 2011, 09:02 AM)
Something I've stumbled across on the net which leaves me very confused. I've always thought for a satellite orbiting  (or geosynchronous) with the Earth, time passes more slowly. Ergo the satellite clock loses time relative to its earthbound mate. I do know that satellite clocks have to be readjusted.

But..but...now I read that the satellite clock ticks faster  - 

"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."

and slower and huh.gif

"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."

Obviously I'm missing something. Anybody help?

http://www.astronomy.ohio-state.edu/~pogge.../Unit5/gps.html

Ed summed it up. You can review this project which takes you through a derivation from the Schwarzschild metric you can use for the GPS or any satellite system. The finished formula is equation [12]. Depending on dt_shell orbit satellite clocks can tick slower, or faster, than ground clocks at dt_shell earth surface.

http://www.eftaylor.com/pub/projecta.pdf.
Winston001
Thanks guys, I'll struggle on and try to understand it.

You've got to admit it is counter-intuitive to have a clock run both fast and slow with both postulations being correct.

I'm going to stick with General Relativity. biggrin.gif
MjolnirPants
QUOTE (Winston001+Nov 16 2011, 04:20 AM)
You've got to admit it is counter-intuitive to have a clock run both fast and slow with both postulations being correct.
Think of a 1 kilogram iron weight between two magnets. One magnet is exerting 10 newtons on it while the other is exerting 9 newtons on it. Even though the two magnets are both exerting a force on it, the weight accelerates towards the stronger magnet at a rate of 1m/s^2 at time = 0 (and faster as time > 0, because as it gets closer to the stronger magnet the relative forces change).

The issue with the satellites is the same. Both postulates are true, and both are affecting the satellite's time, but one does so more powerfully, and so it prevails.

The reason why one is stronger has to do with the speed at which the satellites are moving (not fast enough to produce as much time dilation as earth's gravity does), and the fact that the observer on earth is experiencing time dilation as well, making his clock tick more slowly.
cbennett
Flux Theory of Gravitation
... gravitation ...
"The search for the laws of nature was triggered by cosmological phenomena reported by the Hubble. Among them are the following: (1) Cosmic ripples in the Cosmos that produce cosmic dust that eventually congeals into stars; on the average, a star is born in the Cosmos every minute. (2) Powerful gamma ray bursts of energy a thousand times more intense than ordinary gamma rays in the Cosmos. (3) Waves of stars by the trillions in concentric rings generated by and propagated outward from the point of collision between one of the pair of small galaxies in one direction and a large one in another oblique to it (verifies FTG?s dark-to-visible-matter conversion in the Cosmos) [117]. If the colliding galaxies had opposite spins with common equatorial plane the explosion could have been cataclysmic for our universe. (4) Rapid accelerated dispersal of the galaxies in accordance with Hubble?s law (shown to be equivalent to the rapid radial accelerated expansion of our universe)."
laugh.gif
AlexG
QUOTE (cbennett+Nov 17 2011, 08:49 PM)
Flux Theory of Gravitation
... gravitation ...
"The search for the laws of nature was triggered by cosmological phenomena reported by the Hubble. Among them are the following: (1) Cosmic ripples in the Cosmos that produce cosmic dust that eventually congeals into stars; on the average, a star is born in the Cosmos every minute. (2) Powerful gamma ray bursts of energy a thousand times more intense than ordinary gamma rays in the Cosmos. (3) Waves of stars by the trillions in concentric rings generated by and propagated outward from the point of collision between one of the pair of small galaxies in one direction and a large one in another oblique to it (verifies FTG?s dark-to-visible-matter conversion in the Cosmos) [117]. If the colliding galaxies had opposite spins with common equatorial plane the explosion could have been cataclysmic for our universe. (4) Rapid accelerated dispersal of the galaxies in accordance with Hubble?s law (shown to be equivalent to the rapid radial accelerated expansion of our universe)."
laugh.gif

More from www.crank.net.
Robittybob1
QUOTE (cbennett+Nov 18 2011, 01:49 AM)
Flux Theory of Gravitation
... gravitation ...
"The search for the laws of nature was triggered by cosmological phenomena reported by the Hubble. Among them are the following: (1) Cosmic ripples in the Cosmos that produce cosmic dust that eventually congeals into stars; on the average, a star is born in the Cosmos every minute. (2) Powerful gamma ray bursts of energy a thousand times more intense than ordinary gamma rays in the Cosmos. (3) Waves of stars by the trillions in concentric rings generated by and propagated outward from the point of collision between one of the pair of small galaxies in one direction and a large one in another oblique to it (verifies FTG?s dark-to-visible-matter conversion in the Cosmos) [117]. If the colliding galaxies had opposite spins with common equatorial plane the explosion could have been cataclysmic for our universe. (4) Rapid accelerated dispersal of the galaxies in accordance with Hubble?s law (shown to be equivalent to the rapid radial accelerated expansion of our universe)."
laugh.gif

That just like inside head at the moment. Hubble Rubble Bubble and trouble.
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