Randy Poe wrote: Sue... wrote:
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.
Ya want to show us that?

Special relativity says that there is a time dilation
effect of gamma = sqrt(1 - v^2/c^2). For v c, this is
very close to (1 - v^2/2c^2).

GPS satellites are in circular orbits at 20200 km altitude,
or about 26580 km from the center of earth. The orbital
speed is given by -=-

G*M1*m1 / R^2 = (n - 1)*m1*v1^2 / R
Whe
v1^2 = G*M1 / (n - 1)*R = (6.673E-11)*(5.974E24) / 2.658E7
And, whe
v1 = 3873 - meter / sec
Then:
v1^2 / 2*c^2 = (3873^2 / 2*c^2) = 8.333E-11
Note, particularly:
v1^2 (3873)^2 (R*g1) | GPS ambient density vVLO^2 |
-- -- = -- -- -- = -- --- = |(-- -- -- - -- -- -- ) + (------)|
2*c^2 2*c^2 2*c^2 | vVLO ambient density 2*c^2 |

So, this GUESS iSS RATiO of 8.333E-11 which, adhocly, works..
out to 7.2 microseconds out of 86400 seconds (one day).

Cosmic relief:
The "False Premise" is.. GR "predicts" (within 7 micro-seconds)
EARth's ROTATiON ..and in an EARth-centered frame-of-reference.

CLEARLY, the "EARth" clock OUGHT BE in a Very Low Orbit (a VLO)
for your arithmetic to *REALLY* "work out", as per the equation.
[ The FACT that the EARth clock is sitting *ON* EARth and NOT in
a VLO (so-as the arithmetic works) is REASON for DAiLY reSETs. ]

Other GP Systems can avoid these so-claimed GR "predictions".!!

Show us exactly HOW you factored in EARth DAY's 86400 sec.!!

Go-go Google GROUP SEARCH My BiGGER bang ..idiot.!!

Brian A M Stuckless
^

- Randy
The False Premise Syndrome in Theoretical Science
sci.physics.relativity,sci.physics,
sci.skeptic,sci.philosophy.tech .